from channel import Channel
from field import FieldElement
from merkle import MerkleTree
from polynomial import interpolate_poly, Polynomial
t = [FieldElement(1), FieldElement(3141592)]
while len(t) < 1023:
t.append(t[-2] * t[-2] + t[-1] * t[-1])
g = FieldElement.generator() ** (3 * 2 ** 20)
points = [g ** i for i in range(1024)]
h_gen = FieldElement.generator() ** ((2 ** 30 * 3) // 8192)
h = [h_gen ** i for i in range(8192)]
domain = [FieldElement.generator() * x for x in h]
p = interpolate_poly(points[:-1], t)
100%|██████████| 1023/1023 [00:40<00:00, 25.36it/s]
f_eval = [p.eval(d) for d in domain]
f_merkle = MerkleTree(ev)
ch = Channel()
ch.send(f_merkle.root)
numer0 = p - Polynomial([FieldElement(1)])
denom0 = Polynomial.gen_linear_term(FieldElement(1))
q0, r0 = numer0.qdiv(denom0)
numer1 = p - Polynomial([FieldElement(2338775057)])
denom1 = Polynomial.gen_linear_term(points[1022])
q1, r1 = numer1.qdiv(denom1)
inner_poly0 = Polynomial([FieldElement(0), points[2]])
final0 = p.compose(inner_poly0)
inner_poly1 = Polynomial([FieldElement(0), points[1]])
composition = p.compose(inner_poly1)
final1 = composition * composition
final2 = p * p
numer2 = final0 - final1 - final2
coef = [FieldElement(1)] + [FieldElement(0)] * 1023 + [FieldElement(-1)]
numerator_of_denom2 = Polynomial(coef)
factor0 = Polynomial.gen_linear_term(points[1021])
factor1 = Polynomial.gen_linear_term(points[1022])
factor2 = Polynomial.gen_linear_term(points[1023])
denom_of_denom2 = factor0 * factor1 * factor2
denom2, r_denom2 = numerator_of_denom2.qdiv(denom_of_denom2)
q2, r2 = numer2.qdiv(denom2)
cp0 = q0.scalar_mul(ch.receive_random_field_element())
cp1 = q1.scalar_mul(ch.receive_random_field_element())
cp2 = q2.scalar_mul(ch.receive_random_field_element())
cp = cp0 + cp1 + cp2
cp_ev = [cp.eval(d) for d in domain]
cp_mt = MerkleTree(cp_ev)
ch.send(cp_mt.root)
def next_fri_domain(domain):
return [x ** 2 for x in domain[:len(domain) // 2]]
def next_fri_polynomial(poly, alpha):
odd_coefficients = poly.poly[1::2]
even_coefficients = poly.poly[::2]
odd = Polynomial(odd_coefficients).scalar_mul(alpha)
even = Polynomial(even_coefficients)
return odd + even
def next_fri_layer(poly, dom, alpha):
next_poly = next_fri_polynomial(poly, alpha)
next_dom = next_fri_domain(dom)
next_layer = [next_poly.eval(x) for x in next_dom]
return next_poly, next_dom, next_layer
fri_polys = [cp]
fri_doms = [domain]
fri_layers = [cp_ev]
fri_merkles = [cp_mt]
while fri_polys[-1].degree() > 0:
alpha = ch.receive_random_field_element()
next_poly, next_dom, next_layer = next_fri_layer(fri_polys[-1], fri_doms[-1], alpha)
fri_polys.append(next_poly)
fri_doms.append(next_dom)
fri_layers.append(next_layer)
fri_merkles.append(MerkleTree(next_layer))
ch.send(fri_merkles[-1].root)
ch.send(str(fri_polys[-1].poly[0]))
def decommit_on_fri_layers(idx, channel):
for layer, merkle in zip(fri_layers[:-1], fri_merkles[:-1]):
length = len(layer)
idx = idx % length
sib_idx = (idx + length // 2) % length
channel.send(str(layer[idx]))
channel.send(str(merkle.get_authentication_path(idx)))
channel.send(str(layer[sib_idx]))
channel.send(str(merkle.get_authentication_path(sib_idx)))
channel.send(str(fri_layers[-1][0]))
def decommit_on_query(idx, channel):
channel.send(str(f_eval[idx])) # f(x).
channel.send(str(f_merkle.get_authentication_path(idx))) # auth path for f(x).
channel.send(str(f_eval[idx + 8])) # f(gx).
channel.send(str(f_merkle.get_authentication_path(idx + 8))) # auth path for f(gx).
channel.send(str(f_eval[idx + 16])) # f(g^2x).
channel.send(str(f_merkle.get_authentication_path(idx + 16))) # auth path for f(g^2x).
decommit_on_fri_layers(idx, channel)
def decommit_fri(channel):
for query in range(3):
# Get a random index from the verifier and send the corresponding decommitment.
decommit_on_query(channel.receive_random_int(0, 8191-16), channel)
import time
start = time.time()
print("Generating queries and decommitments...")
decommit_fri(ch)
print(f'{time.time() - start}s')
start = time.time()
print(ch.proof)
print(f'Overall time: {time.time() - start_all}s')
print(f'Uncompressed proof length in characters: {len(str(ch.proof))}')
Generating queries and decommitments...
6.222604751586914s
['send:6c266a104eeaceae93c14ad799ce595ec8c2764359d7ad1b4b7c57a4da52be04', 'receive_random_field_element:2948900820', 'receive_random_field_element:1859037345', 'receive_random_field_element:2654806830', 'send:61f7d8283e244d391a483c420776e351fcfdbce525a698461a8307a1345b5652', 'receive_random_int:2267', 'send:1217334213', "send:['fd22d0af72c43247ce70d7ee3f6532037e95555386934dc886c455e26f8a4675', '8fe2e3193f8eeb219a110f6b6dd57c89626442ab2956c00eeddf9ab06a4c0c5b', 'a914616822dec340c44c5f4b0b26abe9ca42c32e5fbbc3ac7889cc2d4208f361', '672e2b3cdd3fb6e71c7381457e94cbd5ad847b3e7b9679492d8a9b52f5573dc4', '946f939a48abb967c0668c363da30224e8160b0d9d1c7cf0714e2a177044d180', '2f051a45f6eb9968469ff054c7703c2c6d562143b4f66c4a1b21c7e8258c8ed1', '25eabe1e46031279b1199100fbaaa0245ba84ed371689af6425c4fa1e82c3116', '18c939ab0eb3e684b0fa0da83c6654286abb642e56b289580f33890a3ad05019', '3179828dd2d9ffdf150901cc22fd828eac4745412006d63f7e8f038c4d401efe', '0a3cbe18a8d93174098407551c97297b532149c5e90d484f17414f29ecc54250', '196b581e1d0774a0e897b085f43719388465a01c6445d1922084bb19f9d9c060', '0a6a9d531f03bf6f00a4145bc4a468bab0e67f1eb710f39bfd4ba9f62c5a5dc8', '91a46c3750224da19840f1d9a8e2c48dbc191604210da0c0389f1becf6d4b8df']", 'send:280765161', "send:['fd22d0af72c43247ce70d7ee3f6532037e95555386934dc886c455e26f8a4675', '8fe2e3193f8eeb219a110f6b6dd57c89626442ab2956c00eeddf9ab06a4c0c5b', 'a914616822dec340c44c5f4b0b26abe9ca42c32e5fbbc3ac7889cc2d4208f361', '672e2b3cdd3fb6e71c7381457e94cbd5ad847b3e7b9679492d8a9b52f5573dc4', '946f939a48abb967c0668c363da30224e8160b0d9d1c7cf0714e2a177044d180', '2f051a45f6eb9968469ff054c7703c2c6d562143b4f66c4a1b21c7e8258c8ed1', '25eabe1e46031279b1199100fbaaa0245ba84ed371689af6425c4fa1e82c3116', 'a112a205dcdb7f7eae554da391834f8a952396add02e164784e9008e160e38a3', 'd670f599ebe2d9e06c89541cb418e823cbf25aabdb34543a4976db93757fafdf', '0155577335c53f3c02206fea05dab1d82f3665301ac9aeb7f5685f3ba2810048', '8914167e8766f6b760a76c1f06c78be3f7d9c46ea2e9f90d45becf4f630da106', '246e326651f1b179d02b75359ecd73936a570337f347f8bc4e05a727cf3e3fcf', '56c643d6121d9faed1fd0842015f44a80f55a4ec846e8999a50dfc3ef335d425']", 'send:253851839', "send:['fd22d0af72c43247ce70d7ee3f6532037e95555386934dc886c455e26f8a4675', '8fe2e3193f8eeb219a110f6b6dd57c89626442ab2956c00eeddf9ab06a4c0c5b', 'a914616822dec340c44c5f4b0b26abe9ca42c32e5fbbc3ac7889cc2d4208f361', '672e2b3cdd3fb6e71c7381457e94cbd5ad847b3e7b9679492d8a9b52f5573dc4', '946f939a48abb967c0668c363da30224e8160b0d9d1c7cf0714e2a177044d180', '2f051a45f6eb9968469ff054c7703c2c6d562143b4f66c4a1b21c7e8258c8ed1', '25eabe1e46031279b1199100fbaaa0245ba84ed371689af6425c4fa1e82c3116', 'a112a205dcdb7f7eae554da391834f8a952396add02e164784e9008e160e38a3', 'd670f599ebe2d9e06c89541cb418e823cbf25aabdb34543a4976db93757fafdf', '9dfb1a6022c3b9ce8d9ad62a583ce6844d3b8396d6f759568750491c3638e32c', '2c84683efe18448e5cee8e4987710c11d1566ab9bc1007d6bc3a375e3bdab274', '34fb73dee2f0dbe4a796b114ae83be23d5bbc08b612d6f24acf91113dfc4429f', '5999f1aaf20c55fcae3b97e885e6c2b444cb9aadcc8cfda5368938af557cb8ce']", 'receive_random_int:1505', 'send:-778525274', "send:['fd22d0af72c43247ce70d7ee3f6532037e95555386934dc886c455e26f8a4675', '479e1ac8d089851697122112f2ea40be8a9933c4684acb604611bd05733503de', '4678bb0e3770a384898966187cfb8628d18858f383a630a55911736c26c23ed0', 'f96f4533ca52df25432cf272c34545ba85878da033353120a21dbfbcaca9753d', '73fb497fe5d36efaa3f722916ec22487424464eeb87893abd06626949e944408', 'bd8574639c420ebb662e03430385285833132ccc29f04e8997a6680436003171', '63bebd90dc2648288f44b5477398e54920be0c01be66a7da912811548f8f2673', '71e6dcb601b0bd26ab7fb51efe7fb78e7da17cce28040ebecdcfe846d82998db', '5f0b85c25dc95fba00cd6ecf234bfa5632b2288eb7d8cc73b27be015b5c919af', 'e2bd0eb1b6b6b49186b4c4bd0b73d5ee0b6befbb7b68a8d4c7327b61a6c7e865', '4189bf3bf0e1e4b1dae3e5586f8ae156c5c98e7e1f2f91131e4be614c860e789', '6813fc4cf84c1d70b8c92c3196bfd75d96220f3f89767ca1b2aa91d78bf1c63e', '07744b890cfb481aa75f40fb66c4b4a9ae8be2f43114b205f33f6466a04d02b7']", 'send:-22255227', "send:['fd22d0af72c43247ce70d7ee3f6532037e95555386934dc886c455e26f8a4675', '479e1ac8d089851697122112f2ea40be8a9933c4684acb604611bd05733503de', '4678bb0e3770a384898966187cfb8628d18858f383a630a55911736c26c23ed0', 'f96f4533ca52df25432cf272c34545ba85878da033353120a21dbfbcaca9753d', '73fb497fe5d36efaa3f722916ec22487424464eeb87893abd06626949e944408', 'bd8574639c420ebb662e03430385285833132ccc29f04e8997a6680436003171', '63bebd90dc2648288f44b5477398e54920be0c01be66a7da912811548f8f2673', '71e6dcb601b0bd26ab7fb51efe7fb78e7da17cce28040ebecdcfe846d82998db', '5f0b85c25dc95fba00cd6ecf234bfa5632b2288eb7d8cc73b27be015b5c919af', 'c25635f1245bf7403ef556046a151a4da5bdddd250f4b2651c1cb29d6e8d3bae', 'd2aef8d720c02a17ba45e24fe612c95a35db606f634940d4343f6ad9a9c093ec', '74b6101c486822593ee938a7a8dd9565255d3df5c0136a1b97f5bf946c6bbb75', 'e448086772fd3af0fe7dcc16c58dd0578be1ee6318494efbb4c6c34e789164b2']", 'send:-1357094387', "send:['fd22d0af72c43247ce70d7ee3f6532037e95555386934dc886c455e26f8a4675', '479e1ac8d089851697122112f2ea40be8a9933c4684acb604611bd05733503de', '4678bb0e3770a384898966187cfb8628d18858f383a630a55911736c26c23ed0', 'f96f4533ca52df25432cf272c34545ba85878da033353120a21dbfbcaca9753d', '73fb497fe5d36efaa3f722916ec22487424464eeb87893abd06626949e944408', 'bd8574639c420ebb662e03430385285833132ccc29f04e8997a6680436003171', '63bebd90dc2648288f44b5477398e54920be0c01be66a7da912811548f8f2673', '71e6dcb601b0bd26ab7fb51efe7fb78e7da17cce28040ebecdcfe846d82998db', '1b8e7c1582ee9a487526b5c4c59680bfb246cc05149b415cc236d6484f5f4ab1', 'e71245a06b2a553d6d832560acf0e530f2d88ca013eeca0ba295492090b737e4', '8ffecf91a4ccfca543faf65b0131d4d81d22c77ace266b5f835002cad5675c2a', '0e9830dc1fa39ee5cc94d1b45d11ba67f2fba53697407eacc2466dab92017bcb', '9ff38b3d091e0d24f2bd3aa83db7bc26d05fc2305956986dd8af14a6ecbfa914']", 'receive_random_field_element:613396172', 'send:b1512c1840b1284c62a264d40be1e6bc0a03993ed5c02271297d7c83fa710d84', 'receive_random_field_element:1092069065', 'send:3e21ee17d64f8bc7fe59f98ae7cf320cae724c7fe1d0bd542ad3473898e00000', 'receive_random_field_element:183101382', 'send:ece6d076a98743498a21b6517884af38f924d25091409b270e8e5a42679bf177', 'receive_random_field_element:186944365', 'send:e26ace2b328b4d65d17f46cc121a836ace69a339237d0c5ba8cfc0e4f1a2be5f', 'receive_random_field_element:2639793467', 'send:f83491e45f7d9d26b80713448e352dcc73f916215f9c19468a0d1be783f33ff8', 'receive_random_field_element:2854946132', 'send:c88e8ca680922fbe955ec68794a281c7ab210fdbbaa11cadd7feae4bb4ce76b2', 'receive_random_field_element:2894056633', 'send:381080a37c89b555fae7094d92dfa6a9ff39b4963c21e768220b15ab548811c0', 'receive_random_field_element:3135645844', 'send:e7a816b29a5135b9bc0e0abc0f8609603af068ab09a36c01d84bdcc60d93babb', 'receive_random_field_element:989261674', 'send:3ff50805602fa0ac51a25c976becc2bb8489e8fe6110823017c97d08a1aba813', 'receive_random_field_element:877436675', 'send:a9eca4e1058df0b7900538df14b6b6e59ffd0f183c1e3bed032aebcdc99227ef', 'send:-137492480', 'receive_random_int:4923', 'send:-389502067', "send:['76f7d3d788bbf4ab1a4992b8363ace03b8c877db54e735017f2f8d98823acb93', '1e0f533d19224a58c5a8a7f18ea99d4e4aee80dfeee5fd3352fb8ba41f94f113', '2b93ec411e96c55a8d928ba931c08f038ee9bba65698a647fc642498a17b4c30', 'defca812fb93fcbce6634f9433c99cc9f2315453ba11f550c21cd6ee6fe096dd', 'dbcebac71e9ef0d00c4d241a406b7e85685bb9b4baeaa831a8c40387345c679d', 'e4dba401f3165e81def9be8ae398e9e543897aaf8829bb491c0939512add050a', '5ccc2798cb5a8c74adeea023675fb88ff5aec824379a320f77c42c580377d294', 'f4f7690acb511f907571f4a2e6753fd71494ebb72c5cea7717521930bdf0693a', '7ab6a1e0aae7a10ee267ddf684188d8fee934b063df1d8512bb07f6d95103fee', 'e3d98f00a337ef342eb9e6390c6548dba3804526cc9c492e5b4531fb9668534f', '4b65bc10725f29b858067a4c993b89f2b551bffa60bb8fcbe747ee21c7ffa606', '2362d2f727ffa08b7cf5280287fae0460d562ed75ce27c872e3d2283a9a1c0e7', 'f7f49eb10c9c665b6c7b07de8c692f891ce39e8e7fcadb4f8f425ca91f48cb80']", 'send:1003382988', "send:['76f7d3d788bbf4ab1a4992b8363ace03b8c877db54e735017f2f8d98823acb93', '1e0f533d19224a58c5a8a7f18ea99d4e4aee80dfeee5fd3352fb8ba41f94f113', '2b93ec411e96c55a8d928ba931c08f038ee9bba65698a647fc642498a17b4c30', 'defca812fb93fcbce6634f9433c99cc9f2315453ba11f550c21cd6ee6fe096dd', 'dbcebac71e9ef0d00c4d241a406b7e85685bb9b4baeaa831a8c40387345c679d', 'e4dba401f3165e81def9be8ae398e9e543897aaf8829bb491c0939512add050a', 'c203560bf7d32900fe1e69dba3cbe7d298a3f391b9d992ff936d25b30f4896e9', '9470f63d338cb34e53ddc789bb695eb154103b10489e2e83a3a08bea8de127b2', '5353e51b1a92d72d9cf325baae7947fc2ad04347259b7af30c21772ce9e25864', '4a082b999b2560ed18ca05f4cc77fa3d429ba862505229c3bfa06afec77dc388', 'ca6a4b664abfb146210ec336d550b051522ea9d9111db0ca6b9396a4ad079964', 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Overall time: 74.48859810829163s
Uncompressed proof length in characters: 185743