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Microarchitectures are listed in reverse chronological order of when they were introduced. Each library is assigned one foreground color in the table. In the lib25519 distribution, `command/lib25519-speed.c` measures lib25519; `benchmarks/*-*` is the output of `lib25519-speed` on various machines; `speedcomparison/openssl/*` has code to measure OpenSSL, and measurements from various machines; `speedcomparison/s2n/*` has code to measure s2n-bignum, and measurements from various machines; and `autogen/md-speed` extracts the table from those measurements. OpenSSL benchmarks use version 3.3.2 (2024.09.03); s2n-bignum benchmarks use commit acbb18e6343f12a7944de72c1ec0991739600f8c (2024.03.18). The table reports only median cycle counts; see the full output files for differences between multiple measurements and the median. The table reports the following major operations: * "X key": Generating an X25519 public key and secret key. This is `dh_x25519_keypair selected 32` in the `lib25519-speed` output (`lib25519_dh_keypair` in the stable API). For s2n-bignum, this is `x25519-keygen` in the `s2n25519speed` output, measuring the cost of `curve25519_x25519base_byte_alt`, or `curve25519_x25519base_byte` on machines where that works and is faster. For OpenSSL, this is `x25519-keygen-main` in the `openssl25519speed` output, measuring the cost of `EVP_PKEY_Q_keygen(0,0,"X25519")`. This does not include small OpenSSL overheads for converting the public key and secret key to storage format. * "X dh": Generating an X25519 shared secret. This is `dh_x25519 selected 32` in the `lib25519-speed` output (`lib25519_dh` in the stable API). For s2n-bignum, this is `x25519-dh` in the `s2n25519speed` output, measuring the cost of `curve25519_x25519_byte_alt`, or `curve25519_x25519_byte` on machines where that works and is faster. For OpenSSL, this is `x25519-dh-main` in the `openssl25519speed` output, measuring the cost of `EVP_PKEY_derive` (as in OpenSSL's speed-testing utility). This does not include the cost of `EVP_PKEY_new_raw_public_key` to decode the public key (`x25519-dh-pkdecode`, 6836 cycles on Tiger Lake), `EVP_PKEY_CTX_new` and `EVP_PKEY_derive_init` and `EVP_PKEY_derive_set_peer` for initialization (together `x25519-dh-init`, 2423 cycles on Tiger Lake), and `EVP_PKEY_new_raw_private_key` to decode the secret key if it is not decoded already (`x25519-dh-skdecode`, 112114 cycles on Tiger Lake). * "X batch": Cost _per secret_ of generating 16 separate shared secrets. This is `nPbatch_montgomery25519 selected 16` in the `lib25519-speed` output _divided by 16_. * "Ed key": Generating an Ed25519 public key and secret key. This is `sign_ed25519_keypair selected 32` in the `lib25519-speed` output (`lib25519_sign_keypair` in the stable API). For OpenSSL, this is `ed25519-keygen-main` in the `openssl25519speed` output, measuring the cost of `EVP_PKEY_Q_keygen(0,0,"ED25519")`. This does not include small OpenSSL overheads for converting the public key and secret key to storage format. * "Ed sign": Generating an Ed25519 signature of a 59-byte message. This is `sign_ed25519 selected 59` in the `lib25519-speed` output (`lib25519_sign` in the stable API). For OpenSSL, this is `ed25519-sign-main` in the `openssl25519speed` output, measuring the cost of `EVP_DigestSign` (as in OpenSSL's speed-testing utility). This does not include the cost of `EVP_MD_CTX_new` and `EVP_DigestSignInit` (`ed25519-sign-init`, 2808 cycles on Tiger Lake), and `EVP_PKEY_new_raw_private_key` to decode the secret key if it is not decoded already (`ed25519-sign-skdecode`, 114894 cycles on Tiger Lake). * "Ed verif": Verifying an Ed25519 signature and recovering a 59-byte message. This is `sign_ed25519_open selected 59` in the `lib25519-speed` output (`lib25519_sign_open` in the stable API). For OpenSSL, this is `ed25519-verify-main` in the `openssl25519speed` output, measuring the cost of `EVP_DigestVerify` (as in OpenSSL's speed-testing utility). This does not include the cost of `EVP_MD_CTX_new` and `EVP_DigestVerifyInit` (together `ed25519-verify-init`, 2579 cycles on Tiger Lake), and `EVP_PKEY_new_raw_public_key` to decode the public key being used for verification (`ed25519-verify-pkdecode`, 7401 cycles on Tiger Lake). * "Ed MSM": Cost _per point_ of multi-scalar multiplication with 16 points and 16 full-size scalars. This is `multiscalar_ed25519 selected 16` in the `lib25519-speed` output _divided by 16_.