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What We Do within the /and so forth/shadow – Cryptography with Passwords

What We Do within the /and so forth/shadow – Cryptography with Passwords

2023-01-05 14:11:02

Ever because the well-known “Open Sesame” line from One Thousand and One Nights, humanity was doomed to endure from the scourge of passwords.

Something you know. Password.
Something you have. RSA token.
Something you are. Fingerprint.

Something you pretend to be. Happy.
Courtesy of SwiftOnSecurity

Even in a world the place we use {hardware} tokens with uneven cryptography to obviate the necessity for passwords in modern authentication protocols, we’ll nonetheless want to incorporate “one thing you realize” for authorized and political causes.

In the USA, we’ve got the Fifth Modification to the US Structure, which prevents anybody from being pressured to testify towards oneself. This generally consists of revealing a password, so it’s crucial that passwords stay a obligatory part of some encryption applied sciences to stop prosecutors from side-stepping one’s Fifth Modification rights. (Different international locations have completely different legal guidelines about passwords. I’m not a lawyer.)

If you happen to’ve ever learn something from the EFF, you’re in all probability keenly conscious of this, however the US authorities loves to side-step residents’ privateness rights in a court docket of legislation. They do that not out of direct malice in the direction of civil rights (typically), however moderately as a result of it makes their job simpler. Incentives rule all the things round me.

Thus, even in a passwordless future, anybody who actually cares about civil liberties won’t need to dispense with them totally. Moreover, we’ll need these password-based applied sciences to go the Mud Puddle test, in order that we aren’t counting on massive tech firms to guard us from authorities backdoors.

Given all this, most safety professionals will agree that passwords suck. Not solely are people unhealthy sources of randomness, however we’re terrible at memorizing a sequence of characters or phrases for each software, web site, or working system that calls for a password.

None of what I’ve written thus far is in the slightest degree novel or fascinating. However right here’s a spicy take:

The one factor that sucks worse than passwords is the messaging round password-based cryptographic features.

Password-Based mostly Cryptographic Features

That isn’t a time period of the artwork, by the way in which. I’m form of coining it as a superset that features each Password-Based mostly Key Derivation Features and Password Hashing Features.

You is likely to be questioning, “Aren’t these two the identical factor?” No, they don’t seem to be. I’ll clarify in a second.

The intersection of human-memorable secrets and techniques (passwords) and cryptographic protocols manifests in a number of unnecessary complexity and edge-cases that, with a purpose to sufficiently clarify something conversationally, would require me to sound both drunk or like a blue deck participant in Magic: The Gathering.

To that finish, what I’m calling Password-Based mostly Cryptographic Features (PBCFs) consists of all the following:

  • Password-Hashing Features
  • Password-Based mostly Key Derivation Features
  • Balanced Password Authenticated Key Exchanges
  • Augmented Password Authenticated Key Exchanges
  • Doubly-Augmented Password Authenticated Key Exchanges

If you happen to tried to strategy categorization beginning with merely “Key Derivation Features”, you’d shortly run into an issue: What about HKDF? Or any of the NIST SP 800-108 KDFs for that matter?

If you happen to tighten it to “Password-Based mostly KDFs” or “Key-stretching features”, that doesn’t embrace bcrypt. Bcrypt is a password hashing perform, but it surely’s not appropriate for deriving secret keys. I’ve mentioned these nuances previously.

After which you might have some password KDF and/or hashing algorithms which can be memory-hard, some which can be cache-hard.

After which some Password Authenticated Key Exchanges (PAKEs) are quantum-annoying, whereas others aren’t.

To make heads or tails of the completely different algorithms, their properties, and when and the place you need to use them, you’d both must safe postdoc funding for cryptography analysis or spend a number of time studying and watching passwords-focused convention talks.

So let’s discuss these completely different algorithms, why they exist to start with, and a few of their technical particulars.

Why Does Any of This Matter?

The intersection of passwords and cryptography is without doubt one of the foundations of contemporary society, and one that almost all Web customers expertise in all places they go.

You’ll know you might have succeeded in designing a cryptographic algorithm when one of the simplest ways to assault it’s to attempt each doable key. That is known as an exhaustive search, or a brute-force assault, relying on the disposition of the creator.

Keep in mind earlier after I stated passwords suck as a result of people are unhealthy at creating or remembering robust, distinctive passwords for each web site they go to?

Effectively, it seems, that some passwords are extremely common. And even worse, individuals who select widespread passwords are inclined to reuse them in all places.

This introduced a problem to early net purposes: With the intention to have authenticated customers, it’s worthwhile to gather a password from the person and test it on subsequent visits. If you happen to ever get hacked, then it’s probably that your entire customers can be impacted on different web sites they used the identical passwords for.

Together with their financial institution accounts.

So the problem for any password-based scheme is just acknowledged: How are you going to safely authenticate customers based mostly on a secret they know?

Enter: Hashing

Storing a hash of a password is an apparent answer to this predicament. Early options concerned using the user’s password as an encryption key, moderately than constructing atop cryptographic hash features.

Nevertheless, it’s necessary to not name it “password encryption”.

The rationale isn’t merely pedantic; it’s meant to stop a catastrophe from repeating: Adobe famously encrypted passwords with Triple-DES instead of hashing them.

In early UNIX-based working programs, your password hashes have been saved in a file known as /and so forth/passwd, together with different person account information. Nowadays, your precise password hashes are stored in a second file, /etc/shadow, which is just readable by root.

Sadly, the instrument used to create password hashes was known as crypt, so the “encryption” lingo caught.

When Hashing Isn’t Sufficient

Though encrypting hashes is unhealthy, utilizing a quick cryptographic hash perform (e.g. SHA256 or BLAKE2) can also be unhealthy.

LinkedIn realized this lesson the onerous method in 2012, when an attacker leaked 117 million users’ hashed passwords. It seems, they used SHA1 as their password hashing perform.

Hash features are deterministic: If you happen to feed them the identical enter, you’ll at all times get the identical output.

When your password hashing technique is just “simply use SHA1”, two customers with the identical password may have an equivalent password hash.

Persons are unhealthy at creating, or remembering, unpredictable passwords.

While you mix these observations, there are some extremely obvious candidates (123456, password, and so forth.) to prioritize when guessing.

Moreover, you can precompute these hashes as soon as and construct a reverse index of the passwords that hash to a particular output. That is known as a rainbow desk.

Not like most of symmetric cryptography, the place the aim ends at forcing the attacker to carry out an exhaustive brute-force search of each doable key, password-based cryptography has to go the additional mile to stop weak secrets and techniques from being compromised; a really tall order for anybody to cope with.

In direction of Trendy Password Hashing

None of this was a shock to safety consultants in 2012. There have been a pair typically recognized greatest practices since I first realized programming within the 2000s:

  • Salt your passwords (to mitigate rainbow tables)
  • Use an iterated hashing scheme, moderately than a quick hash (to make every step of an exhaustive search slower)

PBKDF2, the primary extensively used password hashing and key derivation perform, did precisely that:

  • PBKDF2 was designed to assist randomly-generated per-user salts.
  • It used HMAC in a loop to drive attackers to spend additional CPU cycles per guess. If an attacker may guess 10 million passwords per second towards SHA-256, then utilizing 100,000 iterations of PBKDF2 slowed them right down to lower than 100 guesses per second (as a result of HMAC calling the hash perform twice).

And that may sound like the top of the story (“PBKDF2 wins”), however the password cracking group is extraordinarily intelligent, so it’s solely simply begun.

Parallel Assaults and GPUs

Since your CPU can solely guess just a few hashes per second, PBKDF2 is a thorny drawback to cope with.

Nevertheless, there’s a straightforward method for attackers to make use of commodity {hardware} to bypass this limitation: Graphics playing cards are specifically designed to carry out a number of low-memory calculations in parallel.

If you happen to can write your password cracking code to leverage the advantages of GPUs as an alternative of CPUs, then PBKDF2 turns into simple potatoes.

The opposite safe password hashing algorithm in use on the time, bcrypt, had solely a linear enchancment over PBKDF2’s safety towards GPU assaults.

Reminiscence-Laborious Password Hashing Algorithms

In 2009, Colin Percival proposed scrypt to mitigate this threat. Scrypt (pronounced “ess crypt”) builds atop PBKDF2-SHA256 by hashing psuedorandom areas of reminiscence with Salsa20/8 (therefore the S in Scrypt) in a method that makes it tough to precompute.

Scrypt hashes require massive quantities of reminiscence to compute (at the very least 16 megabytes, within the beneficial minimal configuration, versus the few kilobytes of incumbent password hashes).

Whereas GPUs (and FPGAs, and ASICs, and …) are nice for cracking password hashes that use CPU-bounded algorithms, algorithms that entry massive quantities of reminiscence are tough to assault successfully.

It’s nonetheless doable for intelligent programmers to work round this reminiscence/bandwidth limitation, however to take action, you have to compute extra operations, which makes it not worthwhile.

Cryptographers and the password-cracking group name this costly time-memory trade-off reminiscence hardness. In 2016, it was decided that scrypt is maximally memory-hard.

Password Hashing Competitors

The Password Hashing Competition (PHC) was kicked off by JP Aumasson in 2012 to develop a brand new normal for password hashing and password-based key derivation.

In 2015, they chose Argon2 as its advice, with 4 finalists receiving particular recognition (Catena, Lyra2, Makwa, and yescrypt–which is predicated on scrypt).


Within the years because the PHC concluded, the advances in password cracking methods haven’t slowed down.

One of many PHC judges lately proposed a brand new algorithm known as bscrypt which purports a property known as “cache onerous” moderately than “reminiscence onerous”. The reasoning is that, for shorter run instances, reminiscence bandwidth and small CPU caches is a tighter bottleneck than total reminiscence necessities.

The truth is, there’s an Argon2 variant (Argon2ds) which affords cache-hardness.

Two Laborious Selections

So which of the 2 do you have to care about, as a defender?

If you happen to’re validating password hashes in an internet service, a cache-hard algorithm would possibly make extra sense. You’re incentivized to have shorter server-side run instances to keep away from DoS assaults, so the advantages of cache-hardness appear extra impactful than memory-hardness.

If you happen to’re deriving a delicate cryptography key from a password and might afford to take a number of seconds of wall-clock time, a memory-hard algorithm is more likely to be a greater match in your risk mannequin.

(Or, like, run each a cache-hard and memory-hard algorithm and use a quick KDF, corresponding to HKDF, to combine the 2 into your last cryptography key.)

In fact, the story doesn’t finish right here. Password Hashing and Password-Based mostly Key Derivation continues to mature because the password cracking group discovers new assaults and engineers defenses towards them.

A Unusual Recreation; The Solely Profitable Transfer is to PAKE

Password hashing is a defense-in-depth towards a system compromise that permits attackers to carry out offline assaults towards a cryptographic output to find out a person’s password.

Nevertheless, for a lot of purposes, the larger query is, “Why even play this sport within the first place?”

Password-Authenticated Key Exchanges

A password authenticated key trade (PAKE) algorithm is an interactive protocol to determine keys based mostly on at the very least one social gathering’s data of a password.

PAKEs are what allow you to log into encrypted WiFi connections and encrypt your visitors. PAKEs stop you from having to disclose the password (or a password-equivalent worth, corresponding to a password hash) to the opposite social gathering.

Though there are a number of proposed PAKE algorithms, the one which most individuals applied was SRP (“Safe Distant Password”), which was intuitively rather a lot like Diffie-Hellman but in addition not Diffie-Hellman (since SRP used addition).

For a very good teardown on SRP, Matthew Green’s blog is highly recommended.

There are just a few real-world cryptography issues with utilizing SRP:

  1. You’ll want to use a particular form of prime quantity in your protocol. The usual Diffie-Hellman moduli are not suitable for SRP; you desire a protected prime (i.e. a lot of the shape N = 2q + 1, the place q can also be prime).
  2. One of many steps in SRP, client-side, is to compute A = g^a (mod N). Right here, A is a public worth whereas a is a secret (normally the SHA1 hash of the username and pasword).

    In case your software program implementation of modular exponentiation (a^x mod P) isn’t constant-time, you leak a, which is a password-equivalent worth.

Moreover, it’s not doable to make use of SRP with elliptic curve teams. (Matthew Inexperienced’s put up I linked above covers this intimately!)

Thus, SRP is mostly thought-about to be deprecated by safety consultants, in favor of different PAKEs.


As early as IETF 104, the Crypto Discussion board Analysis Group (CFRG) started exploring completely different PAKE algorithms to pick for standardization.

One of many motivators for this work is that the WiFi alliance had shoehorned a brand new PAKE known as Dragonfly into their WPA3, which turned out to be badly designed.

The CFRG’s candidate algorithms and critiques have been publicly tracked on GitHub, for those who’re curious.

TL;DR – They settled on recommending OPAQUE as an augmented PAKE and CPace as a balanced PAKE.

Sc00bz has carried out a number of talks at safety conferences over time to speak about PAKEs:

Quantum Annoyance

The PAKEs we’ve mentioned concerned a cyclic group (and the newer ones concerned an elliptic curve group). The safety of those schemes relies on the hardness of a discrete logarithm drawback.

If a cryptography related quantum pc (CRQC) is developed, discrete logarithm issues will stop to be onerous.

Some PAKEs disintegrate the second a discrete log is solvable. That is par for the course for Diffie-Hellman and elliptic curve cryptography.

Others require an attacker to resolve a discrete log for each guess in an offline assault (after capturing a profitable trade). This makes them annoying for quantum attackers.

Whereas they don’t present absolute safety like post-quantum cryptography, they do make attackers armed with a CRQC work tougher.

OPAQUE isn’t quantum annoying. Merely observe all the packets from making an internet guess, resolve the DLP offline, and also you’re again to the realm of classical offline guessing.

The State of the Artwork

At this level, it’s possible you’ll really feel considerably overwhelmed by all of this data. It’s very tempting to simplify all of this historic context and technical element.

You is likely to be telling your self, “Okay, Scrypt, Argon2, CPace, OPAQUE. Bought it. That’s all I would like to recollect. All the pieces else is questionable at greatest. Ask a cryptographer. I’m bailing out, yo!”

See Also

However the story will get worse on two fronts: Actual-world operational necessities, and compliance.

Your Arms Are Tied, Now Swim

If you happen to’re promoting a services or products to the US authorities that makes use of cryptography, it’s worthwhile to first clear a naked minimal bar known as FIPS 140.

FIPS 140 is opinionated about which algorithms you utilize. For password hashing and password-based key derivation, FIPS defers to NIST SP 800-209, which suggests you’re solely permitted to make use of PBKDF2 in any FIPS modules (with a SHA2- household hash perform).

So all the details about memory-hard and cache-hard password hashing algorithms? That is ineffective for you for those who ever attempt to promote to the US authorities.

An open query is whether or not Scrypt is FIPSable as a result of it constructing atop PBKDF2. To be blunt: I’m undecided. Ask a NIST Cryptographic Module Validation Program lab for his or her opinion.

Within the realm of PAKEs, each CPace and OPAQUE are frameworks that can be utilized with a number of elliptic curve teams.

Each frameworks assist NIST P-256, however CPace helps X25519 and OPAQUE helps Ristretto255; these are at present not FIPSable curves.

“I don’t care about FIPS. Argon2 all of the issues!”

JavaScript runtimes don’t present a built-in Argon2 implementation. This poses a number of challenges.

  • Do you care about iOS customers? Lockdown mode prevents you from utilizing WebAssembly, even in a browser extension.
  • Making an attempt to polyfill scrypt or Argon2 in a scripting language is a depressing expertise. We’re speaking quadratic efficiency penalties right here. A number of minutes of CPU time to calculate a hash that’s far too weak to be acceptable in any context.

Consequently, not a single password supervisor I’ve evaluated that gives a browser extension makes use of a memory-hard algorithm for deriving encryption keys.

Replace: I’ve been informed Dashlane uses Argon2.

This Is Irritating

Once I write about cryptography, my aim is at all times to be clear, concise, and useful. I would like whoever reads my writing to, no matter their stage of experience, stroll away extra comfy with the subject material.

At minimal, I would like you to have the ability to intuit when it’s worthwhile to ask an professional for assist, and have a barely higher understanding of how you can phrase your inquiries to get the reply you want. In a great world, you’d even be capable to spot the identical form of weaknesses I do in cryptography designs and implementations after studying sufficient of this weblog.

I can’t do this with password-based cryptography. The use-cases and risk fashions are too assorted to make a clear-cut advice, and it’s too difficult to parcel out in a method that doesn’t really feel reductive or barely contradictory. This results in too many caveats or nook instances.

Passwords suck.

If you happen to ask a password cracking professional and describe your use case, you’ll probably get an opinionated and definitive reply. However each time I’ve requested typically about this topic, and not using a particular use case in thoughts, I received an opinionated reply adopted by a protracted chain of caveats and alternate options.

With that in thoughts, right here’s just a few obscure tips which can be up-to-date as of the top of 2022.

Suggestions for Password-Based mostly Cryptography in 2023

Password Hashing

If you happen to’re authenticating customers in an internet service (storing the hashes in a database), use any of the next algorithms:

  • bcrypt with a price issue applicable to take about 100 milliseconds to compute in your server {hardware} (sometimes at the very least 12)
  • scrypt with N = 32768, r = 8, p = 1 and a random salt at the very least 128 bits in size (256 most popular)
  • Argon2id with a reminiscence price of 64 MiB, ops price of three, and parallelism of 1

If you happen to’re pressured to make use of PBKDF2 for no matter dumb motive, the parameters you need are at least:

  • SHA-512 with 210,000 rounds (most popular)
  • SHA-256 with 600,000 rounds
  • SHA-1 (for those who should) with 1,300,000 rounds

These numbers are based mostly on constraining attackers to lower than 10,000 hashes per second, per GPU.

I’m not at present recommending any algorithms intentionally designed for cache-hardness as a result of they want additional evaluation from different cryptographers. (Bcrypt is minimally cache-hard, however that wasn’t a acknowledged design aim.)

I didn’t consider the opposite PHC finalists nor different designs (Balloon hashing, Ball and Chain, and so forth.). Ask your cryptographer if these are applicable as an alternative.

Password-Based mostly Key Derivation

If you happen to’re deriving an encryption key from a password, use any of the next algorithms:

  • scrypt with N = 1048576, r = 8, p = 1 and a random salt at the very least 128 bits in size (256 most popular)
  • Argon2id with a reminiscence price of 1024 MiB, ops price of 4, and parallelism of 1

If you happen to’re pressured to make use of PBKDF2 for no matter dumb motive, the parameters you need ought to goal between 1 and 10 seconds on the defender’s {hardware}. If that is one way or the other slower than the numbers given for password hashing above, go together with the password hashing benchmarks as an alternative.

Right here’s a dumb PHP script you need to use to shortly discover some goal numbers.

/* Dumb PBKDF2 benchmarking script by Soatok. 2022-12-29 */

$salt = random_bytes(32);
$password = 'right horse battery staple';
$c = '';
$begin = $finish = microtime(true);

foreach(['sha1', 'sha256', 'sha512'] as $alg) {
	foreach ([
		1 << 14,
		1 << 15,
		1 << 16,
		1 << 17,
		1 << 18,
		1 << 19,
		1 << 20,
		1 << 21,
		1 << 22,
		1 << 23,
		1 << 24,
		1 << 25,
	] as $n) {
	   $begin = microtime(true);
	   $c ^= hash_pbkdf2($alg, $password, $salt, $n, 32, true);
	   $finish = microtime(true);
	   $time = $finish - $begin;
	   echo str_pad($n, 12, ' ', STR_PAD_LEFT), 
           " iterations ({$alg}) -> t",
	   if ($time > 5.5) {
		   echo PHP_EOL;

On my laptop computer, focusing on 5.0 seconds means at the very least 4,000,000 rounds of PBKDF2 with SHA1, SHA256, or SHA512 (with SHA256 coming nearer to five,000,000).

If you happen to’re aiming for lower than 1,000 hashes per second per GPU, towards an attacker armed with an RTX 4090:

  • SHA-512 with 3,120,900 iterations (most popular)
  • SHA256 with 8,900,000 iterations
  • SHA-1 with 20,000,000 iterations

Sc00bz tells me that this technology of GPU has higher efficiency/price than earlier generations (which had seen diminishing returns), however requires 1.5x the facility, 1.78x the value, and 2x the bodily area. Sc00bz refers to this as “1.5 GPUs”.

If you happen to modify for these elements, your last PBKDF2 goal turns into:

  • SHA-512 with 2,100,000 iterations (most popular)
  • SHA-256 with 6,000,000 iterations
  • SHA-1 with 13,000,000 iterations

Password Authenticated Key Exchanges

In a client-server mannequin, the place the server isn’t meant to see password-equivalent information, you need an augmented PAKE (or maybe a doubly-augmented PAKE).

You’re overwhelmingly extra more likely to discover OPAQUE assist within the fast future, because of the path the IETF CFRG is shifting at present.

In a extra peer-to-peer mannequin, you desire a balanced PAKE. CPace is the most effective sport on the town.

Don’t use SRP if you can help it.

If you happen to can’t assist it, ensure you use one of the groups defined in RFC 5054, moderately than a generic Diffie-Hellman group. You’ll additionally need an professional to evaluate your implementation to ensure your BigInt library isn’t leaking your customers’ non-public exponents.

Additionally, be at liberty to deviate from SHA1 for calculating the non-public exponent from their username and password. SHA1 sucks. Nothing is stopping you from utilizing a password KDF (or, at worst, SHA256) right here, so long as you achieve this persistently.

(However as at all times, ask your cryptography professional first.)


Password-Based mostly Cryptography is a large number.

If you happen to’re not conscious of the historical past of the sphere and the technical particulars that went into the varied cryptographic algorithms that consultants advocate at present, it’s very simple to say one thing flawed that sounds right to an untrained ear.

On the finish of the day, the most important threat you face with password-based cryptography is not utilizing an appropriate algorithm within the first place, moderately than utilizing a much less optimum algorithm.

Specialists have good causes to hate PBDKF2 (sluggish for defenders, quick for attackers) and SRP (we’ve got higher choices at present, which additionally include precise safety proofs), however they definitely hate unsalted SHA1 and Triple-DES extra.

My solely actual contribution to this matter is an effort to make it simpler to speak about to non-experts by providing a brand new time period for the superset of all of those password-based algorithms: Password-Based mostly Cryptographic Features.

Lastly, the password cracking group is nice. There are a number of good and pleasant folks concerned, they usually’re all working to make this drawback simpler to get proper. If you happen to’re undecided the place to begin, take a look at PasswordsCon.

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