International Association for Cryptologic Research

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Found 14000 results
Isogeny graphs with maximal real multiplication
Eprint
https://eprint.iacr.org/2014/230
Sorina Ionica Emmanuel Thomé
An isogeny graph is a graph whose vertices are principally polarizable abelian varieties and whose edges are isogenies between these varieties. In his thesis, Kohel describes the structure of isogeny graphs for elliptic curves...
last revised 17 Oct 2016
Sorina Ionica
Author
https://iacr.org/cryptodb/data/author.php?authorkey=5762
Université de Picardie
Isogeny graphs of ordinary abelian varieties
Eprint
https://eprint.iacr.org/2016/947
Ernest Hunter Brooks Dimitar Jetchev Benjamin Wesolowski
Fix a prime number $\ell$. Graphs of isogenies of degree a power of $\ell$ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian...
received 30 Sep 2016
Supersingular isogeny graphs and endomorphism rings: reductions and solutions
Eprint
https://eprint.iacr.org/2018/371
Kirsten Eisentraeger Sean Hallgren Kristin Lauter Travis Morrison Christophe Petit
In this paper, we study several related computational problems for supersingular elliptic curves, their isogeny graphs, and their endomorphism rings. We prove reductions between the problem of path finding in the...
last revised 17 Apr 2018
Pairing-based methods for genus 2 jacobians with maximal endomorphism ring
Eprint
https://eprint.iacr.org/2012/167
Sorina Ionica
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the \ell-Tate pairing in terms of the action of the Frobenius on the \ell-torsion of the Jacobian of a genus 2 curve. We apply similar...
last revised 31 Mar 2013
Constructing genus 3 hyperelliptic Jacobians with CM
Eprint
https://eprint.iacr.org/2016/328
Jennifer Balakrishnan Sorina Ionica Kristin Lauter Christelle Vincent
Given a sextic CM field K, we give an explicit method for finding all genus 3 hyperelliptic curves defined over the complex whose Jacobians are simple and have complex multiplication by the maximal order of this field, via an...
last revised 27 May 2016
Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem
Eprint
https://eprint.iacr.org/2017/053
Dimitar Jetchev Benjamin Wesolowski
Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multiplication. Any subgroup of...
last revised 27 Jan 2017
Emmanuel Thomé
Author
https://iacr.org/cryptodb/data/author.php?authorkey=614
Inria
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
Eprint
https://eprint.iacr.org/2018/132
Gora Adj Omran Ahmadi Alfred Menezes
We study the isogeny graphs of supersingular elliptic curves over finite fields, with an emphasis on the vertices corresponding to elliptic curves of $j$-invariant 0 and 1728.
last revised 19 Feb 2019
Supersingular Isogeny Graphs and Endomorphism Rings: Reductions and Solutions
Iacrpub
https://iacr.org/cryptodb/data/paper.php?pubkey=28562
Kirsten Eisenträger Sean Hallgren Kristin E. Lauter Travis Morrison Christophe Petit
Eurocrypt 2018
Towards practical key exchange from ordinary isogeny graphs
Eprint
https://eprint.iacr.org/2018/485
Luca De Feo Jean Kieffer Benjamin Smith
We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev–Stolbunov, long dismissed as impractical. We give algorithmic improvements that accelerate key exchange in this framework, and explore the...
received 21 May 2018
Towards Practical Key Exchange from Ordinary Isogeny Graphs
Iacrpub
https://iacr.org/cryptodb/data/paper.php?pubkey=29195
Luca De Feo Jean Kieffer Benjamin Smith
Asiacrypt 2018
We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev–Stolbunov, long dismissed as impractical. We give algorithmic improvements that accelerate key exchange in this framework, and explore the...
Hard and Easy Problems for Supersingular Isogeny Graphs
Eprint
https://eprint.iacr.org/2017/962
Christophe Petit Kristin Lauter
We consider the endomorphism ring computation problem for supersingular elliptic curves, constructive versions of Deuring's correspondence, and the security of Charles-Goren-Lauter's cryptographic hash function. We show that...
last revised 21 Feb 2018
SIDH on ARM: Faster Modular Multiplications for Faster Post-Quantum Supersingular Isogeny Key Exchange
Iacrpub
https://iacr.org/cryptodb/data/paper.php?pubkey=29036
Hwajeong Seo Zhe Liu Patrick Longa Zhi Hu
Tches 2018
We present high-speed implementations of the post-quantum supersingular isogeny Diffie-Hellman key exchange (SIDH) and the supersingular isogeny key encapsulation (SIKE) protocols for 32-bit ARMv7-A processors with NEON...
SIDH on ARM: Faster Modular Multiplications for Faster Post-Quantum Supersingular Isogeny Key Exchange
Eprint
https://eprint.iacr.org/2018/700
Hwajeong Seo Zhe Liu Patrick Longa Zhi Hu
We present high-speed implementations of the post-quantum supersingular isogeny Diffie-Hellman key exchange (SIDH) and the supersingular isogeny key encapsulation (SIKE) protocols for 32-bit ARMv7-A processors with NEON...
last revised 26 Jul 2018
Faster Cryptographic Hash Function From Supersingular Isogeny Graphs
Eprint
https://eprint.iacr.org/2017/1202
Javad Doliskani Geovandro C. C. F. Pereira Paulo S. L. M. Barreto
We propose a variant of the CGL hash, Charles et al. 2009, that is significantly faster than the original algorithm, and prove that it is preimage and collision resistant. For $n = \log p$ where $p$ is the characteristic of...
last revised 9 Apr 2019
Genus Two Isogeny Cryptography
Eprint
https://eprint.iacr.org/2019/177
E.V. Flynn Yan Bo Ti
We study $(\ell,\ell)$-isogeny graphs of principally polarised supersingular abelian surfaces (PPSSAS). The $(\ell,\ell)$-isogeny graph has cycles of small length that can be used to break the collision resistance assumption...
received 18 Feb 2019
External Reviewers, IACR EUROCRYPT 2010
https://iacr.org/archive/eurocrypt2010/external.html
External Reviewers, IACR EUROCRYPT 2010 Michel Abdalla Masayuki Abe Shweta Agrawal Martin Albrecht Davide Alessio Elena Andreeva Giuseppe Ateniese Roberto Avanzi Ali Bagherzandi Paulo Barreto Anja Becker Mihir Bellare Rikke...
Four-Dimensional GLV via the Weil Restriction
Iacrpub
https://iacr.org/cryptodb/data/paper.php?pubkey=24958
Aurore Guillevic Sorina Ionica
Asiacrypt 2013
On the Hardness of Computing Endomorphism Rings of Supersingular Elliptic Curves
Eprint
https://eprint.iacr.org/2017/986
Kirsten Eisentraeger Sean Hallgren Travis Morrison
Cryptosystems based on supersingular isogenies have been proposed recently for use in post-quantum cryptography. Three problems have emerged related to their hardness: computing an isogeny between two curves, computing the...
received 6 Oct 2017
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