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<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ikdpfme5h5egvnwtvvtjrnntyy" style="color: black;">Electronics</a>
Succinct Non-interactive Arguments of Knowledge (SNARks) are receiving a lot of attention as a core privacy-enhancing technology for blockchain applications. Polynomial commitment schemes are important building blocks for the construction of SNARks. Polynomial commitment schemes enable the prover to commit to a secret polynomial of the prover and convince the verifier that the evaluation of the committed polynomial is correct at a public point later. Bünz et al. recently presented a novel<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/electronics11010131">doi:10.3390/electronics11010131</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j3wly4berffp3lmm75ihoe5olq">fatcat:j3wly4berffp3lmm75ihoe5olq</a> </span>
more »... mial commitment scheme with no trusted setup in Eurocrypt'20. To provide a transparent setup, their scheme is built over an ideal class group of imaginary quadratic fields (or briefly, class group). However, cryptographic assumptions on a class group are relatively new and have, thus far, not been well-analyzed. In this paper, we study an approach to transpose Bünz et al.'s techniques in the discrete log setting because the discrete log setting brings a significant improvement in efficiency and security compared to class groups. We show that the transposition to the discrete log setting can be obtained by employing a proof system for the equality of discrete logarithms over multiple bases. Theoretical analysis shows that the transposition preserves security requirements for a polynomial commitment scheme.
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