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# Sage impl of the powers of tau,
# a Go implementation can be found at: https://github.com/arnaucube/eth-kzg-ceremony-alt
load("bls12-381.sage") # file from https://github.com/arnaucube/math/blob/master/bls12-381.sage
e = Pairing()
def new_empty_SRS(nG1, nG2):
g1s = [None] * nG1
g2s = [None] * nG2
for i in range(0, nG1):
g1s[i] = e.G1
for i in range(0, nG2):
g2s[i] = e.G2
return [g1s, g2s]
def new_tau(random):
return e.F1(random)
def compute_contribution(new_tau, prev_srs):
g1s = [None] * len(prev_srs[0])
g2s = [None] * len(prev_srs[1])
srs = [g1s, g2s]
Q = e.r
# compute [τ'⁰]₁, [τ'¹]₁, [τ'²]₁, ..., [τ'ⁿ⁻¹]₁, where n = len(prev_srs.G1s)
for i in range(0, len(prev_srs[0])):
srs[0][i] = (new_tau^i) * prev_srs[0][i]
# compute [τ'⁰]₂, [τ'¹]₂, [τ'²]₂, ..., [τ'ⁿ⁻¹]₂, where n = len(prev_srs.G2s)
for i in range(0, len(prev_srs[1])):
srs[1][i] = (new_tau^i) * prev_srs[1][i]
return srs
def generate_proof(tau, prev_srs, new_srs):
# g_1^{tau'} = g_1^{p * tau} = SRS_G1s[1] * p
g1_ptau = prev_srs[0][1] * tau
# g_2^{p}
g2_p = tau * e.G2
return [g1_ptau, g2_p]
def verify(prev_srs, new_srs, proof):
# 1. check that elements of the newSRS are valid points
for i in range(0, len(new_srs[0])-1):
assert new_srs[0][i] != None
assert new_srs[0][i] != e.E1(0)
assert new_srs[0][i] in e.E1
for i in range(0, len(new_srs[1])-1):
assert new_srs[1][i] != None
assert new_srs[1][i] != e.E2(0)
assert new_srs[1][i] in e.E2
# 2. check proof.G1PTau == newSRS.G1Powers[1]
assert proof[0] == new_srs[0][1]
# 3. check newSRS.G1s[1] (g₁^τ'), is correctly related to prev_srs.G1s[1] (g₁^τ)
# e([τ]₁, [p]₂) == e([τ']₁, [1]₂)
assert e.pair(prev_srs[0][1], proof[1]) == e.pair(new_srs[0][1], e.G2)
# 4. check newSRS following the powers of tau structure
# i) e([τ'ⁱ]₁, [τ']₂) == e([τ'ⁱ⁺¹]₁, [1]₂), for i ∈ [1, n−1]
for i in range(0, len(new_srs[0])-1):
assert e.pair(new_srs[0][i], new_srs[1][1]) == e.pair(new_srs[0][i+1], e.G2)
# ii) e([τ']₁, [τ'ʲ]₂) == e([1]₁, [τ'ʲ⁺¹]₂), for j ∈ [1, m−1]
for i in range(0, len(new_srs[1])-1):
assert e.pair(new_srs[0][1], new_srs[1][i]) == e.pair(e.G1, new_srs[1][i+1])
(prev_srs) = new_empty_SRS(5, 3)
random = 12345
tau = new_tau(random)
new_srs = compute_contribution(tau, prev_srs)
proof = generate_proof(tau, prev_srs, new_srs)
verify(prev_srs, new_srs, proof)