trezor-firmware/curve25519-donna

curve25519 is an elliptic curve, developed by Dan Bernstein, for fast Diffie-Hellman key agreement. DJB's original implementation was written in a language of his own devising called qhasm. The original qhasm source isn't available, only the x86 32-bit assembly output.

This project provides performant, portable 32-bit & 64-bit implementations. All implementations are of course constant time in regard to secret data.

Performance

Compilers versions are gcc 4.6.3, icc 13.1.1, clang 3.4-1~exp1.

Counts are in thousands of cycles.

Note that SSE2 performance may be less impressive on AMD & older CPUs with slower SSE ops!

E5200 @ 2.5ghz, march=core2

Version	gcc	icc	clang
64-bit SSE2	278k	265k	302k
64-bit	273k	271k	377k
32-bit SSE2	304k	289k	317k
32-bit	1417k	845k	981k

E3-1270 @ 3.4ghz, march=corei7-avx

Version	gcc	icc	clang
64-bit	201k	192k	233k
64-bit SSE2	201k	201k	261k
32-bit SSE2	238k	225k	250k
32-bit	1293k	822k	848k

Compilation

No configuration is needed.

32-bit

gcc curve25519.c -m32 -O3 -c

64-bit

gcc curve25519.c -m64 -O3 -c

SSE2

gcc curve25519.c -m32 -O3 -c -DCURVE25519_SSE2 -msse2
gcc curve25519.c -m64 -O3 -c -DCURVE25519_SSE2

clang, icc, and msvc are also supported

Named Versions

Define CURVE25519_SUFFIX to append a suffix to public functions, e.g. -DCURVE25519_SUFFIX=_sse2 to create curve25519_donna_sse2 and curve25519_donna_basepoint_sse2.

Usage

To use the code, link against curve25519.o and:

#include "curve25519.h"

To generate a private/secret key, generate 32 cryptographically random bytes:

curve25519_key sk;
randombytes(sk, sizeof(curve25519_key));

Manual clamping is not needed, and it is actually not possible to use unclamped keys due to the code taking advantage of the clamped bits internally.

To generate the public key from the private/secret key:

curve25519_key pk;
curve25519_donna_basepoint(pk, sk);

To generate a shared key with your private/secret key and someone elses public key:

curve25519_key shared;
curve25519_donna(shared, mysk, yourpk);

And hash shared with a cryptographic hash before using, or e.g. pass shared through HSalsa20/HChacha as NaCl does.

Testing

Fuzzing against a reference implemenation is now available. See fuzz/README.

Building curve25519.c and linking with test.c will run basic sanity tests and benchmark curve25519_donna.

Papers

djb's curve25519 paper

License

Public Domain, or MIT