## Cryptology ePrint Archive: Report 2020/1516

How to compute all Pointproofs

Alin Tomescu

Abstract: In this short note, we explain how to reduce the time to compute all $N$ proofs in the Pointproofs vector commitment (VC) scheme by Gorbunov et al., from $O(N^2)$ time to $O(N\log{N})$. The key ingredient is representing the computation of all proofs as a product between a Toeplitz matrix and the committed vector, which can be computed fast using Discrete Fourier Transforms (DFTs). We quickly prototype our algorithm in C++ and show it is much faster than the naive algorithm for computing all proofs in Pointproofs.

Category / Keywords: public-key cryptography / vector-commitments, pointproofs, toeplitz, discrete-fourier-transform, dft

Date: received 3 Dec 2020, last revised 4 Dec 2020

Contact author: alint at vmware com

Available format(s): PDF | BibTeX Citation

Note: For an errata, see the latest GitHub diffs: https://github.com/alinush/pointproofs-note/compare/1eed43a..master

Short URL: ia.cr/2020/1516

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