https://github.com/samuelschlesinger/discrete-log-nizkp

A NIZKP of discrete logarithm solution.
https://github.com/samuelschlesinger/discrete-log-nizkp

Last synced: about 1 month ago
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A NIZKP of discrete logarithm solution.

• Host: GitHub
• URL: https://github.com/samuelschlesinger/discrete-log-nizkp
• Owner: SamuelSchlesinger
• Created: 2023-11-04T21:09:42.000Z (about 1 year ago)
• Default Branch: dev
• Last Pushed: 2023-11-05T12:03:12.000Z (about 1 year ago)
• Last Synced: 2024-10-27T19:10:17.873Z (3 months ago)
• Language: Rust
• Size: 3.91 KB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# NIZKP for Discrete Logarithms

Application of the Fiat-Shamir transform to the interactive proof of discrete logarithm.

Also includes an implementation of a signature scheme based on this approach.

## Interactive Proof

To prove that B = A^x (mod p),

1. Prover chooses a random number 0 <= r < p - 1 and sends the verifier h = A^r (mod p).

2. Verifier sends back a random bit b.

3. Prover sends s = (r + bx) (mod (p - 1)).

4. Verifier computes A^s (mod p) which should equal hB^b (mod p).

## Non-Interactive Version

The non-interactive version will choose M random numbers Rs, then compute Hs

via H[i] = A^R\[i\] (mod p). Then, they will hash the Hs to produce a seed to

randomly generate the Bs bits. Then the prover computes S[i] = (R[i] + B[i] *

x) (mod (p - 1)), and the proof consists of:

A, B, p, Hs, Ss.

The verifier checks that for all i, A^S\[i\] (mod p) = hB^B\[i\] (mod p).