mirror of
https://github.com/TheAlgorithms/Python.git
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268 lines
12 KiB
Python
268 lines
12 KiB
Python
from binascii import hexlify
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from hashlib import sha256
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from os import urandom
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# RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups for
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# Internet Key Exchange (IKE) https://tools.ietf.org/html/rfc3526
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primes = {
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# 1536-bit
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5: {
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"prime": int(
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"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
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"29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
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"EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
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"E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
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"EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
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"C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
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"83655D23DCA3AD961C62F356208552BB9ED529077096966D"
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"670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF",
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base=16,
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),
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"generator": 2,
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},
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# 2048-bit
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14: {
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"prime": int(
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"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
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"29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
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"EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
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"E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
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"EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
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"C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
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"83655D23DCA3AD961C62F356208552BB9ED529077096966D"
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"670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
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"E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
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"DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
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"15728E5A8AACAA68FFFFFFFFFFFFFFFF",
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base=16,
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),
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"generator": 2,
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},
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# 3072-bit
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15: {
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"prime": int(
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"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
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"29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
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"EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
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"E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
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"EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
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"C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
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"83655D23DCA3AD961C62F356208552BB9ED529077096966D"
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"670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
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"E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
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"DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
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"15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
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"ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
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"ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
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"F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
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"BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
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"43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF",
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base=16,
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),
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"generator": 2,
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},
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# 4096-bit
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16: {
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"prime": int(
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"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
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"29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
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"EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
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"E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
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"EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
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"C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
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"83655D23DCA3AD961C62F356208552BB9ED529077096966D"
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"670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
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"E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
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"DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
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"15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
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"ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
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"ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
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"F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
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"BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
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"43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
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"88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
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"2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
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"287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
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"1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
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"93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199"
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"FFFFFFFFFFFFFFFF",
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base=16,
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),
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"generator": 2,
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},
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# 6144-bit
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17: {
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"prime": int(
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"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08"
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"8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B"
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"302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9"
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"A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6"
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"49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8"
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"FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D"
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"670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C"
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"180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718"
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"3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D"
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"04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D"
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"B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226"
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"1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
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"BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC"
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"E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26"
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"99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB"
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"04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2"
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"233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127"
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"D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
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"36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406"
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"AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918"
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"DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151"
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"2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03"
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"F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F"
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"BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
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"CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B"
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"B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632"
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"387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E"
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"6DCC4024FFFFFFFFFFFFFFFF",
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base=16,
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),
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"generator": 2,
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},
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# 8192-bit
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18: {
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"prime": int(
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"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"
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"29024E088A67CC74020BBEA63B139B22514A08798E3404DD"
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"EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"
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"E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"
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"EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"
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"C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"
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"83655D23DCA3AD961C62F356208552BB9ED529077096966D"
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"670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"
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"E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"
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"DE2BCBF6955817183995497CEA956AE515D2261898FA0510"
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"15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"
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"ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"
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"ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"
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"F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"
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"BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"
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"43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7"
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"88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA"
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"2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6"
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"287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED"
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"1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9"
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"93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492"
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"36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BD"
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"F8FF9406AD9E530EE5DB382F413001AEB06A53ED9027D831"
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"179727B0865A8918DA3EDBEBCF9B14ED44CE6CBACED4BB1B"
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"DB7F1447E6CC254B332051512BD7AF426FB8F401378CD2BF"
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"5983CA01C64B92ECF032EA15D1721D03F482D7CE6E74FEF6"
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"D55E702F46980C82B5A84031900B1C9E59E7C97FBEC7E8F3"
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"23A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA"
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"CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE328"
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"06A1D58BB7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55C"
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"DA56C9EC2EF29632387FE8D76E3C0468043E8F663F4860EE"
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"12BF2D5B0B7474D6E694F91E6DBE115974A3926F12FEE5E4"
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"38777CB6A932DF8CD8BEC4D073B931BA3BC832B68D9DD300"
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"741FA7BF8AFC47ED2576F6936BA424663AAB639C5AE4F568"
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"3423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9"
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"22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B"
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"4BCBC8862F8385DDFA9D4B7FA2C087E879683303ED5BDD3A"
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"062B3CF5B3A278A66D2A13F83F44F82DDF310EE074AB6A36"
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"4597E899A0255DC164F31CC50846851DF9AB48195DED7EA1"
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"B1D510BD7EE74D73FAF36BC31ECFA268359046F4EB879F92"
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"4009438B481C6CD7889A002ED5EE382BC9190DA6FC026E47"
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"9558E4475677E9AA9E3050E2765694DFC81F56E880B96E71"
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"60C980DD98EDD3DFFFFFFFFFFFFFFFFF",
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base=16,
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),
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"generator": 2,
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},
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}
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class DiffieHellman:
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"""
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Class to represent the Diffie-Hellman key exchange protocol
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>>> alice = DiffieHellman()
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>>> bob = DiffieHellman()
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>>> alice_private = alice.get_private_key()
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>>> alice_public = alice.generate_public_key()
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>>> bob_private = bob.get_private_key()
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>>> bob_public = bob.generate_public_key()
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>>> # generating shared key using the DH object
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>>> alice_shared = alice.generate_shared_key(bob_public)
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>>> bob_shared = bob.generate_shared_key(alice_public)
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>>> assert alice_shared == bob_shared
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>>> # generating shared key using static methods
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>>> alice_shared = DiffieHellman.generate_shared_key_static(
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... alice_private, bob_public
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... )
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>>> bob_shared = DiffieHellman.generate_shared_key_static(
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... bob_private, alice_public
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... )
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>>> assert alice_shared == bob_shared
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"""
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# Current minimum recommendation is 2048 bit (group 14)
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def __init__(self, group: int = 14) -> None:
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if group not in primes:
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raise ValueError("Unsupported Group")
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self.prime = primes[group]["prime"]
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self.generator = primes[group]["generator"]
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self.__private_key = int(hexlify(urandom(32)), base=16)
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def get_private_key(self) -> str:
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return hex(self.__private_key)[2:]
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def generate_public_key(self) -> str:
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public_key = pow(self.generator, self.__private_key, self.prime)
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return hex(public_key)[2:]
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def is_valid_public_key(self, key: int) -> bool:
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# check if the other public key is valid based on NIST SP800-56
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return (
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2 <= key <= self.prime - 2
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and pow(key, (self.prime - 1) // 2, self.prime) == 1
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)
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def generate_shared_key(self, other_key_str: str) -> str:
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other_key = int(other_key_str, base=16)
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if not self.is_valid_public_key(other_key):
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raise ValueError("Invalid public key")
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shared_key = pow(other_key, self.__private_key, self.prime)
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return sha256(str(shared_key).encode()).hexdigest()
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@staticmethod
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def is_valid_public_key_static(remote_public_key_str: int, prime: int) -> bool:
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# check if the other public key is valid based on NIST SP800-56
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return (
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2 <= remote_public_key_str <= prime - 2
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and pow(remote_public_key_str, (prime - 1) // 2, prime) == 1
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)
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@staticmethod
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def generate_shared_key_static(
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local_private_key_str: str, remote_public_key_str: str, group: int = 14
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) -> str:
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local_private_key = int(local_private_key_str, base=16)
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remote_public_key = int(remote_public_key_str, base=16)
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prime = primes[group]["prime"]
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if not DiffieHellman.is_valid_public_key_static(remote_public_key, prime):
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raise ValueError("Invalid public key")
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shared_key = pow(remote_public_key, local_private_key, prime)
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return sha256(str(shared_key).encode()).hexdigest()
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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