[Resource Topic] 2023/1092: Adaptive attack for FESTA

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Adaptive attack for FESTA

Authors: Tomoki Moriya


Isogeny-based cryptography is one of the candidates for post-quantum cryptography. In 2023, Kani’s theorem breaks some isogeny-based schemes including SIDH, which was considered as a promising post-quantum scheme. Though Kani’s theorem damaged isogeny-based cryptography, some researchers try to dig into the applications of Kani’s theorem. FESTA is an isogeny-based trapdoor function that is one trial to apply Kani’s theorem to cryptography.

In this paper, we provide an adaptive attack for a possible PKE scheme based on FESTA trapdoor functions. Our attack reveals the secret key of the function. Our attack may be used if the recipient of the PKE scheme does not check whether the hidden matrix corresponding to the ciphertext is correct. In other words, the recipient can prevent our attack by checking the correctness of the matrix.

ePrint: https://eprint.iacr.org/2023/1092

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