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bulletproofs polynomial commitment: verifier do fast computation of b. comment showing math behind it.

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narodnik
2021-09-22 16:21:08 +02:00
parent e5d87f7d5a
commit 28b7f876b0
1 changed files with 19 additions and 0 deletions
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script/research/bltprf/poly.sage
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@@ -212,6 +212,25 @@ assert a == dot([s_i^-1 for s_i in s], list(final_poly))
assert b_1[0] == dot(s, [x^i for i in range(n)])
b = b_1[0]
# Alternatively we have a faster form of calculating b which
# arises naturally from the structure of how it's computed.
#
# b = (1, x, x^2, x^3, x^4, x^5, x^6, x^7)
# i = 3
# b = ( 1 + u3 x^4,
# x (1 + u3 x^4),
# x^2 (1 + u3 x^4),
# x^3 (1 + u3 x^4))
# i = 2
# b = ( 1 + u3 x^4 + u2 x^2 (1 + u3 x^4),
# x (1 + u3 x^4 + u2 x^2 (1 + u3 x^4)))
# = ( (1 + u2 x^2)(1 + u3 x^4),
# x (1 + u2 x^2)(1 + u3 x^4))
# i = 1
# b = (1 + u1 x)(1 + u2 x^2)(1 + u3 x^4)
assert ((1 + challenge_1 * x)
* (1 + challenge_2 * x^2) * (1 + challenge_3 * x^4)) == b
msm = (P - int(v) * base_G[0] + int(iota) * s_poly_commitment
+ int(challenge_1^-1) * l_1 + int(challenge_1) * r_1
+ int(challenge_2^-1) * l_2 + int(challenge_2) * r_2