Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies

By Luca De Feo, David Jao, Jérôme Plût. Journal of Mathematical Cryptology, 2011

937 citations recorded by the source corpus.

Abstract We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases under the isogeny in order to allow the parties to construct a shared commutative square despite the non-commutativity of the endomorphism ring. We give a precise formulation of the necessary computational assumptions along with a discussion of their validity, and prove the security of our protocols under these assumptions. In addition, we present implementation results showing that our protocols are multiple orders of magnitude faster than previous isogeny-based cryptosystems over ordinary curves. This paper is an extended version of [Lecture Notes in Comput. Sci. 7071, Springer (2011), 19–34]. We add a new zero-knowledge identification scheme and detailed security proofs for the protocols. We also present a new, asymptotically faster, algorithm for key generation, a thorough study of its optimization, and new experimental data.

Subfields: Artificial Intelligence, Information Systems

View Paper: https://www.semanticscholar.org/paper/4f9a2d638c9784ebaac407070a10006c813cfb55

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Citations in the corpus

Quantum technology for military applications (2021, background): “For example, lattice-based cryptography [84], supersingular elliptic curve isogeny cryptography [85], hash-based [86] cryptography , multivariatebased [87] cryptography, code-based cryptography [88] and symmetric key quantum resistance.”
Post-Quantum Zero-Knowledge and Signatures from Symmetric-Key Primitives (2017, methodology): “The scheme is obtained by building upon the identification scheme in [39] and applying the Unruh transform.”
An Efficient Key Recovery Attack on SIDH (2023, positive): “This heavily outperforms previous attack strategies, such as the ones discussed in [11, § 5], [37], [31], [36], both in theory and in practice.”
Towards Post-Quantum Blockchain: A Review on Blockchain Cryptography Resistant to Quantum Computing Attacks (2020, background): “[126], [127], whose key size is usually in the order of a few thousand bits [128].”
Post-quantum cryptography (2008, neutral): “We do not describe isogeny-based cryptography [8, 9, 10], for example, and we do not discuss Kuperberg’s algorithm [11].”