Formally Verified Cryptographic Primitive Implementations

Greg KH greg at
Fri Jan 19 09:29:57 CET 2018

On Thu, Jan 18, 2018 at 04:42:10PM +0100, Jason A. Donenfeld wrote:
> Hi folks,
> Writing crypto code is hard and sometimes scary. Especially on things
> like elliptic curves and big number arithmetic, subtle but critical
> bugs often sit around undetected for years. For this reason, I've been
> working with some researchers at INRIA on using a formally verified
> Curve25519 implementation inside WireGuard. This last week I had the
> pleasure of talking with INRIA researchers and MIT researchers about
> related efforts to automatically generate C implementations of
> elliptic curve scalar multiplication from formal models. These models
> produce proofs of correctness alongside machine-generated C. I've
> taken these implementations and integrated them into WireGuard.
> For 64-bit Curve25519 multiplication, we're using HACL* [1], which has
> specifications written in F* [2] and passes them through KreMLin [3]
> for C generation. You can read the INRIA researchers paper [4] for
> more information. Not only is this formally verified, but it is also
> faster than our previous implementation (agl's donna-64). Mozilla's
> NSS is doing something similar with HACL*.
> For 32-bit Curve25519 multiplication, we're using Fiat-Crypto [5],
> which has specifications written in the abstract proof language Coq
> [6], which also generates C code. These MIT researchers also have a
> paper available [7]. This is faster than what we're using before
> (agl's donna-32) and uses much less stack space, which means we no
> longer need to kmalloc on platforms without separate irq stacks, which
> is a nice boost. Google's BoringSSL is doing something similar with
> Fiat-Crypto.
> Note that not _all_ of our cryptographic primitives are verified.
> We're starting with replacing these two C implementations with
> formally verified ones. Over time, we'll gradually replace remaining
> existing implementations with formally verified counterparts. But
> certainly, as this research is state of the art and quite new, the
> work here is in the evolutionary category.
> Some speed results using my kbench9000 software [8] comparing the new
> (top two lines) and old (bottom two lines), with turbo turned on:
> Xeon E3-1505M v5 [9] -- 14nm Skylake Laptop
> hacl64: 109783 cycles per call
> fiat32: 232710 cycles per call
> donna64: 121794 cycles per call
> donna32: 411588 cycles per call
> Core i5-5200U [10] -- 14 nm Broadwell Laptop
> hacl64: 127001 cycles per call
> fiat32: 253234 cycles per call
> donna64: 137200 cycles per call
> donna32: 438816 cycles per call
> I've updated the WireGuard formal verification site [11] to contain
> this information. In a few days I expect to update this again with
> some further exciting results in the same formal verification genre.
> Let me know if you have any questions.

No questions, just a general, "Wow, this is great work!"

It's wonderful to see this happen, thanks so much for pushing this

greg k-h

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