@ Loup's Impossible? Like that would stop me.

July 2020

Cryptography is not Magic

Don’t roll your own crypto.
Broken crypto often looks like it works.
The best way to build crypto is to learn how to break it.
Use existing, vetted, well reviewed libraries.
Leave it to the experts.

Infosec people and their followers.

The running theme seems to be that cryptography is a kind of Dark Magic, best left to anointed High Priests. Us mere Mortals cannot hope to wield it safely without first becoming one of those vaunted Experts — a futile endeavour for those of us who know their place.

While being a good first order approximation, that kind of gate keeping is problematic on a number of levels. First, some people back in the real world have needs that current crypto systems don’t always fill. Insulting them with “you don’t know what you are doing” does not help. Second, it has a couple perverse effects:

I would like to advocate a different approach. Cryptography has rules, which are both simpler and more fundamental than we might think. We could tell people what they don’t know, and give them some pointers: introductory books or courses, or specific words and concepts. Here, I will outline what you need to look for before you roll your own crypto system. I’ve identified 3 broad categories: implementing crypto, designing protocols, and designing primitives.

Note: this is an opinion piece, so let me clarify where I came from. I program professionally since 2007, and started to teach myself cryptography 4 years ago. I wrote a crypto library, whose recent audit uncovered no major flaw.

Implementing crypto

Perhaps surprisingly, implementing cryptographic primitives & protocols requires little cryptographic knowledge. Choosing what to implement is more delicate (you need to know the state of the art), but once you’ve made your choice, your only worries are side channels and correctness.

Side channels have one rule: don’t let any data flow from secrets to that channel. Interesting side channels include timings, energy consumption, electromagnetic emissions… Most can be ignored most of the time (energy consumption for instance requires physical access), except timings. Never ignore timings, they’re part of most threat models.

On most CPUs, the timing side channel can be eliminated by removing all secret dependent branches and all secret dependent indices. Some CPUs also have variable time arithmetic operations. Watch out for multiplications and shifts by variable amounts in particular.

Also be careful around compilers and interpreters. No mainstream language specifies how to make constant time code, so your tools could insert secret dependent branches where the source code had none. High level languages in particular tend to have variable time arithmetic. In practice, low level languages like C are fairly reasonable, but I’ve seen exceptions.

Note that some primitives are more amenable to constant time software implementations than others: Chacha20 is naturally immune to timing attacks on most platforms, while AES requires special care if you don’t have hardware support.

Then we have correctness. The slightest error may throw cryptographic guarantees out the window, so we cannot tolerate errors. Your code must be bug free, period. It’s not easy, but it is simple: it’s all about tests and proofs.

Correctness of ciphers and hashes

Ciphers and hashes are fairly easy to test. At their core, they are about taking an input, and mangle it so thoroughly that the slightest change in the input will completely garble the output. In practice, the slightest programming error tends to change the end result completely.

All you have to do is compare the output of your primitive with a reference implementation or test vectors. Ideally, do that for all possible input & output lengths. Including zero (empty inputs). Practically, you can stop at a couple iterations of your biggest internal loop, to be sure you hit all data paths.

If you have an init-update-final interface, try all possible cut-off points in the updates to make sure you get the same results. I’ve caught several bugs that way.

Correctness of modular arithmetic

Modular arithmetic (polynomial hashes, elliptic curves…) is more delicate. Now we’re adding or multiplying big numbers (130 bits, 255 bits…) that do not fit in a single machine register. Many libraries don’t run in constant time, and custom code is often faster. So you end up dividing those big numbers in several limbs, which can fit in a single machine register.

(You can think of a limb as a huge digit: instead of working in base 10, we can work in base 2³², and store the corresponding “digits” in 32-bit registers.)

Once you’ve applied the precautions used for ciphers and hashes, the biggest trap is limb overflow. Not a problem with naive implementations, but there is one dangerous trick that often drastically improves performance: delayed carry propagation. Make your limbs smaller than the range of the registers they are stored into (26 bits limbs with 32 bits registers for instance), so that they can temporarily exceed their normal range.

With this trick, some overflow bugs happen rarely enough that random tests will not catch them. There are two ways to address the problem: either don’t delay carry propagation to begin with (it’s safest), or write a mathematical proof that shows your algorithm never triggers an overflow. Ideally you’d have a machine verify that proof.

Correctness of elliptic curves

Elliptic curves have their own traps. If you have explicit formulas telling you what arithmetic operation to perform in what order, no problem (beyond comparing to a reference implementation and limb overflow). If you want to be clever, make sure you know exactly what you are doing. If you see some mathematical term you haven’t seen before (like “birational equivalence”), don’t guess, look it up. I broke that rule once, and it wasn’t pretty.

Also note that Elliptic curves often require conditional selection, swapping, or even lookups. There are techniques to do that in constant time. Use them. Failing to do so has enabled actual exploits.

Correctness of constructions & Protocols

Constructions and protocols are generally much simpler to implement than their underlying primitives. The same precautions apply, with a couple differences:

Designing protocols

That’s where things become interesting. Where implementing crypto was mostly tedious, designing protocols is delicate. One is not necessarily harder than the other, but they’re very different.

This is no longer about faithfully implementing an unambiguous specification. This is about addressing a threat model. This means being aware of what you’re up against, addressing that threat, and proving that you have done so. On top of that, the protocol should allow, even encourage, good APIs that are hard to misuse.

Threat model

We need to realistically and precisely define the capabilities of the adversary. A typical threat model is the untrusted network, where the adversary can basically do anything: watch messages, intercept messages, forge messages, replay messages…

Some adversaries can also steal your keys. Maybe the police comes with a warrant. Maybe your computer is being hacked. You can limit the damage with forward secrecy (messages sent before the key was stolen can’t be decrypted), and key compromise impersonation resistance (where stealing your keys don’t allow the attacker to impersonate others when they are talking to you).

Yet another threat is meta data analysis. Maybe you want to hide your identity to outsiders. Some protocols achieve some measure of anonymity, where it is hard for the attacker to determine who is talking to whom.

Or maybe you fear traffic analysis, where the size and timings of the messages reveal too much about the content. You could mitigate that by padding your messages to some standard size, or even send a constant stream of data, and fill the bandwidth you don’t use with noise.


Once you know your threat model, you need to demonstrate that your protocol addresses it. For instance, when the adversary is an untrusted network, you need IND-CCA2 (indistinguishability under adaptive chosen ciphertext attack). It’s a formalisation of what you need to combat active adversaries (man in the middle). It’s defined thus:

Let’s try an example with passive adversaries, for which we only need IND-CPA: independence under chosen plaintext attack. It’s the same as IND-CCA2, except we don’t have the decryption oracle.

Alice needs to send messages to Bob, using a shared secret key K0, and a stream cipher Stream that takes a key as input, and outputs an arbitrarily long key stream. (Real stream ciphers also have a nonce, but we’ll make do without one for the sake of the exercise.) To send her messages, Alice will use key erasure, or ratchet:

K1, S1 = Stream(K0)
msg1   = plaintext XOR S1
K2, S2 = Stream(K1)
msg2   = plaintext XOR S2
K3, S3 = Stream(K2)
msg3   = plaintext XOR S3

To send a message, we first split the key stream in two parts: a new encryption key, and a data stream. Note that K1 is the first bytes of Stream(K0), and S1 is the rest, so they’re independent from each other. Same for K2 and S2, etc. We can’t break that one with the encryption oracle alone (IND-CPA). Here’s why:

Not the most rigorous proof. That will do for this simple construction under this simple threat model, but a more complex protocol may not tolerate as much hand waving. And if you want a machine to check your proof (a good thing to strive for), it’ll have to be perfect.

Another limitation is my choice of the symbolic model: I am assuming the stream cipher is unbreakable, and will always be indistinguishable from a true random number generator to anyone who doesn’t know the key. Works well enough for most purposes, but keep in mind that real cryptographic primitives aren’t perfect: they can’t generate a genuinely infinite stream without repeating themselves, and a finite amount of computing work is enough to break them. Those limits are high enough to be ignored in many cases, but depending on the primitive you use, and what you use them for, they may not be.

The biggest limitation of all of course is that we only proved IND-CPA here. This construction is only immune to passive attackers, that only listen and never talk. What we really want is to protect against active attackers, that could perform a full Man in the Middle attack. A chosen ciphertext attack easily destroys our construction:

We basically tricked the oracle into decrypting the challenge ciphertext, without breaking the rules: we didn’t directly asked to decrypt c, we only took advantage of ciphertext malleability to get around the restriction. To avoid this, we need authentication, which I’ll leave as an exercise to the reader for brevity’s sake.


The proper way to achieve IND-CCA2 is to first encrypt the plaintext, then compute an authentication tag over the ciphertext. Encrypt-then-mac. We could instead authenticate the plaintext, and only then encrypt the whole thing (including the authentication tag). Mac-then-encrypt. It can be done correctly, and we can even prove IND-CCA2. It is also a bad idea.

Ideally, we want the recipient to verify first. This has some advantages:

What your users need is authenticated encryption, where decryption either successfully decrypts the message, or does nothing at all. That’s the only way you can be sure no information will leak because of corrupted messages.

In fact, “success or nothing” is a rule I try generalise to all my APIs: check the inputs, then act on them. If the inputs are wrong, don’t do anything, just return an error to the caller.

Designing primitives

That’s the tough one. There’s generally no way to prove that a given primitive is indeed as secure as it claims to be. There’s an obvious tension between performance and security, and designing something as secure and as fast as the state of the art is not trivial to say the least.

I have also no experience in the domain. I can only give a few pointers, that will hopefully make you realise what it means to stare into the abyss.

Symmetric crypto

All ciphers and hashes I know are designed around a core permutation: mangling the hell out of a block of data to produce a pseudo-random result:

Some permutations (Keccak, Xoodoo, Gimli…) are designed to rule them all, but they don’t have to. The most popular ciphers and hashes have their own permutation, tailored just for them. Chacha20’s permutation for instance produces zero when the input is all zero. Not very random, but we don’t care, because the input is never zero: part of it is a constant, that aims to “break symmetry”.

Speaking of which: before you make a serious attempt at designing your hash, cipher, or permutation, there are some terms and concepts you probably should be deeply familiar with:

Those are an incomplete list of terms I stumbled upon. My hope is by the time you get familiar with those, you’ll have a better idea of what else you should study.

Polynomial hashes

The primary use case of of polynomial hashes is message authentication codes. They’re not as easy to use as regular hashes, but they’re very fast, and their security properties are provable. If you’re going to invent one, you need to produce a proper security reduction (a mathematical proof of how secure it is, given some assumptions).

Also note that Poly1305 and GHASH already cover a lot of ground. Poly1305 is designed to allow simple and efficient software implementations, while GHASH is very hardware friendly. One of them may already offer what you need.

Elliptic curves

The modern way to use the difficulty of discrete logarithm. Unlike other primitives, I feel like elliptic curves are found more than they are invented. Granted, they’re not trivial. The maths involved are definitely intimidating, and a single mistake could destroy security.

One way to find a curve is to target a security level, choose a prime that matches that security level (generally twice as big), and follow the SafeCurves recommendations. The first curve you find is almost certainly the one you want.

If you want to play with extension fields instead of prime fields, I can only point out that some extension fields are more efficient on tiny embedded targets, and the security literature around binary extension fields is less stable than it is for prime fields.

I also strongly advise sticking to Montgomery or (twisted) Edwards curves. They are relatively simple, and they’re fast. They don’t have a prime order, but that can be worked around, or even solved entirely. Avoid short Weierstraß curves. They’re not broken, but they are slower and harder to implement securely.

Post quantum cryptography

I know even less than Jon Snow. Can’t help you, sorry.


I won’t sugar coat it, rolling your own crypto is not easy. Mistakes are easy to make, and the stakes are often high — getting it wrong can even get people killed. Don’t rush it, and if you can, seek guidance and feedback. Some communities are very welcoming.

Still, we can teach ourselves. The rules may not be easy to follow, but they are simple:

Discuss on r/crypto, r/programming, Lobsters, Hacker News.