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- W3037762284 abstract "We propose two new supersingular isogeny-based public key encryptions: SiGamal and C-SiGamal. They were developed by giving an additional point of the order $$2^r$$ to CSIDH. SiGamal is similar to ElGamal encryption, while C-SiGamal is a compressed version of SiGamal. We prove that SiGamal and C-SiGamal are IND-CPA secure without using hash functions under a new assumption: the P-CSSDDH assumption. This assumption comes from the expectation that no efficient algorithm can distinguish between a random point and a point that is the image of a public point under a hidden isogeny. Next, we propose a Naor-Reingold type pseudo random function (PRF) based on SiGamal. If the P-CSSDDH assumption and the CSSDDH $$^*$$ assumption, which guarantees the security of CSIDH that uses a prime p in the setting of SiGamal, hold, then our proposed function is a pseudo random function. Moreover, we estimate that the computational costs of group actions to compute our proposed PRF are about $$sqrt{frac{8T}{3pi }}$$ times that of the group actions in CSIDH, where T is the Hamming weight of the input of the PRF. Finally, we experimented with group actions in SiGamal and C-SiGamal. The computational costs of group actions in SiGamal-512 with a 256-bit plaintext message space were about 2.62 times that of a group action in CSIDH-512." @default.
- W3037762284 created "2020-07-02" @default.
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- W3037762284 date "2020-01-01" @default.
- W3037762284 modified "2023-10-17" @default.
- W3037762284 title "SiGamal: A Supersingular Isogeny-Based PKE and Its Application to a PRF" @default.
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- W3037762284 doi "https://doi.org/10.1007/978-3-030-64834-3_19" @default.
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