Public-Key Cryptosystem Based on Isogenies

By A. Rostovtsev, A. Stolbunov. IACR Cryptology ePrint Archive, 2006

358 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b8e1d6a2bab818aae08e08c103a6e790bda98df1

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Citations in the corpus

Post-quantum cryptography (2008, unknown): “We do not describe isogeny-based cryptography [20, 21, 22], for example, and we do not discuss Kuperberg’s algorithm [23].”
Towards Post-Quantum Blockchain: A Review on Blockchain Cryptography Resistant to Quantum Computing Attacks (2020, methodology): “These schemes are based on the isogeny protocol for ordinary elliptic curves presented in [124], but enhanced to withstand the quantum attack detailed in [125].”
Constructing elliptic curve isogenies in quantum subexponential time (2010, background): “Although quantum attacks are known against several cryptographic protocols of an algebraic nature [12, 19, 34], until now there has been no nontrivial quantum algorithm for constructing isogenies.”
CSIDH: An Efficient Post-Quantum Commutative Group Action (2018, methodology): “Starting from these observations, the desired adaptation of the Couveignes–Rostovtsev–Stolbunov scheme almost unrolls itself; the details can be found in Section 4.”
An Efficient Key Recovery Attack on SIDH (2023, unknown): “In particular, it cannot be adjusted in an obvious way to attack primitives that do not reveal this information, such as CRS/CSIDH [10], [39], [7] and SQISign [12], and the general supersingular isogeny path problem remains unaﬀected [44].”
Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies (2011, methodology): “In this section we present a key-exchange protocol and a public-key cryptosystem analogous to those of [34, 43], and a zero-knowledge identification scheme, all using supersingular elliptic curves.”