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nostr/notes/0004-schnorr-signature-scheme-in-erlang/README_ANNEXE1.md
niamtokik 1984e20549 Schnorr Signature Scheme and NIP/01 Implementation 
This (very) huge commit is containing the whole implementation
of the Schnorr signature scheme and the NIP/01 standard in
full Erlang. It includes documentation, test suites with eunit
and commont_test, partial specification, and articles/notes
on the implementation.

This commit is also probably one of the most important, it
defines the structure of the nostrlib module and all the
low level record used to encode and decode events.

99% coverages on nostrlib_schnorr. 85% on nostrlib.
2023-03-10 20:04:53 +00:00

12 KiB
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ANNEXE 1 - BIP-0340 Implementation in Python

Here the steps to extract and execute BIP-0340 implementation in Python with debug mode activated.

git clone https://github.com/bitcoin/bips
cd bips/bip-0340
sed -i "s/^DEBUG = False/DEBUG = True/" reference.py
python reference.py

Here the output:

Test vector  #0:
   Variables in function schnorr_sign at line 118:
           msg == 0x0000000000000000000000000000000000000000000000000000000000000000
        seckey == 0x0000000000000000000000000000000000000000000000000000000000000003
      aux_rand == 0x0000000000000000000000000000000000000000000000000000000000000000
            d0 == 0x0000000000000000000000000000000000000000000000000000000000000003
             P == ('0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9',
                   '0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672')

             d == 0x0000000000000000000000000000000000000000000000000000000000000003
             t == 0x54f169cfc9e2e5727480441f90ba25c488f461c70b5ea5dcaaf7af69270aa517
            k0 == 0x1d2dc1652fee3ad08434469f9ad30536a5787feccfa308e8fb396c8030dd1c69
             R == ('0xe907831f80848d1069a5371b402410364bdf1c5f8307b0084c55f1ce2dca8215',
                   '0x849b08486a5b16ea5fd009a3ade472b48a2dc817aeebc33ab4fa25ebbd599f27')

             k == 0xe2d23e9ad011c52f7bcbb960652cfac815365cf9dfa59752c498f20c9f5924d8
             e == 0x6bb6b93a91f2ecc0cd924f4f9baabb5e6eb21745bb00f2cebdaac908bb5d86ce
           sig == 0xe907831f80848d1069a5371b402410364bdf1c5f8307b0084c55f1ce2dca821525f66a4a85ea8b71e482a74f382d2ce5ebeee8fdb2172f477df4900d310536c0
   Variables in function schnorr_verify at line 141:
           msg == 0x0000000000000000000000000000000000000000000000000000000000000000
        pubkey == 0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9
           sig == 0xe907831f80848d1069a5371b402410364bdf1c5f8307b0084c55f1ce2dca821525f66a4a85ea8b71e482a74f382d2ce5ebeee8fdb2172f477df4900d310536c0
             P == ('0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9',
                   '0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672')

             r == 0xe907831f80848d1069a5371b402410364bdf1c5f8307b0084c55f1ce2dca8215
             s == 0x25f66a4a85ea8b71e482a74f382d2ce5ebeee8fdb2172f477df4900d310536c0
             e == 0x6bb6b93a91f2ecc0cd924f4f9baabb5e6eb21745bb00f2cebdaac908bb5d86ce
             R == ('0xe907831f80848d1069a5371b402410364bdf1c5f8307b0084c55f1ce2dca8215',
                   '0x7b64f7b795a4e915a02ff65c521b8d4b75d237e851143cc54b05da1342a65d08')

 * Passed signing test.
   Variables in function schnorr_verify at line 141:
           msg == 0x0000000000000000000000000000000000000000000000000000000000000000
        pubkey == 0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9
           sig == 0xe907831f80848d1069a5371b402410364bdf1c5f8307b0084c55f1ce2dca821525f66a4a85ea8b71e482a74f382d2ce5ebeee8fdb2172f477df4900d310536c0
             P == ('0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9',
                   '0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672')

             r == 0xe907831f80848d1069a5371b402410364bdf1c5f8307b0084c55f1ce2dca8215
             s == 0x25f66a4a85ea8b71e482a74f382d2ce5ebeee8fdb2172f477df4900d310536c0
             e == 0x6bb6b93a91f2ecc0cd924f4f9baabb5e6eb21745bb00f2cebdaac908bb5d86ce
             R == ('0xe907831f80848d1069a5371b402410364bdf1c5f8307b0084c55f1ce2dca8215',
                   '0x7b64f7b795a4e915a02ff65c521b8d4b75d237e851143cc54b05da1342a65d08')

 * Passed verification test.

Test vector  #1:
   Variables in function schnorr_sign at line 118:
           msg == 0x243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec4e6c89
        seckey == 0xb7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a784d9045190cfef
      aux_rand == 0x0000000000000000000000000000000000000000000000000000000000000001
            d0 == 0xb7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a784d9045190cfef
             P == ('0xdff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659',
                   '0x2ce19b946c4ee58546f5251d441a065ea50735606985e5b228788bec4e582898')

             d == 0xb7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a784d9045190cfef
             t == 0x5966c1816cb27e627c8543d63478bdce03c1b115838e469a416b0899fe5723dd
            k0 == 0xf7becdac22c3d61a97ff4e84a004e1c4919c0e0c51f50dd5bee15c9cbd27318e
             R == ('0x6896bd60eeae296db48a229ff71dfe071bde413e6d43f917dc8dcf8c78de3341',
                   '0x20bc7663da14be43c22eb2ccb49cd746573b2766b277273fcb20a2f6c1a60c6c')

             k == 0xf7becdac22c3d61a97ff4e84a004e1c4919c0e0c51f50dd5bee15c9cbd27318e
             e == 0xcfb58e748d9648b71fdc909fb7432fc0c954da5bd75cdc9d4804d32648f9839a
           sig == 0x6896bd60eeae296db48a229ff71dfe071bde413e6d43f917dc8dcf8c78de33418906d11ac976abccb20b091292bff4ea897efcb639ea871cfa95f6de339e4b0a
   Variables in function schnorr_verify at line 141:
           msg == 0x243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec4e6c89
        pubkey == 0xdff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659
           sig == 0x6896bd60eeae296db48a229ff71dfe071bde413e6d43f917dc8dcf8c78de33418906d11ac976abccb20b091292bff4ea897efcb639ea871cfa95f6de339e4b0a
             P == ('0xdff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659',
                   '0x2ce19b946c4ee58546f5251d441a065ea50735606985e5b228788bec4e582898')

             r == 0x6896bd60eeae296db48a229ff71dfe071bde413e6d43f917dc8dcf8c78de3341
             s == 0x8906d11ac976abccb20b091292bff4ea897efcb639ea871cfa95f6de339e4b0a
             e == 0xcfb58e748d9648b71fdc909fb7432fc0c954da5bd75cdc9d4804d32648f9839a
             R == ('0x6896bd60eeae296db48a229ff71dfe071bde413e6d43f917dc8dcf8c78de3341',
                   '0x20bc7663da14be43c22eb2ccb49cd746573b2766b277273fcb20a2f6c1a60c6c')

 * Passed signing test.
   Variables in function schnorr_verify at line 141:
           msg == 0x243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec4e6c89
        pubkey == 0xdff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659
           sig == 0x6896bd60eeae296db48a229ff71dfe071bde413e6d43f917dc8dcf8c78de33418906d11ac976abccb20b091292bff4ea897efcb639ea871cfa95f6de339e4b0a
             P == ('0xdff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659',
                   '0x2ce19b946c4ee58546f5251d441a065ea50735606985e5b228788bec4e582898')
             r == 0x6896bd60eeae296db48a229ff71dfe071bde413e6d43f917dc8dcf8c78de3341
             s == 0x8906d11ac976abccb20b091292bff4ea897efcb639ea871cfa95f6de339e4b0a
             e == 0xcfb58e748d9648b71fdc909fb7432fc0c954da5bd75cdc9d4804d32648f9839a
             R == ('0x6896bd60eeae296db48a229ff71dfe071bde413e6d43f917dc8dcf8c78de3341', '0x20bc7663da14be43c22eb2ccb49cd746573b2766b277273fcb20a2f6c1a60c6c')
 * Passed verification test.

Test vector  #2:
   Variables in function schnorr_sign at line 118:
           msg == 0x7e2d58d8b3bcdf1abadec7829054f90dda9805aab56c77333024b9d0a508b75c
        seckey == 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b14e5c9
      aux_rand == 0xc87aa53824b4d7ae2eb035a2b5bbbccc080e76cdc6d1692c4b0b62d798e6d906
            d0 == 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b14e5c9
             P == ('0xdd308afec5777e13121fa72b9cc1b7cc0139715309b086c960e18fd969774eb8',
                   '0xf594bb5f72b37faae396a4259ea64ed5e6fdeb2a51c6467582b275925fab1394')
             d == 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b14e5c9
             t == 0xbad44f6e1f50e3c2ad9d2ba5768ad6ab84dc4b8f9b893444234a9c39e8fc58e1
            k0 == 0xf5878384ed63c5ec428e7ab31bdb446b6884dfad76b7e0599af3f5e838409aab
             R == ('0x5831aaeed7b44bb74e5eab94ba9d4294c49bcf2a60728d8b4c200f50dd313c1b',
                   '0x5f193d22f6f1d925a7f8c4ceff20cc2a53ba1c3310ca843cf83156c1514bb284')
             k == 0xf5878384ed63c5ec428e7ab31bdb446b6884dfad76b7e0599af3f5e838409aab
             e == 0x9bc1ba4a0abbc0792066b2ca0ef771d88af676b322a83dd7517f7c1fd149215a
           sig == 0x5831aaeed7b44bb74e5eab94ba9d4294c49bcf2a60728d8b4c200f50dd313c1bab745879a5ad954a72c45a91c3a51d3c7adea98d82f8481e0e1e03674a6f3fb7
   Variables in function schnorr_verify at line 141:
           msg == 0x7e2d58d8b3bcdf1abadec7829054f90dda9805aab56c77333024b9d0a508b75c
        pubkey == 0xdd308afec5777e13121fa72b9cc1b7cc0139715309b086c960e18fd969774eb8
           sig == 0x5831aaeed7b44bb74e5eab94ba9d4294c49bcf2a60728d8b4c200f50dd313c1bab745879a5ad954a72c45a91c3a51d3c7adea98d82f8481e0e1e03674a6f3fb7
             P == ('0xdd308afec5777e13121fa72b9cc1b7cc0139715309b086c960e18fd969774eb8',
                   '0xf594bb5f72b37faae396a4259ea64ed5e6fdeb2a51c6467582b275925fab1394')
             r == 0x5831aaeed7b44bb74e5eab94ba9d4294c49bcf2a60728d8b4c200f50dd313c1b
             s == 0xab745879a5ad954a72c45a91c3a51d3c7adea98d82f8481e0e1e03674a6f3fb7
             e == 0x9bc1ba4a0abbc0792066b2ca0ef771d88af676b322a83dd7517f7c1fd149215a
             R == ('0x5831aaeed7b44bb74e5eab94ba9d4294c49bcf2a60728d8b4c200f50dd313c1b',
                   '0x5f193d22f6f1d925a7f8c4ceff20cc2a53ba1c3310ca843cf83156c1514bb284')
 * Passed signing test.
   Variables in function schnorr_verify at line 141:
           msg == 0x7e2d58d8b3bcdf1abadec7829054f90dda9805aab56c77333024b9d0a508b75c
        pubkey == 0xdd308afec5777e13121fa72b9cc1b7cc0139715309b086c960e18fd969774eb8
           sig == 0x5831aaeed7b44bb74e5eab94ba9d4294c49bcf2a60728d8b4c200f50dd313c1bab745879a5ad954a72c45a91c3a51d3c7adea98d82f8481e0e1e03674a6f3fb7
             P == ('0xdd308afec5777e13121fa72b9cc1b7cc0139715309b086c960e18fd969774eb8',
                   '0xf594bb5f72b37faae396a4259ea64ed5e6fdeb2a51c6467582b275925fab1394')
             r == 0x5831aaeed7b44bb74e5eab94ba9d4294c49bcf2a60728d8b4c200f50dd313c1b
             s == 0xab745879a5ad954a72c45a91c3a51d3c7adea98d82f8481e0e1e03674a6f3fb7
             e == 0x9bc1ba4a0abbc0792066b2ca0ef771d88af676b322a83dd7517f7c1fd149215a
             R == ('0x5831aaeed7b44bb74e5eab94ba9d4294c49bcf2a60728d8b4c200f50dd313c1b',
                   '0x5f193d22f6f1d925a7f8c4ceff20cc2a53ba1c3310ca843cf83156c1514bb284')
 * Passed verification test.

...

Test vector #12:
   Variables in function schnorr_verify at line 134:
           msg == 0x243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec4e6c89
        pubkey == 0xdff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659
           sig == 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f69e89b4c5564d00349106b8497785dd7d1d713a8ae82b32fa79d5f7fc407d39b
             P == ('0xdff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659',
                   '0x2ce19b946c4ee58546f5251d441a065ea50735606985e5b228788bec4e582898')
             r == 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
             s == 0x69e89b4c5564d00349106b8497785dd7d1d713a8ae82b32fa79d5f7fc407d39b
 * Passed verification test.

Test vector #13:
   Variables in function schnorr_verify at line 134:
           msg == 0x243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec4e6c89
        pubkey == 0xdff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659
           sig == 0x6cff5c3ba86c69ea4b7376f31a9bcb4f74c1976089b2d9963da2e5543e177769fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
             P == ('0xdff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659',
                   '0x2ce19b946c4ee58546f5251d441a065ea50735606985e5b228788bec4e582898')
             r == 0x6cff5c3ba86c69ea4b7376f31a9bcb4f74c1976089b2d9963da2e5543e177769
             s == 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
 * Passed verification test.

Test vector #14:
   Variables in function schnorr_verify at line 134:
           msg == 0x243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec4e6c89
        pubkey == 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30
           sig == 0x6cff5c3ba86c69ea4b7376f31a9bcb4f74c1976089b2d9963da2e5543e17776969e89b4c5564d00349106b8497785dd7d1d713a8ae82b32fa79d5f7fc407d39b
             P == None
             r == 0x6cff5c3ba86c69ea4b7376f31a9bcb4f74c1976089b2d9963da2e5543e177769
             s == 0x69e89b4c5564d00349106b8497785dd7d1d713a8ae82b32fa79d5f7fc407d39b
 * Passed verification test.

All test vectors passed.