Welcome to the resource topic for 2023/1468
QFESTA: Efficient Algorithms and Parameters for FESTA using Quaternion Algebras
Authors: Kohei Nakagawa, Hiroshi OnukiAbstract:
In 2023, Basso, Maino, and Pope proposed FESTA~(Fast Encryption from Supersingular Torsion Attacks), an isogeny-based public-key encryption (PKE) protocol that uses the SIDH attack for decryption. In the same paper, they proposed a parameter for that protocol, but the parameter requires high-degree isogeny computations. In this paper, we introduce QFESTA (Quaternion Fast Encapsulation from Supersingular Torsion Attacks), a new variant of FESTA that works with better parameters using quaternion algebras and achieves IND-CCA security in QROM. To realize our protocol, we construct a new algorithm to compute an isogeny of non-smooth degree using quaternion algebra and the SIDH attack. Our protocol relies solely on (2,2)-isogeny and 3-isogeny computations, promising a substantial reduction in computational costs. In addition, our protocol has significantly smaller data sizes for public keys and ciphertexts, approximately one-third the size of the original FESTA.
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