Results 31 to 40 of about 22,173,063 (167)
Improvement of the square-root Vélu's formulas for isogeny-based cryptography
JSIAM Letters, 2023 Summary: Isogeny-based cryptography is a promising candidate for post-quantum cryptography. Speeding up the isogeny computation of large prime degrees up to several thousands is a main research topic in isogeny-based cryptography. The currently most efficient method for computing isogenies is the square-root Vélu's formulas.
Saki Otsuki +2 more
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Batching CSIDH Group Actions using AVX-512
Transactions on Cryptographic Hardware and Embedded Systems, 2021 Commutative Supersingular Isogeny Diffie-Hellman (or CSIDH for short) is a recently-proposed post-quantum key establishment scheme that belongs to the family of isogeny-based cryptosystems.
Hao Cheng +4 more
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Highly Vectorized SIKE for AVX-512
Transactions on Cryptographic Hardware and Embedded Systems, 2022 It is generally accepted that a large-scale quantum computer would be capable to break any public-key cryptosystem used today, thereby posing a serious threat to the security of the Internet’s public-key infrastructure.
Hao Cheng +3 more
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Research Status, Challenges, and Future Development of Post-Quantum Cryptography [PDF]
中国工程科学As an important strategic resource for safeguarding national information security and the healthy development of digital economy, cryptography is the cornerstone of protecting the security of critical infrastructure, government affairs data, financial ...
Guizhen Zhu +5 more
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Constructing elliptic curve isogenies in quantum subexponential time
Journal of Mathematical Cryptology, 2014 Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew +2 more
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CTIDH: faster constant-time CSIDH
Transactions on Cryptographic Hardware and Embedded Systems, 2021 This paper introduces a new key space for CSIDH and a new algorithm for constant-time evaluation of the CSIDH group action. The key space is not useful with previous algorithms, and the algorithm is not useful with previous key spaces, but combining the ...
Gustavo Banegas +7 more
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IEEE Access, 2021 Since the introduction of the Supersingular isogeny Diffie–Hellman (SIDH) key exchange protocol by Jao and de Feo in 2011, it and its variation (SIKE) have gained significant attention as a promising candidate for post-quantum cryptography (PQC ...
Seog Chung Seo
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Mathematics of Isogeny Based Cryptography
CoRR, 2017 These lectures notes were written for a summer school on Mathematics for post-quantum cryptography in Thiès, Senegal. They try to provide a guide for Masters' students to get through the vast literature on elliptic curves, without getting lost on their way to learning isogeny based cryptography.
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The Role of Non-Positional Arithmetic on Efficient Emerging Cryptographic Algorithms
IEEE Access, 2020 Number representation systems establish ways in which numbers are mapped to computer architectures, and how operations over the numbers are translated into computer instructions.
Paulo Martins, Leonel Sousa
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A subexponential-time, polynomial quantum space algorithm for inverting the CM group action
Journal of Mathematical Cryptology, 2020 We present a quantum algorithm which computes group action inverses of the complex multiplication group action on isogenous ordinary elliptic curves, using subexponential time, but only polynomial quantum space.
Jao David +3 more
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