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Conference Papers Year : 2023

A Direct Key Recovery Attack on SIDH

Abstract

We present an attack on SIDH utilising isogenies between polarized products of two supersingular elliptic curves. In the case of arbitrary starting curve, our attack (discovered independently from [8]) has subexponential complexity, thus significantly reducing the security of SIDH and SIKE. When the endomorphism ring of the starting curve is known, our attack (here derived from [8]) has polynomial-time complexity assuming the generalised Riemann hypothesis. Our attack applies to any isogeny-based cryptosystem that publishes the images of points under the secret isogeny, for example Séta and B-SIDH. It does not apply to CSIDH, CSI-FiSh, or SQISign.
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hal-04023441 , version 1 (10-03-2023)

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Luciano Maino, Chloe Martindale, Lorenz Panny, Giacomo Pope, Benjamin Wesolowski. A Direct Key Recovery Attack on SIDH. Advances in Cryptology – EUROCRYPT 2023, 2023, Lyon, France. pp.448-471, ⟨10.1007/978-3-031-30589-4_16⟩. ⟨hal-04023441⟩
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