trezor-firmware/ed25519-donna

ed25519 is an Elliptic Curve Digital Signature Algortithm, developed by Dan Bernstein, Niels Duif, Tanja Lange, Peter Schwabe, and Bo-Yin Yang.

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

Performance

SSE2 code and benches have not been updated yet. I will do those next.

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

Batch verification time (in parentheses) is the average time per 1 verification in a batch of 64 signatures. Counts are in thousands of cycles.

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

Visual Studio performance for ge25519_scalarmult_base_niels will lag behind a bit until optimized assembler versions of ge25519_scalarmult_base_choose_niels are made.

E5200 @ 2.5ghz, march=core2

Implementation	Sign	gcc	icc	clang	Verify	gcc	icc	clang
ed25519-donna 64bit		100k	110k	137k		327k (144k)	342k (163k)	422k (194k)
amd64-64-24k		102k				355k (158k)
ed25519-donna-sse2 64bit		108k	111k	116k		353k (155k)	345k (154k)	360k (161k)
amd64-51-32k		116k				380k (175k)
ed25519-donna-sse2 32bit		147k	147k	156k		380k (178k)	381k (173k)	430k (192k)
ed25519-donna 32bit		597k	335k	380k		1693k (720k)	1052k (453k)	1141k (493k)

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

Implementation	Sign	gcc	icc	clang	Verify	gcc	icc	clang
amd64-64-24k		68k				225k (104k)
ed25519-donna 64bit		71k	75k	90k		226k (105k)	226k (112k)	277k (125k)
amd64-51-32k		72k				218k (107k)
ed25519-donna-sse2 64bit		79k	82k	92k		252k (122k)	259k (124k)	282k (131k)
ed25519-donna-sse2 32bit		94k	95k	103k		296k (146k)	294k (137k)	306k (147k)
ed25519-donna 32bit		525k	299k	316k		1502k (645k)	959k (418k)	954k (416k)

Compilation

No configuration is needed if you are compiling against OpenSSL.

Hash Options

If you are not compiling aginst OpenSSL, you will need a hash function.

To use a simple/slow implementation of SHA-512, use -DED25519_REFHASH when compiling ed25519.c. This should never be used except to verify the code works when OpenSSL is not available.

To use a custom hash function, use -DED25519_CUSTOMHASH when compiling ed25519.c and put your custom hash implementation in ed25519-hash-custom.h. The hash must have a 512bit digest and implement

struct ed25519_hash_context;

void ed25519_hash_init(ed25519_hash_context *ctx);
void ed25519_hash_update(ed25519_hash_context *ctx, const uint8_t *in, size_t inlen);
void ed25519_hash_final(ed25519_hash_context *ctx, uint8_t *hash);
void ed25519_hash(uint8_t *hash, const uint8_t *in, size_t inlen);

Random Options

If you are not compiling aginst OpenSSL, you will need a random function for batch verification.

To use a custom random function, use -DED25519_CUSTOMRANDOM when compiling ed25519.c and put your custom hash implementation in ed25519-randombytes-custom.h. The random function must implement:

void ED25519_FN(ed25519_randombytes_unsafe) (void *p, size_t len);

Use -DED25519_TEST when compiling ed25519.c to use a deterministically seeded, non-thread safe CSPRNG variant of Bob Jenkins ISAAC

Minor options

Use -DED25519_INLINE_ASM to disable the use of custom assembler routines and instead rely on portable C.

Use -DED25519_FORCE_32BIT to force the use of 32 bit routines even when compiling for 64 bit.

32-bit

gcc ed25519.c -m32 -O3 -c

64-bit

gcc ed25519.c -m64 -O3 -c

SSE2

gcc ed25519.c -m32 -O3 -c -DED25519_SSE2 -msse2
gcc ed25519.c -m64 -O3 -c -DED25519_SSE2

clang and icc are also supported

Usage

To use the code, link against ed25519.o -mbits and:

#include "ed25519.h"

Add -lssl -lcrypto when using OpenSSL (Some systems don't need -lcrypto? It might be trial and error).

To generate a private key, simply generate 32 bytes from a secure cryptographic source:

ed25519_secret_key sk;
randombytes(sk, sizeof(ed25519_secret_key));

To generate a public key:

ed25519_public_key pk;
ed25519_publickey(sk, pk);

To sign a message:

ed25519_signature sig;
ed25519_sign(message, message_len, sk, pk, signature);

To verify a signature:

int valid = ed25519_sign_open(message, message_len, pk, signature) == 0;

To batch verify signatures:

const unsigned char *mp[num] = {message1, message2..}
size_t ml[num] = {message_len1, message_len2..}
const unsigned char *pkp[num] = {pk1, pk2..}
const unsigned char *sigp[num] = {signature1, signature2..}
int valid[num]

/* valid[i] will be set to 1 if the individual signature was valid, 0 otherwise */
int all_valid = ed25519_sign_open_batch(mp, ml, pkp, sigp, num, valid) == 0;

Note: Batch verification uses ed25519_randombytes_unsafe, implemented in ed25519-randombytes.h, to generate random scalars for the verification code. The default implementation now uses OpenSSLs RAND_bytes.

Unlike the SUPERCOP version, signatures are not appended to messages, and there is no need for padding in front of messages. Additionally, the secret key does not contain a copy of the public key, so it is 32 bytes instead of 64 bytes, and the public key must be provided to the signing function.

Curve25519

Curve25519 public keys can be generated thanks to Adam Langley leveraging Ed25519's precomputed basepoint scalar multiplication.

curved25519_key sk, pk;
randombytes(sk, sizeof(curved25519_key));
curved25519_scalarmult_basepoint(pk, sk);

Note the name is curved25519, a combination of curve and ed25519, to prevent name clashes. Performance is slightly faster than short message ed25519 signing due to both using the same code for the scalar multiply.

Testing

Fuzzing against reference implemenations is now available. See fuzz/README.

Building ed25519.c with -DED25519_TEST and linking with test.c will run basic sanity tests and benchmark each function. test-batch.c has been incorporated in to test.c.

test-internals.c is standalone and built the same way as ed25519.c. It tests the math primitives with extreme values to ensure they function correctly. SSE2 is now supported.

Papers

Available on the Ed25519 website