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95 lines
2.5 KiB
95 lines
2.5 KiB
from hashlib import sha256
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# Ring Signatures
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# bLSAG: Back’s Linkable Spontaneous Anonymous Group signatures
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# A Rust implementation of this scheme can be found at:
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# https://github.com/arnaucube/ring-signatures-rs
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def hashToPoint(a):
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# TODO use a proper hash-to-point
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h = sha256((str(a)).encode('utf-8'))
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r = int(h.hexdigest(), 16) * g
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return r
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def hash(R, m, A, B, q):
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h = sha256((
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str(R) + str(m) + str(A) + str(B)
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).encode('utf-8'))
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r = int(h.hexdigest(), 16)
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return int(mod(r, q))
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def print_ring(a):
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print("ring of c's:")
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for i in range(len(a)):
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print(i, a[i])
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print("")
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class Prover(object):
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def __init__(self, F, g):
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self.F = F # Z_p
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self.g = g # elliptic curve generator
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self.q = self.g.order() # order of group
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def new_key(self):
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self.w = int(self.F.random_element())
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self.K = self.g * self.w
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return self.K
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def sign(self, m, R):
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# determine pi (the position of signer's public key in R
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pi = -1
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for i in range(len(R)):
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if self.K == R[i]:
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pi = i
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break
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assert pi>=0
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a = int(self.F.random_element())
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r = [None] * len(R)
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# for i \in {1, 2, ..., n} \ {i=pi}
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for i in range(0, len(R)):
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if i==pi:
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continue
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r[i] = int(mod(int(self.F.random_element()), self.q))
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c = [None] * len(R)
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# c_{pi+1}
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pi1 = mod(pi + 1, len(R))
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c[pi1] = hash(R, m, a * self.g, hashToPoint(R[pi]) * a, self.q)
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key_image = self.w * hashToPoint(self.K)
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# do c_{i+1} from i=pi+1 to pi-1:
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for j in range(0, len(R)-1):
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i = mod(pi1+j, len(R))
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i1 = mod(pi1+j +1, len(R))
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c[i1] = hash(R, m, r[i] * self.g + c[i] * R[i], r[i] * hashToPoint(R[i]) + c[i] * key_image, self.q)
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# compute r_pi
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r[pi] = int(mod(a - c[pi] * self.w, self.q))
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print_ring(c)
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return [c[0], r]
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def verify(g, R, m, key_image, sig):
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q = g.order()
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c1 = sig[0]
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r = sig[1]
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assert len(R) == len(r)
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# check that key_image \in G (EC), by l * key_image == 0
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assert q * key_image == 0 # in sage 0 EC point is represented as (0:1:0)
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# for i \in 1,2,...,n
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c = [None] * len(R)
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c[0] = c1
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for j in range(0, len(R)):
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i = mod(j, len(R))
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i1 = mod(j+1, len(R))
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c[i1] = hash(R, m, r[i] * g + c[i] * R[i], r[i] * hashToPoint(R[i]) + c[i] * key_image, q)
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print_ring(c)
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assert c1 == c[0]
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