Cryptology ePrint Archive: Report 2019/890

An Adaptive Attack on 2-SIDH

Samuel Dobson and Steven D. Galbraith and Jason LeGrow and Yan Bo Ti and Lukas Zobernig

Abstract: We present a polynomial-time adaptive attack on the 2-SIDH protocol. The 2-SIDH protocol is a special instance of the countermeasure proposed by Azarderakhsh, Jao and Leonardi to perform isogeny-based key exchange with static keys in the presence of an adaptive attack. This countermeasure has also been recently explicitly proposed by Kayacan.

Our attack extends the adaptive attack by Galbraith, Petit, Shani and Ti (GPST) to recover a static secret key using malformed points. The extension of GPST is non-trivial and requires learning additional information. In particular, the attack needs to recover intermediate elliptic curves in the isogeny path, and points on them. We also discuss how to extend the attack to k-SIDH when k > 2 and explain that the attack complexity is exponential in k.

Category / Keywords: public-key cryptography / cryptanalysis, supersingular isogeny Diffie-Hellman

Date: received 1 Aug 2019, last revised 5 Sep 2020

Contact author: samuel dobson nz at gmail com, s galbraith at auckland ac nz, jlegrow at waterloo ca, yanbo ti at gmail com, lukas zobernig at auckland ac nz

Available format(s): PDF | BibTeX Citation

Note: Updated paper.

Version: 20200905:102220 (All versions of this report)

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