Papers tagged as Isogenies
  1. CSIDH: An Efficient Post-Quantum Commutative Group Action 2018 Asiacrypt Isogenies KeyExchange PQC
    Wouter Castryck and Tanja Lange and Chloe Martindale and Lorenz Panny and Joost Renes

    We propose an efficient commutative group action suitable for non-interactive key exchange in a post-quantum setting. Our construction follows the layout of the Couveignes-Rostovtsev-Stolbunov cryptosystem, but we apply it to supersingular elliptic curves defined over a large prime field Fp, rather than to ordinary elliptic curves. The Diffie-Hellman scheme resulting from the group action allows for public-key validation at very little cost, runs reasonably fast in practice, and has public keys of only 64 bytes at a conjectured AES-128 security level, matching NIST’s post-quantum security category I.

  2. A Post-Quantum Digital Signature Scheme Based on Supersingular Isogenies 2017 FinancialCryptography Isogenies PQC Signatures
    Youngho Yoo, Reza Azarderakhsh, Amir Jalali, David Jao, Vladimir Soukharev

    We present the first general-purpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is an application of Unruh’s construction of non-interactive zero-knowledge proofs to an interactive zero-knowledge proof proposed by De Feo, Jao, and Plût. We implement our proposed scheme on an x86-64 PC platform as well as an ARM-powered device. We exploit the state-of-the-art techniques to speed up the computations for general C and assembly. Finally, we provide timing results for real world applications.

  3. Efficient compression of SIDH public keys 2017 Diffie-Hellman EllipticCurves Eurocrypt Isogenies PQC
    Craig Costello, David Jao, Patrick Longa, Michael Naehrig, Joost Renes, and David Urbanik

    Supersingular isogeny Diffie-Hellman (SIDH) is an attractive candidate for post-quantum key exchange, in large part due to its relatively small public key sizes. A recent paper by Azarderakhsh, Jao, Kalach, Koziel and Leonardi showed that the public keys defined in Jao and De Feo’s original SIDH scheme can be further compressed by around a factor of two, but reported that the performance penalty in utilizing this compression blew the overall SIDH runtime out by more than an order of magnitude. Given that the runtime of SIDH key exchange is currently its main drawback in relation to its lattice- and code-based post-quantum alternatives, an order of magnitude performance penalty for a factor of two improvement in bandwidth presents a trade-off that is unlikely to favor public-key compression in many scenarios.

    In this paper, we propose a range of new algorithms and techniques that accelerate SIDH public-key compression by more than an order of magnitude, making it roughly as fast as a round of standalone SIDH key exchange, while further reducing the size of the compressed public keys by approximately 12.5%. These improvements enable the practical use of compression, achieving public keys of only 330 bytes for the concrete parameters used to target 128 bits of quantum security and further strengthens SIDH as a promising post-quantum primitive.