Dhole Moments

2020-07-07 14:05:09

There are a lot of random topics I’ve wanted to write about since I started Dhole Moments, and for one reason or another, haven’t actually written about. I know from past experience with other projects that if you don’t occasionally do some housekeeping, your backlog eventually collapses under its own gravity and you can never escape from it.

So, to prevent that, I’d like to periodically take some time to clean up some of those loose ends that collect over time.

Random-Access AEAD

AEAD stands for Authenticated Encryption with Associated Data. Typically, AEAD constructions involve a stream cipher (which may also be a block cipher in counter mode) and a message authentication code (which may also be an almost-universal hash function).

AEAD modes are designed for one-shot APIs: Encrypt (then authenticate) all at once; (verify then) decrypt all at once. AES-GCM, ChaPoly, etc.

AEADs are less great at providing random access to the underlying plaintext. For example: If you’re encrypting a 240 GB file with AES-GCM, but you only need a 512 KB chunk at some arbitrary point in the file, you’re forced to choose between either:

1. Authenticating the rest of the AES-GCM ciphertext, then decrypting only the relevant chunk. (Performance sucks.)
2. Sacrificing integrity and decrypting the desired chunk with AES-CTR.

Being forced to choose between speed and security will almost certainly result in a loss of security. The incentives of software developers (especially with fly-by-night startup engineers) all-but-guarantee this outcome.

Consequently, there have been several implementations of streaming-friendly AEAD. The most famous of which is Phil Rogaway’s STREAM construction.

Source: Rogaway’s paper

The downside to STREAM is that it requires an additional T bytes (e.g. 16 for an 128-bit authentication tag) for each chunk of the plaintext.

A similar solution, as implemented in the AWS Encryption SDK, is to carefully separate plaintexts into equal-sized frames and have special rules governing IV/nonce selection. This lets you facilitate random access while still making the security of the whole system easy to reason about.

Can we do better than STREAM and message framing?

The most straightforward idea is to use a Merkle tree on the ciphertext with a stream cipher for extracting a distinct key for each leaf node. This can be applied to existing AEAD ciphertexts, out of band, to create a sort of deep authentication tag that can be used to authenticate any random subset of the message (provided you have the correct nonce/key).

However, I haven’t found the time to develop this idea into something that can be toyed with by myself and other researchers.

More Introductory Articles

Let’s face it:

Art by Riley

I’ve previously suggested an alternative strategy for programmers to learn cryptography. I’d like to do more posts covering introductory material for the topics I’m familiar with, so anyone who wants to actually employ my proposed strategy can carry themselves across the finish line.

Dissecting Dog-Whistles

Random fact: My fursona is a dhole–also known as a whistling dog.

Soatok is a dhole, not a fox. Art by Khia.

Coincidentally, I’m deeply fascinated by language, and planned to start a series analyzing dog-whistle language (especially the kind commonly used against queer subcultures).

However, the very nature of dog-whistle language provides a veneer of plausible deniability for the whistler’s intent, which makes it very difficult to address them in a meaningful way that doesn’t undermine your own credibility.

So, for the time being, this is on the back-burner.

Reader Questions

I’ve received quite a few questions via email and social media since I started this blog in April. The most obvious thing to do with these questions would be to periodically collate a bunch of them into a Questions and Answer style post.

However! I have an open source projected called FAQ Off that is way more efficient at the Q&A format than a long-form blog post. If you’d like to see it in action, start here.

Art by Kyume

General Punditry

I make a lot of dumb jokes, typically involving puns and other wordplay. Most of these live in private Telegram conversations with other furries, but a few have leaked out onto Twitter over the years.

Is automated vulnerability scanning a nessusity?

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) November 23, 2017

Nurse: "I suspect this patient attempted to shove a foreign object into their urethra for pleasure"

Doctor: "I believe your theory is sound"

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) June 25, 2018

A lot of them involve queer lingo.

People say it's lonely at the top.

No wonder there's so many bottoms in this fandom 😛

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) December 30, 2019

BitTorrent users are thirsty bottoms. Always complaining about wanting more seed.

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) August 4, 2019

My RAID controller has big disk synergy

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) August 1, 2018

Some of them involve furry in-jokes.

Q) Why are foxes so prevalent in the furry fandom?

A) We're a sub-culture not a dom-culture.

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) May 24, 2018

Intrusion detection systems are old hat. What we need is a protrusion detection system.

Introducing OwO

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) February 1, 2018

Some are just silly.

Using mined bitcoins to buy a pumpkin spice latte makes you an ASIC bitch, right?

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) February 6, 2018

So in gay male furry culture if you give into a booty call from your ex-boyfriend… does that mean you were craving the XD?

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) August 25, 2018

If SQL is pronounced "sequel" then PHP must be pronounced "fap".

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) July 23, 2019

What do you call a submissive dragon with a mathematics background who's already lubed up for you?

A sliding scale.

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) December 26, 2018

Did you hear about the clairvoyant babyfur that broke RSA?

Turns out, all you needed was a padding oracle.

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) October 1, 2017

I should look for my next partner in a nuclear chemistry lab.

I hear they're good at dating.

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) December 8, 2016

In my humble opinion, there haven’t been nearly enough puns on this blog (unless the embedded tweets above count).

Normally, this is where I’d proclaim, “I shall rectify this mistake” and proceed to make an ass out of myself, but I don’t like forced and obvious puns.

A lot of furries get this wrong: “Pawesome” is not clever, unless you’re talking to someone with a marsupial fursona. Then maybe.

The best puns come in two forms: They’re either so clever that you never saw it coming, or they’re just clever enough that the punchline lands at the same time you realized a bad pun was even possible.

Only Soatok brand puns are 100% whole groan

— Mastodon: soatok@furry.engineer, Cohost: soatok (@SoatokDhole) January 26, 2018

Miscellaneous / Meta

The past few blog posts touched a little on political subjects (especially How and Why America Was Hit So Hard By COVID-19, but this short-term trend actually started with my Pride Month post).

At some point in the future, I may write a post dedicated to politics, but for the time being, it’s not really a subject I care enough about in and of itself to emphasize all the time.

Let me be clear: Being gay in America is inherently political. Developing technology is inherently political (although you don’t always realize it). Being a gay technologist, saying something politically significant is an inevitability.

But I’m not interested in the traditional roles and narratives that infect politics and political discourse. Labels are stupid and I’m not interested in being a Useful Idiot for anyone’s propaganda.

---

The most difficult thing about writing blog posts for me is coming up with a meaningful title. I’ve lost many hours due to the writer’s block that ensues.

The second most difficult thing for me is writing closing statements that aren’t totally redundant.

https://www.youtube.com/embed/l44OV2jlN7A?start=665&feature=oembed
George Carlin – “Count the Superfluous Redundant Pleonastic Tautologies” – Skip to 11:05 if WordPress breaks something
Some bloggers like to sign off like they’re writing an email. “Happy hacking!” and whatnot. To me, this feels forced and inauthentic, like a bad pun.

So instead, here’s a totally sick piece of art I got from @MrJimmyDaFloof.
Furry artists are, like the rest of the fandom, amazing.
https://soatok.blog/2020/07/07/dont-forget-to-brush-your-fur/

Dhole Moments

2020-06-10 04:05:06

A question I get asked frequently is, “How did you learn cryptography?”

I could certainly tell everyone my history as a self-taught programmer who discovered cryptography when, after my website for my indie game projects kept getting hacked, I was introduced to cryptographic hash functions… but I suspect the question folks want answered is, “How would you recommend I learn cryptography?” rather than my cautionary tale about poorly-implemented password hash being a gateway bug.

The Traditional Ways to Learn

There are two traditional ways to learn cryptography.

If you want a book to augment your journey in either traditional path, I recommend Serious Cryptography by Jean-Philippe Aumasson.

Academic Cryptography

The traditional academic way to learn cryptography involves a lot of self-study about number theory, linear algebra, discrete mathematics, probability, permutations, and field theory.

You’d typically start off with classical ciphers (Caesar, etc.) then work your way through the history of ciphers until you finally reach an introduction to the math underpinning RSA and Diffie-Hellman, and maybe taught about Schneier’s Law and cautioned to only use AES and SHA-2… and then you’re left to your own devices unless you pursue a degree in cryptography.

The end result of people carelessly exploring this path is a lot of designs like Telegram’s MTProto that do stupid things with exotic block cipher modes and misusing vanilla cryptographic hash functions as message authentication codes; often with textbook a.k.a. unpadded RSA, AES in ECB, CBC, or some rarely-used mode that the author had to write custom code to handle (using ECB mode under the hood), and (until recently) SHA-1.

People who decide to pursue cryptography as a serious academic discipline will not make these mistakes. They’re far too apt for the common mistakes. Instead, they run the risk of spending years involved in esoteric research about homomorphic encryption, cryptographic pairings, and other cool stuff that might not see real world deployment (outside of novel cryptocurrency hobby projects) for five or more years.

That is to say: Academia is a valid path to pursue, but it’s not for everyone.

If you want to explore this path, Cryptography I by Dan Boneh is a great starting point.

Security Industry-Driven Cryptography

The other traditional way to learn cryptography is to break existing cryptography implementations. This isn’t always as difficult as it may sound: Reverse engineering video games to defeat anti-cheat protections has led several of my friends into learning about cryptography.

For security-minded folks, the best place to start is the CryptoPals challenges. Another alternative is CryptoHack.

There are also plenty of CTF events all year around, but they’re rarely a good cryptography learning exercise above what CryptoPals offers. (Though there are notable exceptions.)

A Practical Approach to Learning Cryptography

Art by Kyume.

If you’re coming from a computer programming background and want to learn cryptography, the traditional approaches carry the risk of Reasoning By Lego.

Instead, the approach I recommend is to start gaining experience with the safest, highest-level libraries and then slowly working your way down into the details.

This approach has two benefits:

1. If you have to implement something while you’re still learning, your knowledge and experience is stilted towards “use something safe and secure” not “hack together something with Blowfish in ECB mode and MD5 because they’re familiar”.
2. You can let your own curiosity guide your education rather than follow someone else’s study guide.

To illustrate what this looks like, here’s how a JavaScript developer might approach learning cryptography, starting from the most easy-mode library and drilling down into specifics.

Super Easy Mode: DholeCrypto

Disclaimer: This is my project.

Dhole Crypto is an open source library, implemented in JavaScript and PHP and powered by libsodium, that tries to make security as easy as possible.

I designed Dhole Crypto for securing my own projects without increasing the cognitive load of anyone reviewing my code.

If you’re an experienced programmer, you should be able to successfully use Dhole Crypto in a Node.js/PHP project. If it does not come easy, that is a bug that should be fixed immediately.

Easy Mode: Libsodium

Using libsodium is slightly more involved than Dhole Crypto: Now you have to know what a nonce is, and take care to manage them carefully.

Advantage: Your code will be faster than if you used Dhole Crypto.

Libsodium is still pretty easy. If you use this cheat sheet, you can implement something secure without much effort. If you deviate from the cheat sheet, pay careful attention to the documentation.

If you’re writing system software (i.e. programming in C), libsodium is an incredibly easy-to-use library.

Moderate Difficulty: Implementing Protocols

Let’s say you’re working on a project where libsodium is overkill, and you only need a few cryptography primitives and constructions (e.g. XChaCha20-Poly1305). A good example: In-browser JavaScript.

Instead of forcing your users to download the entire Sodium library, you might opt to implement a compatible construction using JavaScript implementations of these primitives.

Since you have trusted implementations to test your construction against, this should be a comparatively low-risk effort (assuming the primitive implementations are also secure), but it’s not one that should be undertaken without all of the prior experience.

Note: At this stage you are not implementing the primitives, just using them.

Hard Difficulty: Designing Protocols and Constructions

Repeat after me: “I will not roll my own crypto before I’m ready.” Art by AtlasInu.

To distinguish: TLS and Noise are protocols. AES-GCM and XChaCha20-Poly1305 are constructions.

Once you’ve implemented protocols and constructions, the next step in your self-education is to design new ones.

Maybe you want to combine XChaCha20 with a MAC based on the BLAKE3 hash function, with some sort of SIV to make the whole shebang nonce-misuse resistant?

You wouldn’t want to dive headfirst into cryptography protocol/construction design without all of the prior experience.

Very Hard Mode: Implementing Cryptographic Primitives

It’s not so much that cryptography primitives are hard to implement. You could fit RC4 in a tweet before they raised the character limit to 280. (Don’t use RC4 though!)

The hard part is that they’re hard to implement securely. See also: LadderLeak.

Usually when you get to this stage in your education, you will have also picked up one or both of the traditional paths to augment your understanding. If not, you really should.

Nightmare Mode: Designing Cryptography Primitives

A lot of people like to dive straight into this stage early in their education. This usually ends in tears.

If you’ve mastered every step in my prescribed outline and pursued both of the traditional paths to the point that you have a novel published attack in a peer-reviewed journal (and mirrored on ePrint), then you’re probably ready for this stage.

---

Bonus: If you’re a furry and you become a cryptography expert, you can call yourself a cryptografur. If you had no other reason to learn cryptography, do it just for pun!

Header art by circuitslime.

https://soatok.blog/2020/06/10/how-to-learn-cryptography-as-a-programmer/

#cryptography #education #programming #Technology

Dhole Moments

2022-05-19 07:36:36

Earlier this year, Cendyne published A Deep Dive into Ed25519 Signatures, which covered some of the different types of digital signature algorithms, but mostly delved into the Ed25519 algorithm. Truth in advertising.

This got me thinking, “Why isn’t there a better comparison of different elliptic curve signature algorithms available online?”

Art: LvJ

Most people just defer to SafeCurves, but it’s a little dated: We have complete addition formulas for Weierstrass curves now, but SafeCurves doesn’t reflect that.

For the purpose of simplicity, I’m not going to focus on a general treatment of Elliptic Curve Cryptography (ECC), which includes pairing-based cryptography, Elliptic-Curve Diffie-Hellman, and (arguably) isogeny cryptography.

Instead, I’m going to focus entirely on elliptic curve digital signature algorithms.

Note: The content of this post is a bit lower-level than most programmers ever need to be concerned with. If you’re a programmer and interested in learning cryptography, start here. If you’re looking for library recommendations, libsodium is a good safe default.

Compliance Rules Everything Around Me

If you have to meet some arbitrary compliance requirements (i.e. FIPS 140-3, CNSA, etc.), your decision is already made for you, and you shouldn’t waste your time reading blogs like this that will only get your hopes up about the options available to you.

Choose the option your compliance officer demands, and hope it’s good enough.

“Sure, let me check that box.”
Art: LvJ

Elliptic Curves for Signature Algorithms

Let’s start with the same curve Cendyne analyzed: Ed25519.

Ed25519 (EdDSA, Curve25519)

Ed25519 is one of the two digital signature algorithms today that use the EdDSA algorithm framework. The other is Ed448, which targets a higher security level (224-bit vs 128-bit) but is also slower and uses SHAKE256 (which is overkill and not great for performance).

Ed25519 is a safe default choice for most applications where a digital signature is appropriate, for many reasons:

1. Ed25519 uses deterministic nonces, which means you’re severely unlikely to ever reproduce the Sony ECDSA k-reuse bug in your system.
   The deterministic nonce is calculated from the SHA512 hash of the secret key and message. Two invocations to crypto_sign_ed25519() with the same message and secret key will produce the same signature, but the intermediate nonce value is never revealed to an attacker.
2. Ed25519 includes the public key in the data hashed to produce the signature (more specifically s from the (R,s) pair). This offers a property that ECDSA lacks: Exclusive Ownership. I’ve written about this property before.
   Without Exclusive Ownership, it’s possible to create a single signature value that’s valid for multiple different (message, public key) pairs.

Years ago, there would have an additional list item: Ed25519 uses Edward Curves, which have complete addition formulas and are therefore safer to implement in constant-time than Weierstrass curves (i.e. the NIST curves). However, we now have complete addition formulas for Weierstrass curves, so this has become a moot point (assuming your implementation uses complete addition formulas).

Ed25519 targets the 128-bit security level.

Why Not Use Ed25519?

There is one minor pitfall of Ed25519 that makes it unsuitable for esoteric uses (say, Ring Signature Schemes or zero-knowledge proofs): Ed25519 is not a prime-order group; it has a cofactor h = 8. This detail famously created a double-spend vulnerability in all CryptoNote-based cryptocurrencies (including Monero).

For systems that want the security of Ed25519 and its various well-studied implementations, but still need a prime-order group for their protocol, cryptographers have developed the Ristretto Group to meet your needs.

If you’re working on embedded systems, the determinism inherent to EdDSA might be undesirable due to the possibility of fault attacks. You can use a hedged variant of Ed25519 to mitigate this risk.

Additionally, Ed25519 is not approved for many government applications, although it did make the latest draft revision of FIPS 186 in 2019. If you care about compliance (see above), you cannot use Ed25519. Yet.

A niche Internet meme for cryptography engineers

Guidance for Ed25519

Unless legally prohibited, Ed25519 should be your default choice, unless you need a prime-order group. In that case, build your desired protocol atop Ristretto255.

If you’re not sure if you need a prime-order group, you probably don’t. It’s a specialized requirement for uncommon use cases (ring signatures, password authenticated key exchange protocols, zero-knowledge proofs, etc.).

Art: LvJ

The Bitcoin Curve (ECDSA, secp256k1)

Secp256k1 is a Koblitz curve, which is a special case of Weierstrass curves that are more performant when used in binary fields, of the form, . This curve is almost exclusively used in cryptocurrency software.

There is no specified reason why Bitcoin chose secp256k1 over another elliptic curve at the time of its inception, but we can speculate:

The author was a pseudonymous contributor to the Metzdowd mailing list for cypherpunks, and probably didn’t trust the NIST curves. Since Ed25519 didn’t exist at the time, the only obvious choice for a hipster elliptic curve parameter selection was to rely on the SECG recommendations, which specify the NIST and Koblitz curves. If you cross the NIST curves off the list, only the Koblitz curves remained.

Therefore, the selection of secp256k1 is likely an artefact of computer history and not a compelling reason to select secp256k1 in new designs. Please look elsewhere.

Fact: Imgflip didn’t have a single secp256k1 meme until I made this one.

Secp256k1 targets the 128-bit security level.

Guidance for secp256k1

Don’t bother, there are better options. (i.e. Ed25519)

If you’re writing software for a cryptocurrency-related project, and you feel compelled to use secp256k1 for the sake of reducing your code footprint, please strongly consider the option of burning everything to the proverbial ground.

Cryptocurrency sucks!
Art: Swizz

Cryptocurrency Aside, Why Avoid Secp256k1?

As we noted above, secp256k1 isn’t widely used outside of cryptocurrency.

As a direct consequence of this (as we’ll discuss in the NIST P-256 section), most cryptography libraries don’t offer optimized, side-channel-resistant implementations of secp256k1; even if they do offer optimized implementations of NIST P-256.

(Meanwhile, Ed25519 is designed to be side-channel and misuse-resistant, partly due to its Schnorr construction and constant-time ladder for scalar multiplication, so any library that implements Ed25519 is overwhelmingly likely to be constant-time.)

Therefore, any secp256k1 library for most programming languages that isn’t an FFI wrapper for libsecp256k1 will have worse performance than the other 256-bit curves.

https://twitter.com/bascule/status/1320183684935290882

Additionally, secp256k1 implementations are often a source of exploitable side-channels that permit attackers to pilfer your secret keys.

The previously linked article was about BouncyCastle’s implementation (which covers Java and .NET), but there’s still plenty of secp256k1 implementations that don’t FFI libsecp256k1.

From a quick Google Search:

• Python (uses EEA rather than Binary GCD for modular inverse)
• Go (uses Numbers, which weren’t designed for cryptography)
• PHP (uses GMP, which isn’t constant-time)
• JavaScript (calls here, which uses bn.js, which isn’t constant-time)

If you’re using secp256k1, and you’re not basing your choice on cybercash-interop, you’re playing with fire at the implementation and ecosystem levels–even if there are no security problems with the Koblitz curve itself.

You are much better off choosing any different curve than secp256k1 if you don’t have a Bitcoin/Ethereum/etc. interoperability requirement.

“No thanks, I use Ed25519.”
Art: LvJ

NIST P-256 (ECDSA, secp256r1)

NIST P-256 is the go-to curve to use with ECDSA in the modern era. Unlike Ed25519, P-256 uses a prime-order group, and is an approved algorithm to use in FIPS-validated modules.

Most cryptography libraries offer optimized assembly implementations of NIST P-256, which makes it less likely that your signing operations will leak timing information or become a significant performance bottleneck.

P-256 targets the 128-bit security level.

Why Not Use P-256?

Once upon a time, P-256 was riskier than Ed25519 (for signatures) and X25519 (for Diffie-Hellman), due to the incomplete addition formulas that led to timing-leaky implementations.

If you’re running old software, you may still be vulnerable to timing attacks that can recover your ECDSA secret key. However, there is a good chance that you’re on a modern and secure implementation in 2022, especially if you’re outsourcing this to OpenSSL or its derivatives.

ECDSA requires a secure randomness source to sign data. If you don’t have one available, and you sign anything, you’re coughing up your secret key to any attacker capable of observing multiple signatures.

Guidance for P-256

P-256 is an acceptable choice, especially if you’re forced to cope with FIPS and/or the CNSA suite requirements when using cryptography.

Of course, if you can get away with Ed25519, use Ed25519 instead.

If you use P-256, make sure you’re using it with SHA-256. Some implementations may default to something weaker (e.g. SHA-1).

If you’re also going to be performing ECDH with P-256, make sure you use compressed points. There used to be a patent; it died in 2018.

If you can afford it, make sure you use deterministic ECDSA (RFC 6979) or hedged signatures (if fault attacks are relevant to your threat model).

Art: LvJ

NIST P-384 (ECDSA, secp384r1)

NIST P-384 has a larger field than the curves we’ve previously examined, which allows P-384 to target the 192-bit security level. That’s the primary reason why anyone would choose P-384.

Naturally, elliptic curve security is more complicated than merely security against the Elliptic Curve Discrete Logarithm Problem (ECDLP).

P-384 is most often paired with SHA-384, which is the most widely used flavor of the SHA-2 family hash functions that isn’t susceptible to length-extension attacks. (There are also truncated SHA-512 variants specified later, but that’s also what SHA-384 is under-the-hood.)

If you’re aiming to build a “secure-by-default” tool for a system that the US government might one day become a customer of, with minimal cryptographic primitive choice, using NIST P-384 with SHA-384 makes for a reasonably minimalistic bundle.

Why Not Use P-384?

Unlike P-256, most P-384 implementations don’t use constant-time, optimized, and/or formally verified assembly code. (Notable counter-examples: AWS-LC and Go x/crypto.)

Like P-256, P-384 also requires a secure randomness source to sign data. If you aren’t providing one, expect your signing key to end up on fail0verflow one day.

Guidance for P-384

If you use P-384, make sure you’re using it with SHA-384.

The standard NIST curve advice of RFC 6979 and point compression and/or hedged signatures applies here too.

Art: Kyume

NIST P-521 (ECDSA, secp521r1)

Biggest curve is best curve! — the clueless

https://www.youtube.com/watch?v=i_APoSfCYwU

Systems that choose P-521 often have an interesting threat model, even though said threat model is rarely formally specified.

It’s overwhelmingly likely that what eventually breaks the 256-bit elliptic curves will also break P-521 in short order: Cryptography Relevant Quantum Computers.

The only thing P-521 does against CRQCs that P-256 doesn’t is require more quantum memory. If you’re worried about QRQCs, you might want to look into hybrid post-quantum signature schemes.

If you’re choosing P-521 in your designs, you’re basically saying, “I want to have 256 bits of asymmetric cryptographic security, come hell or high water!” even though the 128-bit security level is likely just fine for your actual threats.

Aside: P-521 and 512-bit ECC Security

P-521 is not a typo, although people sometimes think it is. P-521 uses the Mersenne prime instead of a 512-bit near-Mersenne prime.

This has led to an unfortunate trend in cryptography media to map ECC key sizes to symmetric security levels that misleads people as to the relationship between the two. For example:

Source
Source

Regrettably, this is misleading, because plotting the ECC Key Size versus equivalent Symmetric Security isn’t a how ECDLP security works. The ratio of the exponents involved is totally linear; it doesn’t suddenly increase beyond 384-bit curves for a mysterious mathematical reason.

• 256-bit Curves target the 128-bit security level
• 384-bit Curves target the 192-bit security level
• 512-bit Curves target the 256-bit security level
• 521-bit Curves actually target the 260-bit security level, but that meets or exceeds the 256-bit security level, so that’s how the standards are interpreted

The reason for this boils down entirely to the best attack against the Elliptic Curve Discrete Logarithm Problem: Pollard’s Rho, which recovers the secret key from an -bit public key (which has a search space) in guesses.

Taking the square root of a number is the same as halving its exponent, so the security level is half: .

Takeaway: If someone tells you that you need a 521-bit curve to meet the 256-bit security level, they are mistaken and it’s not their fault.

Art: Harubaki

Why Not Use P-521?

It’s slow. Much slower than P-256 and Ed25519. Modestly slower than P-384.

Unlike P-384, you’re less likely to find an optimized, constant-time P-521 implementation.

Guidance for P-521

First, make a concerted effort to figure out the motivation for P-521 in your designs. Chances are, someone is putting too much emphasis on the wrong things for security.

If you use P-521, make sure you’re using it with SHA-512.

The standard NIST curve advice of RFC 6979 and point compression and/or hedged signatures applies here too.

Art: LvJ

Ed448 (EdDSA, Curve448)

Ed448 is the P-521 of the Edwards curves: It mostly exists to give standards committees a psychological comfort for the unlikely event that 256-bit ECC is desperately broken but ECC larger than 384 bits is somehow still safe.

https://twitter.com/dchest/status/703017144053833728

The very concept of having multiple “security levels” for raw cryptography primitives is mostly an artefact of the historical military roots of cryptography, rather than a serious consideration in the modern world.

Unfortunately, this leads to implementations that prioritize runtime algorithm selection negotiation, which maximizes the risk of protocol-level vulnerabilities. See also: JWT.

Ed448 was specified to use SHAKE256, which is a needlessly conservative decision which leads to an unnecessary performance bottleneck.

Why Not Use Ed448?

Aside from the performance hit mentioned previously, there’s no compelling reason to avoid Ed448 that isn’t also true of either Ed25519 or P-384.

Guidance for Ed448

If you want more speed, go with Ed25519. In addition to being faster, Ed25519 is also very widely supported.

If you need a prime-order field, use Decaf with Ed448 or consider P-384.

The Brainpool Curves

The main motivation for the Brainpool curves is that the NIST curves were not generated in a “verifiable pseudo-random way”.

The only reasons you’d ever want to support the Brainpool curves include:

1. You think the NIST curves are somehow backdoored by the NSA
2. You don’t appreciate small attack surfaces in cryptography libraries
3. The German government told you to (see: compliance)

Most of the advice for the NIST Curves at each security level can be copy/pasted for the Brainpool curves, with one important caveat:

When considering real-world implementations, Brainpool curves are more likely to use the general purpose Big Number procedures (which aren’t always constant-time), rather than optimized assembly code, than the NIST curves are.

Therefore, my general guidance for the Brainpool curves is simply:

1. Proceed at your own peril
2. Consider hiring a cryptography engineer to study the implementation you’re relying on, especially with regard to timing attacks

Me when I hear “brainpool”
Art: LvJ

Re-Examining the SafeCurves Criteria

Here’s a 2022 refresh of the SafeCurves criteria for all of the curves considered by this blog post.

SafeCurve Criteria	Relevance to the Curves Listed Above
Fields	All relevant curves satisfy the requirements
Equations	All relevant curves satisfy the requirements
Base Points	All relevant curves satisfy the requirements
Rho	All relevant curves satisfy the requirements
Transfers	All relevant curves satisfy the requirements
Discriminants	Only secp256k1 doesn’t satisfy the requirements (out of the curves listed in this blog post)
Rigidity	The NIST curves do not meet this requirement. If you care about whether or not the standards were manipulated to insert a backdoor, rigidity matters to you. Otherwise, it’s not a deal-breaker.
Ladders	While a Montgomery ladder is beneficial for speed and implementation security, it isn’t strictly speaking required. This is an icing-on-the-cake consideration.
Twists	The only curve listed above that doesn’t meet the requirement is the 256-bit Brainpool curve (brainpoolp256t1).
Completeness	All relevant curves satisfy the requirements, as of 2015. SafeCurves is out of date here.
Indistinguishability	All relevant curves satisfy the requirements, as of 2014.

SafeCurves continues to be a useful resource, especially if you stray from the guidance on this page.

For example: You wouldn’t want to use pairing-friendly curves for general purpose ECC digital signatures, because they’re suitable for specialized problems. SafeCurves correctly recommends not using BN(2,254).

However, SafeCurves is showing its age in 2022. BN curves still end up in digital signature protocol standards even though BLS-12-381 is clearly a better choice.

The Internet would benefit greatly for an updated SafeCurves that focuses on newer elliptic curve algorithms.

Art: Scruff

TL;DR

Ed25519 is great. NIST P-256 and P-384 are okay (with caveats). Anything else is questionable, and their parameter selection should come with a clear justification.

https://soatok.blog/2022/05/19/guidance-for-choosing-an-elliptic-curve-signature-algorithm-in-2022/

#asymmetricCryptography #BrainpoolCurves #cryptography #digitalSignatureAlgorithm #ECDSA #Ed25519 #Ed448 #EdDSA #ellipticCurveCryptography #P256 #P384 #P521 #secp256k1 #secp256r1 #secp384r1 #secp521r1 #SecurityGuidance

Dhole Moments

2020-05-13 10:00:22

If you’re reading this wondering if you should stop using AES-GCM in some standard protocol (TLS 1.3), the short answer is “No, you’re fine”.

I specialize in secure implementations of cryptography, and my years of experience in this field have led me to dislike AES-GCM.

This post is about why I dislike AES-GCM’s design, not “why AES-GCM is insecure and should be avoided”. AES-GCM is still miles above what most developers reach for when they want to encrypt (e.g. ECB mode or CBC mode). If you want a detailed comparison, read this.

To be clear: This is solely my opinion and not representative of any company or academic institution.

What is AES-GCM?

AES-GCM is an authenticated encryption mode that uses the AES block cipher in counter mode with a polynomial MAC based on Galois field multiplication.

In order to explain why AES-GCM sucks, I have to first explain what I dislike about the AES block cipher. Then, I can describe why I’m filled with sadness every time I see the AES-GCM construction used.

What is AES?

The Advanced Encryption Standard (AES) is a specific subset of a block cipher called Rijndael.

Rijndael’s design is based on a substitution-permutation network, which broke tradition from many block ciphers of its era (including its predecessor, DES) in not using a Feistel network.

AES only includes three flavors of Rijndael: AES-128, AES-192, and AES-256. The difference between these flavors is the size of the key and the number of rounds used, but–and this is often overlooked–not the block size.

As a block cipher, AES always operates on 128-bit (16 byte) blocks of plaintext, regardless of the key size.

This is generally considered acceptable because AES is a secure pseudorandom permutation (PRP), which means that every possible plaintext block maps directly to one ciphertext block, and thus birthday collisions are not possible. (A pseudorandom function (PRF), conversely, does have birthday bound problems.)

Why AES Sucks

Art by Khia.

Side-Channels

The biggest reason why AES sucks is that its design uses a lookup table (called an S-Box) indexed by secret data, which is inherently vulnerable to cache-timing attacks (PDF).

There are workarounds for this AES vulnerability, but they either require hardware acceleration (AES-NI) or a technique called bitslicing.

The short of it is: With AES, you’re either using hardware acceleration, or you have to choose between performance and security. You cannot get fast, constant-time AES without hardware support.

Block Size

AES-128 is considered by experts to have a security level of 128 bits.

Similarly, AES-192 gets certified at 192-bit security, and AES-256 gets 256-bit security.

However, the AES block size is only 128 bits!

That might not sound like a big deal, but it severely limits the constructions you can create out of AES.

Consider the case of AES-CBC, where the output of each block of encryption is combined with the next block of plaintext (using XOR). This is typically used with a random 128-bit block (called the initialization vector, or IV) for the first block.

This means you expect a collision after encrypting (at 50% probability) blocks.

When you start getting collisions, you can break CBC mode, as this video demonstrates:

https://www.youtube.com/watch?v=v0IsYNDMV7A

This is significantly smaller than the you expect from AES.

Post-Quantum Security?

With respect to the number of attempts needed to find the correct key, cryptographers estimate that AES-128 will have a post-quantum security level of 64 bits, AES-192 will have a post-quantum security level of 96 bits, and AES-256 will have a post-quantum security level of 128 bits.

This is because Grover’s quantum search algorithm can search unsorted items in time, which can be used to reduce the total number of possible secrets from to . This effectively cuts the security level, expressed in bits, in half.

Note that this heuristic estimate is based on the number of guesses (a time factor), and doesn’t take circuit size into consideration. Grover’s algorithm also doesn’t parallelize well. The real-world security of AES may still be above 100 bits if you consider these nuances.

But remember, even AES-256 operates on 128-bit blocks.

Consequently, for AES-256, there should be approximately (plaintext, key) pairs that produce any given ciphertext block.

Furthermore, there will be many keys that, for a constant plaintext block, will produce the same ciphertext block despite being a different key entirely. (n.b. This doesn’t mean for all plaintext/ciphertext block pairings, just some arbitrary pairing.)

Concrete example: Encrypting a plaintext block consisting of sixteen NUL bytes will yield a specific 128-bit ciphertext exactly once for each given AES-128 key. However, there are times as many AES-256 keys as there are possible plaintext/ciphertexts. Keep this in mind for AES-GCM.

This means it’s conceivable to accidentally construct a protocol that, despite using AES-256 safely, has a post-quantum security level on par with AES-128, which is only 64 bits.

This would not be nearly as much of a problem if AES’s block size was 256 bits.

Real-World Example: Signal

The Signal messaging app is the state-of-the-art for private communications. If you were previously using PGP and email, you should use Signal instead.

Signal aims to provide private communications (text messaging, voice calls) between two mobile devices, piggybacking on your pre-existing contacts list.

Part of their operational requirements is that they must be user-friendly and secure on a wide range of Android devices, stretching all the way back to Android 4.4.

The Signal Protocol uses AES-CBC + HMAC-SHA256 for message encryption. Each message is encrypted with a different AES key (due to the Double Ratchet), which limits the practical blast radius of a cache-timing attack and makes practical exploitation difficult (since you can’t effectively replay decryption in order to leak bits about the key).

Thus, Signal’s message encryption is still secure even in the presence of vulnerable AES implementations.

Hooray for well-engineered protocols managing to actually protect users.
Art by Swizz.

However, the storage service in the Signal App uses AES-GCM, and this key has to be reused in order for the encrypted storage to operate.

This means, for older phones without dedicated hardware support for AES (i.e. low-priced phones from 2013, which Signal aims to support), the risk of cache-timing attacks is still present.

This is unacceptable!

What this means is, a malicious app that can flush the CPU cache and measure timing with sufficient precision can siphon the AES-GCM key used by Signal to encrypt your storage without ever violating the security boundaries enforced by the Android operating system.

As a result of the security boundaries never being crossed, these kind of side-channel attacks would likely evade forensic analysis, and would therefore be of interest to the malware developers working for nation states.

Of course, if you’re on newer hardware (i.e. Qualcomm Snapdragon 835), you have hardware-accelerated AES available, so it’s probably a moot point.

Why AES-GCM Sucks Even More

AES-GCM is an authenticated encryption mode that also supports additional authenticated data. Cryptographers call these modes AEAD.

AEAD modes are more flexible than simple block ciphers. Generally, your encryption API accepts the following:

1. The plaintext message.
2. The encryption key.
3. A nonce (: A number that must only be used once).
4. Optional additional data which will be authenticated but not encrypted.

The output of an AEAD function is both the ciphertext and an authentication tag, which is necessary (along with the key and nonce, and optional additional data) to decrypt the plaintext.

Cryptographers almost universally recommend using AEAD modes for symmetric-key data encryption.

That being said, AES-GCM is possibly my least favorite AEAD, and I’ve got good reasons to dislike it beyond simply, “It uses AES”.

The deeper you look into AES-GCM’s design, the harder you will feel this sticker.

GHASH Brittleness

The way AES-GCM is initialized is stupid: You encrypt an all-zero block with your AES key (in ECB mode) and store it in a variable called . This value is used for authenticating all messages authenticated under that AES key, rather than for a given (key, nonce) pair.
Diagram describing Galois/Counter Mode, taken from Wikipedia.
This is often sold as an advantage: Reusing allows for better performance. However, it makes GCM brittle: Reusing a nonce allows an attacker to recover H and then forge messages forever. This is called the “forbidden attack”, and led to real world practical breaks.

Let’s contrast AES-GCM with the other AEAD mode supported by TLS: ChaCha20-Poly1305, or ChaPoly for short.

ChaPoly uses one-time message authentication keys (derived from each key/nonce pair). If you manage to leak a Poly1305 key, the impact is limited to the messages encrypted under that (ChaCha20 key, nonce) pair.

While that’s still bad, it isn’t “decrypt all messages under that key forever” bad like with AES-GCM.

Note: “Message Authentication” here is symmetric, which only provides a property called message integrity, not sender authenticity. For the latter, you need asymmetric cryptography (wherein the ability to verify a message doesn’t imply the capability to generate a new signature), which is totally disparate from symmetric algorithms like AES or GHASH. You probably don’t need to care about this nuance right now, but it’s good to know in case you’re quizzed on it later.

H Reuse and Multi-User Security

If you recall, AES operates on 128-bit blocks even when 256-bit keys are used.

If we assume AES is well-behaved, we can deduce that there are approximately different 256-bit keys that will map a single plaintext block to a single ciphertext block.

This is trivial to calculate. Simply divide the number of possible keys () by the number of possible block states () to yield the number of keys that produce a given ciphertext for a single block of plaintext: .

Each key that will map an arbitrarily specific plaintext block to a specific ciphertext block is also separated in the keyspace by approximately .

This means there are approximately independent keys that will map a given all-zero plaintext block to an arbitrarily chosen value of (if we assume AES doesn’t have weird biases).

Credit: Harubaki

“Why Does This Matter?”

It means that, with keys larger than 128 bits, you can model the selection of as a 128-bit pseudorandom function, rather than a 128-bit permutation. As a result, you an expect a collision with 50% probability after only different keys are selected.

Note: Your 128-bit randomly generated AES keys already have this probability baked into their selection, but this specific analysis doesn’t really apply for 128-bit keys since AES is a PRP, not a PRF, so there is no “collision” risk. However, you end up at the same upper limit either way.

But 50% isn’t good enough for cryptographic security.

In most real-world systems, we target a collision risk. So that means our safety limit is actually different AES keys before you have to worry about reuse.

This isn’t the same thing as symmetric wear-out (where you need to re-key after a given number of encryptions to prevent nonce reuse). Rather, it means after your entire population has exhausted the safety limit of different AES keys, you have to either accept the risk or stop using AES-GCM.

If you have a billion users (), the safety limit is breached after AES keys per user (approximately 262,000).

“What Good is H Reuse for Attackers if HF differs?”

There are two numbers used in AES-GCM that are derived from the AES key. is used for block multiplication, and (the value of with a counter of 0 from the following diagram) is XORed with the final result to produce the authentication tag.

The arrow highlighted with green is HF.

It’s tempting to think that a reuse of isn’t a concern because will necessarily be randomized, which prevents an attacker from observing when collides. It’s certainly true that the single-block collision risk discussed previously for will almost certainly not also result in a collision for . And since isn’t reused unless a nonce is reused (which also leaks directly), this might seem like a non-issue.

Art by Khia.

However, it’s straightforward to go from a condition of reuse to an adaptive chosen-ciphertext attack.

1. Intercept multiple valid ciphertexts.
   
   • e.g. Multiple JWTs encrypted with {"alg":"A256GCM"}

   
   

2. Use your knowledge of , the ciphertext, and the AAD to calculate the GCM tag up to the final XOR. This, along with the existing authentication tag, will tell you the value of for a given nonce.
3. Calculate a new authentication tag for a chosen ciphertext using and your candidate value, then replay it into the target system.

While the blinding offered by XORing the final output with is sufficient to stop from being leaked directly, the protection is one-way.

Ergo, a collision in is not sufficiently thwarted by .

“How Could the Designers Have Prevented This?”

The core issue here is the AES block size, again.

If we were analyzing a 256-bit block variant of AES, and a congruent GCM construction built atop it, none of what I wrote in this section would apply.

However, the 128-bit block size was a design constraint enforced by NIST in the AES competition. This block size was during an era of 64-bit block ciphers (e.g. Triple-DES and Blowfish), so it was a significant improvement at the time.

NIST’s AES competition also inherited from the US government’s tradition of thinking in terms of “security levels”, which is why there are three different permitted key sizes (128, 192, or 256 bits).

“Why Isn’t This a Vulnerability?”

There’s always a significant gap in security, wherein something isn’t safe to recommend, but also isn’t susceptible to a known practical attack. This gap is important to keep systems secure, even when they aren’t on the bleeding edge of security.

Using 1024-bit RSA is a good example of this: No one has yet, to my knowledge, successfully factored a 1024-bit RSA public key. However, most systems have recommended a minimum 2048-bit for years (and many recommend 3072-bit or 4096-bit today).

With AES-GCM, the expected distance between collisions in is , and finding an untargeted collision requires being able to observe more than different sessions, and somehow distinguish when collides.

As a user, you know that after different keys, you’ve crossed the safety boundary for avoiding collisions. But as an attacker, you need bites at the apple, not . Additionally, you need some sort of oracle or distinguisher for when this happens.

We don’t have that kind of distinguisher available to us today. And even if we had one available, the amount of data you need to search in order for any two users in the population to reuse/collide is challenging to work with. You would need the computational and data storages of a major cloud service provider to even think about pulling the attack off.

Naturally, this isn’t a practical vulnerability. This is just another gripe I have with AES-GCM, as someone who has to work with cryptographic algorithms a lot.

Short Nonces

Although the AES block size is 16 bytes, AES-GCM nonces are only 12 bytes. The latter 4 bytes are dedicated to an internal counter, which is used with AES in Counter Mode to actually encrypt/decrypt messages.

(Yes, you can use arbitrary length nonces with AES-GCM, but if you use nonces longer than 12 bytes, they get hashed into 12 bytes anyway, so it’s not a detail most people should concern themselves with.)

If you ask a cryptographer, “How much can I encrypt safely with AES-GCM?” you’ll get two different answers.

1. Message Length Limit: AES-GCM can be used to encrypt messages up to bytes long, under a given (key, nonce) pair.
2. Number of Messages Limit: If you generate your nonces randomly, you have a 50% chance of a nonce collision after messages.
   However, 50% isn’t conservative enough for most systems, so the safety margin is usually much lower. Cryptographers generally set the key wear-out of AES-GCM at random nonces, which represents a collision probability of one in 4 billion.

These limits are acceptable for session keys for encryption-in-transit, but they impose serious operational limits on application-layer encryption with long-term keys.

Random Key Robustness

Before the advent of AEAD modes, cryptographers used to combine block cipher modes of operation (e.g. AES-CBC, AES-CTR) with a separate message authentication code algorithm (e.g. HMAC, CBC-MAC).

You had to be careful in how you composed your protocol, lest you invite Cryptographic Doom into your life. A lot of developers screwed this up. Standardized AEAD modes promised to make life easier.

Many developers gained their intuition for authenticated encryption modes from protocols like Signal’s (which combines AES-CBC with HMAC-SHA256), and would expect AES-GCM to be a drop-in replacement.

Unfortunately, GMAC doesn’t offer the same security benefits as HMAC: Finding a different (ciphertext, HMAC key) pair that produces the same authentication tag is a hard problem, due to HMAC’s reliance on cryptographic hash functions. This makes HMAC-based constructions “message committing”, which instills Random Key Robustness.

Critically, AES-GCM doesn’t have this property. You can calculate a random (ciphertext, key) pair that collides with a given authentication tag very easily.

This fact prohibits AES-GCM from being considered for use with OPAQUE (which requires RKR), one of the upcoming password-authenticated key exchange algorithms. (Read more about them here.)

Better-Designed Algorithms

You might be thinking, “Okay random furry, if you hate AES-GCM so much, what would you propose we use instead?”

I’m glad you asked!

XChaCha20-Poly1305

For encrypting messages under a long-term key, you can’t really beat XChaCha20-Poly1305.

• ChaCha is a stream cipher based on a 512-bit ARX hash function in counter mode. ChaCha doesn’t use S-Boxes. It’s fast and constant-time without hardware acceleration.
• ChaCha20 is ChaCha with 20 rounds.
• XChaCha nonces are 24 bytes, which allows you to generate them randomly and not worry about a birthday collision until about messages (for the same collision probability as AES-GCM).
• Poly1305 uses different 256-bit key for each (nonce, key) pair and is easier to implement in constant-time than AES-GCM.
• XChaCha20-Poly1305 uses the first 16 bytes of the nonce and the 256-bit key to generate a distinct subkey, and then employs the standard ChaCha20-Poly1305 construction used in TLS today.

For application-layer cryptography, XChaCha20-Poly1305 contains most of the properties you’d want from an authenticated mode.

However, like AES-GCM (and all other Polynomial MACs I’ve heard of), it is not message committing.

The Gimli Permutation

For lightweight cryptography (n.b. important for IoT), the Gimli permutation (e.g. employed in libhydrogen) is an attractive option.

Gimli is a Round 2 candidate in NIST’s Lightweight Cryptography project. The Gimli permutation offers a lot of applications: a hash function, message authentication, encryption, etc.

Critically, it’s possible to construct a message-committing protocol out of Gimli that will hit a lot of the performance goals important to embedded systems.

Closing Remarks

Despite my personal disdain for AES-GCM, if you’re using it as intended by cryptographers, it’s good enough.

Don’t throw AES-GCM out just because of my opinions. It’s very likely the best option you have.

Although I personally dislike AES and GCM, I’m still deeply appreciative of the brilliance and ingenuity that went into both designs.

My desire is for the industry to improve upon AES and GCM in future cipher designs so we can protect more people, from a wider range of threats, in more diverse protocols, at a cheaper CPU/memory/time cost.

We wouldn’t have a secure modern Internet without the work of Vincent Rijmen, Joan Daemen, John Viega, David A. McGrew, and the countless other cryptographers and security researchers who made AES-GCM possible.

Change Log

• 2021-10-26: Added section on H Reuse and Multi-User Security.

https://soatok.blog/2020/05/13/why-aes-gcm-sucks/

#AES #AESGCM #cryptography #GaloisCounterMode #opinion #SecurityGuidance #symmetricCryptography

Dhole Moments

2020-10-07 02:46:12

This is the first entry in a (potentially infinite) series of dead end roads in the field of cryptanalysis.

Cryptography engineering is one of many specialties within the wider field of security engineering. Security engineering is a discipline that chiefly concerns itself with studying how systems fail in order to build better systems–ones that are resilient to malicious acts or even natural disasters. It sounds much simpler than it is.

If you want to develop and securely implement a cryptography feature in the application you’re developing, it isn’t enough to learn how to implement textbook descriptions of cryptography primitives during your C.S. undergrad studies (or equivalent). An active interest in studying how cryptosystems fail is the prerequisite for being a cryptography engineer.

Thus, cryptography engineering and cryptanalysis research go hand-in-hand.

Pictured: How I feel when someone tells me about a novel cryptanalysis technique relevant to the algorithm or protocol I’m implementing. (Art by Khia.)

If you are interested in exploring the field of cryptanalysis–be it to contribute on the attack side of cryptography or to learn better defense mechanisms–you will undoubtedly encounter roads that seem enticing and not well-tread, and it might not be immediately obvious why the road is a dead end. Furthermore, beyond a few comparison tables on Wikipedia or obscure Stack Exchange questions, the cryptology literature is often sparse on details about why these avenues lead nowhere.

So let’s explore where some of these dead-end roads lead, and why they stop where they do.

(Art by Kyume.)

Length Extension Attacks

It’s difficult to provide a better summary of length extension attacks than what Skull Security wrote in 2012. However, that only addresses “What are they?”, “How do you use them?”, and “Which algorithms and constructions are vulnerable?”, but leaves out a more interesting question: “Why were they even possible to begin with?”

An Extensive Tale

Tale, not tail! (Art by Swizz.)

To really understand length extension attacks, you have to understand how cryptographic hash functions used to be designed. This might sound intimidating, but we don’t need to delve too deep into the internals.

A cryptographic hash function is a keyless pseudorandom transformation from a variable length input to a fixed-length output. Hash functions are typically used as building blocks for larger constructions (both reasonable ones like HMAC-SHA-256, and unreasonable ones like my hash-crypt project).

However, hash functions like SHA-256 are designed to operate on sequential blocks of input. This is because sometimes you need to stream data into a hash function rather than load it all into memory at once. (This is why you can sha256sum a file larger than your available RAM without crashing your computer or causing performance headaches.)

A streaming hash function API might look like this:
class MyCoolHash(BaseHashClass): @staticmethod def init(): """ Initialize the hash state. """ def update(data): """ Update the hash state with additional data. """ def digest(): """ Finalize the hash function. """ def compress(): """ (Private method.) """
To use it, you’d call hash = MyCoolHash.init() and then chain together hash.update() calls with data as you load it from disk or the network, until you’ve run out of data. Then you’d call digest() and obtain the hash of the entire message.

There are two things to take away right now:

1. You can call update() multiple times, and that’s valid.
2. Your data might not be an even multiple of the internal block size of the hash function. (More often than not, it won’t be!)

So what happens when you call digest() and the amount of data you’ve passed to update() is not an even multiple of the hash size?

For most hash functions, the answer is simple: Append some ISO/IEC 7816-4 padding until you get a full block, run that through a final iteration of the internal compression function–the same one that gets called on update()–and then output the current internal state.

Let’s take a slightly deeper look at what a typical runtime would look like for the MyCoolHash class I sketched above:

1. hash = MyCoolHash.init()
   
   • Initialize some variables to some constants (initialization vectors).

   
   

2. hash.update(blockOfData)
   
   • Start with any buffered data (currently none), count up to 32 bytes. If you’ve reached this amount, invoke compress() on that data and clear the buffer. Otherwise, just append blockOfData to the currently buffered data.
   • For every 32 byte of data not yet touched by compress(), invoke compress() on this block (updating the internal state).
   • If you have any leftover bytes, append to the internal buffer for the next invocation to process.

   
   

3. hash.update(moreData)
   
   • Same as before, except there might be some buffered data from step 2.

   
   

4. output = hash.digest()
   
   • If you have any data left in the buffer, append a 0x80 byte followed by a bunch of 0x00 bytes of padding until you reach the block size. If you don’t, you have an entire block of padding (0x80 followed by 0x00s).
   • Call compress() one last time.
   • Serialize the internal hash state as a byte array or hexadecimal-encoded string (depending on usage). Return that to the caller.

   
   

This is fairly general description that will hold for most older hash functions. Some details might be slightly wrong (subtly different padding scheme, whether or not to include a block of empty padding on digest() invocations, etc.).

The details aren’t super important. Just the rhythm of the design.

• init()
• update()
  
  • load buffer, compress()
  • compress()
  • compress()
  • …
  • buffer remainder

  
  

• update()
  
  • load buffer, compress()
  • compress()
  • compress()
  • …
  • buffer remainder

  
  

• …
• digest()
  
  • load buffer, pad, compress()
  • serialize internal state
  • return

  
  

And thus, without having to know any of the details about what compress() even looks like, the reason why length extension attacks were ever possible should leap out at you!

Art by Khia.

If it doesn’t, look closely at the difference between update() and digest().

There are only two differences:

1. update() doesn’t pad before calling compress()
2. digest() returns the internal state that compress() always mutates

The reason length-extension attacks are possible is that, for some hash functions, the output of digest() is its full internal state.

This means that you can run take an existing hash function and pretend it’s the internal state after an update() call instead of a digest() call by appending the padding and then, after calling compress(), appending additional data of your choice.

The (F)Utility of Length Extension

Length-Extension Attacks are mostly used for attacking naive message authentication systems where someone attempts to authenticate a message (M) with a secret key (k), but they construct it like so:
auth_code = vulnerable_hash(k.append(M))
If this sounds like a very narrow use-case, that’s because it is. However, it still broke Flickr’s API once, and it’s a popular challenge for CTF competitions around the world.

Consequently, length-extension attacks are sometimes thought to be vulnerabilities of the construction rather than a vulnerability of the hash function. For a Message Authentication Code construction, these are classified under canonicalization attacks.

After all, even though SHA-256 is vulnerable to length-extension, but you can’t actually exploit it unless someone is using it in a vulnerable fashion.

That being said, it’s often common to say that hash functions like SHA-256 and SHA-512 are prone to length-extension.

Ways to Avoid Length-Extension Attacks

Use HMAC. HMAC was designed to prevent these kinds of attacks.

Alternatively, if you don’t have any cryptographic secrets, you can always do what bitcoin did: Hash your hash again.
return sha256(sha256(message))
Note: Don’t actually do that, it’s dangerous for other reasons. You also don’t want to take this to an extreme. If you iterate your hash too many times, you’ll reinvent PBKDF1 and its insecurity. Two is plenty.

Or you can do something really trivial (which ultimately became another standard option in the SHA-2 family of hash functions):

Always start with a 512-bit hash and then truncate your output so the attacker never recovers the entire internal state of your hash in order to extend it.

That’s why you’ll sometimes see SHA-512/224 and SHA-512/256 in a list of recommendations. This isn’t saying “use one or the other”, that’s the (rather confusing) notation for a standardized SHA-512 truncation.

Note: This is actually what SHA-384 has done all along, and that’s one of the reasons why you see SHA-384 used more than SHA-512.

If you want to be extra fancy, you can also just use a different hash function that isn’t vulnerable to length extension, such as SHA-3 or BLAKE2.

Questions and Answers

Art by Khia.

Why isn’t BLAKE2 vulnerable to length extension attacks?

Quite simply: It sets a flag in the internal hash state before compressing the final buffer.

If you try to deserialize this state then invoke update(), you’ll get a different result than BLAKE2’s compress() produced during digest().

For a secure hash function, a single bit of difference in the internal state should result in a wildly different output. (This is called the avalanche effect.)

Why isn’t SHA-3 vulnerable to length extension attacks?

SHA-3 is a sponge construction whose internal state is much larger than the hash function output. This prevents an attacker from recovering the hash function’s internal state from a message digest (similar to the truncated hash function discussed above).

Why don’t length-extension attacks break digital signature algorithms?

Digital signature algorithms–such as RSASSA, ECDSA, and EdDSA–take a cryptographic hash of a message and then perform some asymmetric cryptographic transformation of the hash with the secret key to produce a signature that can be verified with a public key. (The exact details are particular to the signature algorithm in question.)

Length-extension attacks only allow you to take a valid H(k || m) and produce a valid H(k || m || padding || extra) hash that will validate, even if you don’t know k. They don’t magically create collisions out of thin air.

Even if you use a weak hash function like SHA-1, knowing M and H(M) is not sufficient to calculate a valid signature. (You need to be able to know these values in order to verify the signature anyway.)

The security of digital signature algorithms depends entirely on the secrecy of the signing key and the security of the asymmetric cryptographic transformation used to generate a signature. (And its resilience to side-channel attacks.)

However, a more interesting class of attack is possible for systems that expect digital signatures to have similar properties as cryptographic hash functions. This would qualify as a protocol vulnerability, not a length-extension vulnerability.

TL;DR

Art by Khia.

Length-extension attacks exploit a neat property of a few cryptographic hash functions–most of which you shouldn’t be using in 2020 anyway (SHA-2 is still fine)–but can only be exploited by a narrow set of circumstances.

If you find yourself trying to use length-extension to break anything else, you’ve probably run into a cryptographic dead end and need to backtrack onto more interesting avenues of exploitation–of which there are assuredly many (unless your cryptography is boring).

---

Next: Timing Side-Channels

https://soatok.blog/2020/10/06/dead-ends-in-cryptanalysis-1-length-extension-attacks/

#cryptanalysis #crypto #cryptographicHashFunction #cryptography #lengthExtensionAttacks

Dhole Moments

2020-05-13 10:00:22

If you’re reading this wondering if you should stop using AES-GCM in some standard protocol (TLS 1.3), the short answer is “No, you’re fine”.

I specialize in secure implementations of cryptography, and my years of experience in this field have led me to dislike AES-GCM.

This post is about why I dislike AES-GCM’s design, not “why AES-GCM is insecure and should be avoided”. AES-GCM is still miles above what most developers reach for when they want to encrypt (e.g. ECB mode or CBC mode). If you want a detailed comparison, read this.

To be clear: This is solely my opinion and not representative of any company or academic institution.

What is AES-GCM?

AES-GCM is an authenticated encryption mode that uses the AES block cipher in counter mode with a polynomial MAC based on Galois field multiplication.

In order to explain why AES-GCM sucks, I have to first explain what I dislike about the AES block cipher. Then, I can describe why I’m filled with sadness every time I see the AES-GCM construction used.

What is AES?

The Advanced Encryption Standard (AES) is a specific subset of a block cipher called Rijndael.

Rijndael’s design is based on a substitution-permutation network, which broke tradition from many block ciphers of its era (including its predecessor, DES) in not using a Feistel network.

AES only includes three flavors of Rijndael: AES-128, AES-192, and AES-256. The difference between these flavors is the size of the key and the number of rounds used, but–and this is often overlooked–not the block size.

As a block cipher, AES always operates on 128-bit (16 byte) blocks of plaintext, regardless of the key size.

This is generally considered acceptable because AES is a secure pseudorandom permutation (PRP), which means that every possible plaintext block maps directly to one ciphertext block, and thus birthday collisions are not possible. (A pseudorandom function (PRF), conversely, does have birthday bound problems.)

Why AES Sucks

Art by Khia.

Side-Channels

The biggest reason why AES sucks is that its design uses a lookup table (called an S-Box) indexed by secret data, which is inherently vulnerable to cache-timing attacks (PDF).

There are workarounds for this AES vulnerability, but they either require hardware acceleration (AES-NI) or a technique called bitslicing.

The short of it is: With AES, you’re either using hardware acceleration, or you have to choose between performance and security. You cannot get fast, constant-time AES without hardware support.

Block Size

AES-128 is considered by experts to have a security level of 128 bits.

Similarly, AES-192 gets certified at 192-bit security, and AES-256 gets 256-bit security.

However, the AES block size is only 128 bits!

That might not sound like a big deal, but it severely limits the constructions you can create out of AES.

Consider the case of AES-CBC, where the output of each block of encryption is combined with the next block of plaintext (using XOR). This is typically used with a random 128-bit block (called the initialization vector, or IV) for the first block.

This means you expect a collision after encrypting (at 50% probability) blocks.

When you start getting collisions, you can break CBC mode, as this video demonstrates:

https://www.youtube.com/watch?v=v0IsYNDMV7A

This is significantly smaller than the you expect from AES.

Post-Quantum Security?

With respect to the number of attempts needed to find the correct key, cryptographers estimate that AES-128 will have a post-quantum security level of 64 bits, AES-192 will have a post-quantum security level of 96 bits, and AES-256 will have a post-quantum security level of 128 bits.

This is because Grover’s quantum search algorithm can search unsorted items in time, which can be used to reduce the total number of possible secrets from to . This effectively cuts the security level, expressed in bits, in half.

Note that this heuristic estimate is based on the number of guesses (a time factor), and doesn’t take circuit size into consideration. Grover’s algorithm also doesn’t parallelize well. The real-world security of AES may still be above 100 bits if you consider these nuances.

But remember, even AES-256 operates on 128-bit blocks.

Consequently, for AES-256, there should be approximately (plaintext, key) pairs that produce any given ciphertext block.

Furthermore, there will be many keys that, for a constant plaintext block, will produce the same ciphertext block despite being a different key entirely. (n.b. This doesn’t mean for all plaintext/ciphertext block pairings, just some arbitrary pairing.)

Concrete example: Encrypting a plaintext block consisting of sixteen NUL bytes will yield a specific 128-bit ciphertext exactly once for each given AES-128 key. However, there are times as many AES-256 keys as there are possible plaintext/ciphertexts. Keep this in mind for AES-GCM.

This means it’s conceivable to accidentally construct a protocol that, despite using AES-256 safely, has a post-quantum security level on par with AES-128, which is only 64 bits.

This would not be nearly as much of a problem if AES’s block size was 256 bits.

Real-World Example: Signal

The Signal messaging app is the state-of-the-art for private communications. If you were previously using PGP and email, you should use Signal instead.

Signal aims to provide private communications (text messaging, voice calls) between two mobile devices, piggybacking on your pre-existing contacts list.

Part of their operational requirements is that they must be user-friendly and secure on a wide range of Android devices, stretching all the way back to Android 4.4.

The Signal Protocol uses AES-CBC + HMAC-SHA256 for message encryption. Each message is encrypted with a different AES key (due to the Double Ratchet), which limits the practical blast radius of a cache-timing attack and makes practical exploitation difficult (since you can’t effectively replay decryption in order to leak bits about the key).

Thus, Signal’s message encryption is still secure even in the presence of vulnerable AES implementations.

Hooray for well-engineered protocols managing to actually protect users.
Art by Swizz.

However, the storage service in the Signal App uses AES-GCM, and this key has to be reused in order for the encrypted storage to operate.

This means, for older phones without dedicated hardware support for AES (i.e. low-priced phones from 2013, which Signal aims to support), the risk of cache-timing attacks is still present.

This is unacceptable!

What this means is, a malicious app that can flush the CPU cache and measure timing with sufficient precision can siphon the AES-GCM key used by Signal to encrypt your storage without ever violating the security boundaries enforced by the Android operating system.

As a result of the security boundaries never being crossed, these kind of side-channel attacks would likely evade forensic analysis, and would therefore be of interest to the malware developers working for nation states.

Of course, if you’re on newer hardware (i.e. Qualcomm Snapdragon 835), you have hardware-accelerated AES available, so it’s probably a moot point.

Why AES-GCM Sucks Even More

AES-GCM is an authenticated encryption mode that also supports additional authenticated data. Cryptographers call these modes AEAD.

AEAD modes are more flexible than simple block ciphers. Generally, your encryption API accepts the following:

1. The plaintext message.
2. The encryption key.
3. A nonce (: A number that must only be used once).
4. Optional additional data which will be authenticated but not encrypted.

The output of an AEAD function is both the ciphertext and an authentication tag, which is necessary (along with the key and nonce, and optional additional data) to decrypt the plaintext.

Cryptographers almost universally recommend using AEAD modes for symmetric-key data encryption.

That being said, AES-GCM is possibly my least favorite AEAD, and I’ve got good reasons to dislike it beyond simply, “It uses AES”.

The deeper you look into AES-GCM’s design, the harder you will feel this sticker.

GHASH Brittleness

The way AES-GCM is initialized is stupid: You encrypt an all-zero block with your AES key (in ECB mode) and store it in a variable called . This value is used for authenticating all messages authenticated under that AES key, rather than for a given (key, nonce) pair.
Diagram describing Galois/Counter Mode, taken from Wikipedia.
This is often sold as an advantage: Reusing allows for better performance. However, it makes GCM brittle: Reusing a nonce allows an attacker to recover H and then forge messages forever. This is called the “forbidden attack”, and led to real world practical breaks.

Let’s contrast AES-GCM with the other AEAD mode supported by TLS: ChaCha20-Poly1305, or ChaPoly for short.

ChaPoly uses one-time message authentication keys (derived from each key/nonce pair). If you manage to leak a Poly1305 key, the impact is limited to the messages encrypted under that (ChaCha20 key, nonce) pair.

While that’s still bad, it isn’t “decrypt all messages under that key forever” bad like with AES-GCM.

Note: “Message Authentication” here is symmetric, which only provides a property called message integrity, not sender authenticity. For the latter, you need asymmetric cryptography (wherein the ability to verify a message doesn’t imply the capability to generate a new signature), which is totally disparate from symmetric algorithms like AES or GHASH. You probably don’t need to care about this nuance right now, but it’s good to know in case you’re quizzed on it later.

H Reuse and Multi-User Security

If you recall, AES operates on 128-bit blocks even when 256-bit keys are used.

If we assume AES is well-behaved, we can deduce that there are approximately different 256-bit keys that will map a single plaintext block to a single ciphertext block.

This is trivial to calculate. Simply divide the number of possible keys () by the number of possible block states () to yield the number of keys that produce a given ciphertext for a single block of plaintext: .

Each key that will map an arbitrarily specific plaintext block to a specific ciphertext block is also separated in the keyspace by approximately .

This means there are approximately independent keys that will map a given all-zero plaintext block to an arbitrarily chosen value of (if we assume AES doesn’t have weird biases).

Credit: Harubaki

“Why Does This Matter?”

It means that, with keys larger than 128 bits, you can model the selection of as a 128-bit pseudorandom function, rather than a 128-bit permutation. As a result, you an expect a collision with 50% probability after only different keys are selected.

Note: Your 128-bit randomly generated AES keys already have this probability baked into their selection, but this specific analysis doesn’t really apply for 128-bit keys since AES is a PRP, not a PRF, so there is no “collision” risk. However, you end up at the same upper limit either way.

But 50% isn’t good enough for cryptographic security.

In most real-world systems, we target a collision risk. So that means our safety limit is actually different AES keys before you have to worry about reuse.

This isn’t the same thing as symmetric wear-out (where you need to re-key after a given number of encryptions to prevent nonce reuse). Rather, it means after your entire population has exhausted the safety limit of different AES keys, you have to either accept the risk or stop using AES-GCM.

If you have a billion users (), the safety limit is breached after AES keys per user (approximately 262,000).

“What Good is H Reuse for Attackers if HF differs?”

There are two numbers used in AES-GCM that are derived from the AES key. is used for block multiplication, and (the value of with a counter of 0 from the following diagram) is XORed with the final result to produce the authentication tag.

The arrow highlighted with green is HF.

It’s tempting to think that a reuse of isn’t a concern because will necessarily be randomized, which prevents an attacker from observing when collides. It’s certainly true that the single-block collision risk discussed previously for will almost certainly not also result in a collision for . And since isn’t reused unless a nonce is reused (which also leaks directly), this might seem like a non-issue.

Art by Khia.

However, it’s straightforward to go from a condition of reuse to an adaptive chosen-ciphertext attack.

1. Intercept multiple valid ciphertexts.
   
   • e.g. Multiple JWTs encrypted with {"alg":"A256GCM"}

   
   

2. Use your knowledge of , the ciphertext, and the AAD to calculate the GCM tag up to the final XOR. This, along with the existing authentication tag, will tell you the value of for a given nonce.
3. Calculate a new authentication tag for a chosen ciphertext using and your candidate value, then replay it into the target system.

While the blinding offered by XORing the final output with is sufficient to stop from being leaked directly, the protection is one-way.

Ergo, a collision in is not sufficiently thwarted by .

“How Could the Designers Have Prevented This?”

The core issue here is the AES block size, again.

If we were analyzing a 256-bit block variant of AES, and a congruent GCM construction built atop it, none of what I wrote in this section would apply.

However, the 128-bit block size was a design constraint enforced by NIST in the AES competition. This block size was during an era of 64-bit block ciphers (e.g. Triple-DES and Blowfish), so it was a significant improvement at the time.

NIST’s AES competition also inherited from the US government’s tradition of thinking in terms of “security levels”, which is why there are three different permitted key sizes (128, 192, or 256 bits).

“Why Isn’t This a Vulnerability?”

There’s always a significant gap in security, wherein something isn’t safe to recommend, but also isn’t susceptible to a known practical attack. This gap is important to keep systems secure, even when they aren’t on the bleeding edge of security.

Using 1024-bit RSA is a good example of this: No one has yet, to my knowledge, successfully factored a 1024-bit RSA public key. However, most systems have recommended a minimum 2048-bit for years (and many recommend 3072-bit or 4096-bit today).

With AES-GCM, the expected distance between collisions in is , and finding an untargeted collision requires being able to observe more than different sessions, and somehow distinguish when collides.

As a user, you know that after different keys, you’ve crossed the safety boundary for avoiding collisions. But as an attacker, you need bites at the apple, not . Additionally, you need some sort of oracle or distinguisher for when this happens.

We don’t have that kind of distinguisher available to us today. And even if we had one available, the amount of data you need to search in order for any two users in the population to reuse/collide is challenging to work with. You would need the computational and data storages of a major cloud service provider to even think about pulling the attack off.

Naturally, this isn’t a practical vulnerability. This is just another gripe I have with AES-GCM, as someone who has to work with cryptographic algorithms a lot.

Short Nonces

Although the AES block size is 16 bytes, AES-GCM nonces are only 12 bytes. The latter 4 bytes are dedicated to an internal counter, which is used with AES in Counter Mode to actually encrypt/decrypt messages.

(Yes, you can use arbitrary length nonces with AES-GCM, but if you use nonces longer than 12 bytes, they get hashed into 12 bytes anyway, so it’s not a detail most people should concern themselves with.)

If you ask a cryptographer, “How much can I encrypt safely with AES-GCM?” you’ll get two different answers.

1. Message Length Limit: AES-GCM can be used to encrypt messages up to bytes long, under a given (key, nonce) pair.
2. Number of Messages Limit: If you generate your nonces randomly, you have a 50% chance of a nonce collision after messages.
   However, 50% isn’t conservative enough for most systems, so the safety margin is usually much lower. Cryptographers generally set the key wear-out of AES-GCM at random nonces, which represents a collision probability of one in 4 billion.

These limits are acceptable for session keys for encryption-in-transit, but they impose serious operational limits on application-layer encryption with long-term keys.

Random Key Robustness

Before the advent of AEAD modes, cryptographers used to combine block cipher modes of operation (e.g. AES-CBC, AES-CTR) with a separate message authentication code algorithm (e.g. HMAC, CBC-MAC).

You had to be careful in how you composed your protocol, lest you invite Cryptographic Doom into your life. A lot of developers screwed this up. Standardized AEAD modes promised to make life easier.

Many developers gained their intuition for authenticated encryption modes from protocols like Signal’s (which combines AES-CBC with HMAC-SHA256), and would expect AES-GCM to be a drop-in replacement.

Unfortunately, GMAC doesn’t offer the same security benefits as HMAC: Finding a different (ciphertext, HMAC key) pair that produces the same authentication tag is a hard problem, due to HMAC’s reliance on cryptographic hash functions. This makes HMAC-based constructions “message committing”, which instills Random Key Robustness.

Critically, AES-GCM doesn’t have this property. You can calculate a random (ciphertext, key) pair that collides with a given authentication tag very easily.

This fact prohibits AES-GCM from being considered for use with OPAQUE (which requires RKR), one of the upcoming password-authenticated key exchange algorithms. (Read more about them here.)

Better-Designed Algorithms

You might be thinking, “Okay random furry, if you hate AES-GCM so much, what would you propose we use instead?”

I’m glad you asked!

XChaCha20-Poly1305

For encrypting messages under a long-term key, you can’t really beat XChaCha20-Poly1305.

• ChaCha is a stream cipher based on a 512-bit ARX hash function in counter mode. ChaCha doesn’t use S-Boxes. It’s fast and constant-time without hardware acceleration.
• ChaCha20 is ChaCha with 20 rounds.
• XChaCha nonces are 24 bytes, which allows you to generate them randomly and not worry about a birthday collision until about messages (for the same collision probability as AES-GCM).
• Poly1305 uses different 256-bit key for each (nonce, key) pair and is easier to implement in constant-time than AES-GCM.
• XChaCha20-Poly1305 uses the first 16 bytes of the nonce and the 256-bit key to generate a distinct subkey, and then employs the standard ChaCha20-Poly1305 construction used in TLS today.

For application-layer cryptography, XChaCha20-Poly1305 contains most of the properties you’d want from an authenticated mode.

However, like AES-GCM (and all other Polynomial MACs I’ve heard of), it is not message committing.

The Gimli Permutation

For lightweight cryptography (n.b. important for IoT), the Gimli permutation (e.g. employed in libhydrogen) is an attractive option.

Gimli is a Round 2 candidate in NIST’s Lightweight Cryptography project. The Gimli permutation offers a lot of applications: a hash function, message authentication, encryption, etc.

Critically, it’s possible to construct a message-committing protocol out of Gimli that will hit a lot of the performance goals important to embedded systems.

Closing Remarks

Despite my personal disdain for AES-GCM, if you’re using it as intended by cryptographers, it’s good enough.

Don’t throw AES-GCM out just because of my opinions. It’s very likely the best option you have.

Although I personally dislike AES and GCM, I’m still deeply appreciative of the brilliance and ingenuity that went into both designs.

My desire is for the industry to improve upon AES and GCM in future cipher designs so we can protect more people, from a wider range of threats, in more diverse protocols, at a cheaper CPU/memory/time cost.

We wouldn’t have a secure modern Internet without the work of Vincent Rijmen, Joan Daemen, John Viega, David A. McGrew, and the countless other cryptographers and security researchers who made AES-GCM possible.

Change Log

• 2021-10-26: Added section on H Reuse and Multi-User Security.

https://soatok.blog/2020/05/13/why-aes-gcm-sucks/

#AES #AESGCM #cryptography #GaloisCounterMode #opinion #SecurityGuidance #symmetricCryptography