At Asiacrypt 2020, Moriya et al. introduced two new IND-CPA secure supersingular isogeny based Public Key Encryption (PKE) protocols: SiGamal and C-SiGamal. Unlike the PKEs canonically derived from SIDH CSIDH, protocols provide security without use of hash functions. C-SiGamal are however not IND-CCA secure. suggested a variant that could be secure, but left its study as an open problem. In thi...

<p style='text-indent:20px;'>Since its proposal in Asiacrypt 2018, the commutative isogeny-based key exchange protocol (CSIDH) has spurred considerable attention to improving performance and re-evaluating classical quantum security guarantees. In this paper we discuss how optimal strategies employed by Supersingular Isogeny Diffie-Hellman (SIDH) agreement can be naturally extended CSIDH. ...

Recently, a radical isogeny was proposed to boost commutative supersingular Diffie–Hellman (CSIDH) implementation. Radical isogenies reduce the generation of kernel small prime order when implementing CSIDH. However, size base field increases, exponentiation, core component computing isogenies, becomes more computationally intensive. As inevitably grows resist quantum attack, so it is necessary...

In a secret sharing scheme, is distributed among several participants in such way that only any authorized subset of able to recover the secret. So far, security many schemes has been based on hardness some mathematical problems, as discrete logarithm and factorization. These problems can be solved polynomial time using Shor?s algorithm for quantum computer. this paper, we propose an efficient ...

We give a description of endomorphism rings of Weil restrictions of abelian varieties with respect to finite Galois extensions of fields. The results are applied to study the isogeny decompositions of Weil restrictions. 2000 Mathematics Subject Classification Primary: 14K15, Secondary: 11G10.

We exhibit the isogeny classes of supersingular abelian threefolds over F2n containing the Jacobian of a genus 3 curve. In particular, we prove that for even n > 6 there always exist a maximal and a minimal curve over F2n . All the curves can be obtained explicitly.