[ed25519](https://ed25519.cr.yp.to) is an [Elliptic Curve Digital Signature Algortithm](https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm), developed by [Dan Bernstein](https://cr.yp.to/djb.html), [Niels Duif](https://www.nielsduif.nl), [Tanja Lange](https://hyperelliptic.org/tanja), [Peter Schwabe](https://cryptojedi.org/peter), and [Bo-Yin Yang](https://www.iis.sinica.edu.tw/pages/byyang). 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 <table> <thead><tr><th>Implementation</th><th>Sign</th><th>gcc</th><th>icc</th><th>clang</th><th>Verify</th><th>gcc</th><th>icc</th><th>clang</th></tr></thead> <tbody> <tr><td>ed25519-donna 64bit </td><td></td><td>100k</td><td>110k</td><td>137k</td><td></td><td>327k (144k) </td><td>342k (163k) </td><td>422k (194k) </td></tr> <tr><td>amd64-64-24k </td><td></td><td>102k</td><td> </td><td> </td><td></td><td>355k (158k) </td><td> </td><td> </td></tr> <tr><td>ed25519-donna-sse2 64bit</td><td></td><td>108k</td><td>111k</td><td>116k</td><td></td><td>353k (155k) </td><td>345k (154k) </td><td>360k (161k) </td></tr> <tr><td>amd64-51-32k </td><td></td><td>116k</td><td> </td><td> </td><td></td><td>380k (175k) </td><td> </td><td> </td></tr> <tr><td>ed25519-donna-sse2 32bit</td><td></td><td>147k</td><td>147k</td><td>156k</td><td></td><td>380k (178k) </td><td>381k (173k) </td><td>430k (192k) </td></tr> <tr><td>ed25519-donna 32bit </td><td></td><td>597k</td><td>335k</td><td>380k</td><td></td><td>1693k (720k)</td><td>1052k (453k)</td><td>1141k (493k)</td></tr> </tbody> </table> ##### E3-1270 @ 3.4ghz, march=corei7-avx <table> <thead><tr><th>Implementation</th><th>Sign</th><th>gcc</th><th>icc</th><th>clang</th><th>Verify</th><th>gcc</th><th>icc</th><th>clang</th></tr></thead> <tbody> <tr><td>amd64-64-24k </td><td></td><td> 68k</td><td> </td><td> </td><td></td><td>225k (104k) </td><td> </td><td> </td></tr> <tr><td>ed25519-donna 64bit </td><td></td><td> 71k</td><td> 75k</td><td> 90k</td><td></td><td>226k (105k) </td><td>226k (112k) </td><td>277k (125k) </td></tr> <tr><td>amd64-51-32k </td><td></td><td> 72k</td><td> </td><td> </td><td></td><td>218k (107k) </td><td> </td><td> </td></tr> <tr><td>ed25519-donna-sse2 64bit</td><td></td><td> 79k</td><td> 82k</td><td> 92k</td><td></td><td>252k (122k) </td><td>259k (124k) </td><td>282k (131k) </td></tr> <tr><td>ed25519-donna-sse2 32bit</td><td></td><td> 94k</td><td> 95k</td><td>103k</td><td></td><td>296k (146k) </td><td>294k (137k) </td><td>306k (147k) </td></tr> <tr><td>ed25519-donna 32bit </td><td></td><td>525k</td><td>299k</td><td>316k</td><td></td><td>1502k (645k)</td><td>959k (418k) </td><td>954k (416k) </td></tr> </tbody> </table> #### 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](https://en.wikipedia.org/wiki/ISAAC_%28cipher%29) ##### 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](https://bench.cr.yp.to/supercop.html) 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](https://www.imperialviolet.org/2013/05/10/fastercurve25519.html) 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](fuzz/README.md). 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](https://ed25519.cr.yp.to/papers.html)