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Title:
Circle STARKs
Authors: Ulrich Haböck, David Levit, Shahar Papini
Abstract:Traditional STARKs require a cyclic group of a smooth order in the field. This allows efficient interpolation of points using the FFT algorithm, and writing constraints that involve neighboring rows. The Elliptic Curve FFT (ECFFT, Part I and II) introduced a way to make efficient STARKs for any finite field, by using a cyclic group of an elliptic curve. We show a simpler construction in the lines of ECFFT over the circle curve x^2 + y^2 = 1. When p + 1 is divisible by a large power of 2, this construction is as efficient as traditional STARKs and ECFFT. Applied to the Mersenne prime p = 2^{31} − 1, which has been recently advertised in the IACR eprint 2023:824, our preliminary benchmarks indicate a speed-up by a factor of 1.4 compared to a traditional STARK using the Babybear prime p = 2^{31} − 2^{27} + 1.
ePrint: https://eprint.iacr.org/2024/278
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