The state of elliptic curve cryptography

N Koblitz, A Menezes, S Vanstone - Designs, codes and cryptography, 2000 - Springer
Since the introduction of public-key cryptography by Diffie and Hellman in 1976, the
potential for the use of the discrete logarithm problem in public-key cryptosystems has been …

[PDF][PDF] An overview of independent component analysis and its applications

GR Naik, DK Kumar - Informatica, 2011 - informatica.si
The problem of source separation is an inductive inference problem. There is not enough
information to deduce the solution, so one must use any available information to infer the …

A direct key recovery attack on SIDH

L Maino, C Martindale, L Panny, G Pope… - … Conference on the …, 2023 - Springer
We present an attack on SIDH utilising isogenies between polarized products of two
supersingular elliptic curves. In the case of arbitrary starting curve, our attack (discovered …

SQISign: compact post-quantum signatures from quaternions and isogenies

L De Feo, D Kohel, A Leroux, C Petit… - Advances in Cryptology …, 2020 - Springer
We introduce a new signature scheme, SQISign,(for Short Quaternion and Isogeny
Signature) from isogeny graphs of supersingular elliptic curves. The signature scheme is …

CSIDH: an efficient post-quantum commutative group action

W Castryck, T Lange, C Martindale, L Panny… - Advances in Cryptology …, 2018 - Springer
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 …

An attack on SIDH with arbitrary starting curve

L Maino, C Martindale - Cryptology ePrint Archive, 2022 - eprint.iacr.org
We present an attack on SIDH which does not require any endomorphism information on the
starting curve. Our attack has subexponential complexity thus significantly reducing the …

CSI-FiSh: efficient isogeny based signatures through class group computations

W Beullens, T Kleinjung, F Vercauteren - … on the theory and application of …, 2019 - Springer
In this paper we report on a new record class group computation of an imaginary quadratic
field having 154-digit discriminant, surpassing the previous record of 130 digits. This class …

Feynman integrals

S Weinzierl - arXiv preprint arXiv:2201.03593, 2022 - Springer
Feynman integrals are indispensable for precision calculations in quantum field theory. They
occur as soon as one goes beyond the leading order in perturbative quantum field theory …

FESTA: fast encryption from supersingular torsion attacks

A Basso, L Maino, G Pope - International Conference on the Theory and …, 2023 - Springer
We introduce FESTA, an efficient isogeny-based public-key encryption (PKE) protocol based
on a constructive application of the SIDH attacks. At its core, FESTA is based on a novel …

SQISignHD: new dimensions in cryptography

P Dartois, A Leroux, D Robert, B Wesolowski - … Conference on the Theory …, 2024 - Springer
We introduce SQIsignHD, a new post-quantum digital signature scheme inspired by
SQIsign. SQIsignHD exploits the recent algorithmic breakthrough underlying the attack on …