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Title:
An attack on SIDH with arbitrary starting curve
Authors: Luciano Maino, Chloe Martindale
Abstract:We present an attack on SIDH which does not require any endomorphism information on the starting curve. Our attack is not polynomial-time, but significantly reduces the security of SIDH and SIKE; our analysis and preliminary implementation suggests that our algorithm will be feasible for the Microsoft challenge parameters p = 2^{110}3^{67}-1 on a regular computer. Our attack applies to any isogeny-based cryptosystem that publishes the images of points under the secret isogeny, for example Séta [26] and B-SIDH [9]. It does not apply to CSIDH [8], CSI-FiSh [3], or SQISign [11].
ePrint: https://eprint.iacr.org/2022/1026
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