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fix
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10
DESIGN.md
10
DESIGN.md
@ -348,13 +348,13 @@ creating a proof pi = ECVRF_prove(pk, sk, message):
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Verify(pk, pi, message) for one message and its signature:
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- (gamma, c, s) = pi
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- ```
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```
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u = pk^c * g^s
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= g^(sk*c)*g^(k - c*sk)
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= g^k
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```
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- h = ECVRF_hash_to_curve(pk, message)
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- ```
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```
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v = gamma^c * h^s
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= h^(sk*c)*h^(k - c*sk)
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= h^k
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@ -373,7 +373,7 @@ Aggregate(pk', pi', [pk], PI) with [pk] list of public keys and PI aggregated si
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- set W' = h_0^-s_1 * h_1^-s_0
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- else:
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- W == (h_0 ^ (s_0 - S) * .. * h_n^(s_n - S))
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- ```
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```
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W' = W * (h_0^-s') * .. * (h_n^-s') * (h'^-S)
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= (h_0 ^ (s_0 - S - s') * .. * h_n^(s_n - S - s')) * h'^(s' - S')
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= (h_0 ^ (s_0 - S') * .. * h_n^(s_n - S')) * h'^(s' - S')
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@ -390,14 +390,14 @@ Verify([pk], PI, [message]):
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- p_i = pk_i^c_i
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- h_i = ECVRF_hash_to_curve(pk_i, message_i)
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- v_i = gamma_i^c_i * h_i^S
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- ```
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```
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U = (p_0* .. * p_n) * g^S
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= pk_0^c_0 * .. * pk_n ^ c_n * g^((k_0 - c_0*sk_0) + .. + (k_n - c_n*sk_n))
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= g^(sk0 * c_0 + .. + sk_n * c_n + (k_0 - c_0*sk_0) + .. + (k_n - c_n*sk_n))
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= g^(k_0 + .. + k_n)
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```
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-```
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```
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V = v_0 * .. * v_n * W
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= gamma_0^c_0 * .. * gamma_n^c_n * h_0^S * .. * h_n^S * h_0^(s_0 - S) * .. * h_n^(s_n - S)
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= h_0^(sk_0*c_0) * .. * h_n^(sk_n*c_n) * h_0^s_0 * .. * h_n^s_n
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