International Association for Cryptologic Research

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Found 2000 results
Computing Modular Polynomials
Denis Charles Kristin Lauter
We present a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves and are useful in many aspects of computational number theory and...
last revised 15 Jun 2005
Modular polynomials for genus 2
Reinier Broker Kristin Lauter
Modular polynomials are an important tool in many algorithms involving elliptic curves. In this article we generalize this concept to the genus 2 case. We give the theoretical framework describing the genus 2 modular...
received 9 Apr 2008
Cryptographic Hash Functions from Expander Graphs
Denis Xavier Charles Eyal Z. Goren Kristin E. Lauter
Jofc 2009
Computing Hilbert Class Polynomials
Juliana Belding Reinier Broker Andreas Enge Kristin Lauter
We present and analyze two algorithms for computing the Hilbert class polynomial H_D(X). The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese...
received 4 Feb 2008
Cryptographic hash functions from expander graphs
Denis Charles Eyal Goren Kristin Lauter
We propose constructing provable collision resistant hash functions from expander graphs. As examples, we investigate two specific families of optimal expander graphs for provable hash function constructions: the families of...
received 23 Jan 2006
Improved CRT Algorithm for Class Polynomials in Genus 2
Kristin Lauter Damien Robert
We present a generalization to genus~2 of the probabilistic algorithm of Sutherland for computing Hilbert class polynomials. The improvement over the Br{\"o}ker-Gruenewald-Lauter algorithm for the genus~2 case is that we do...
last revised 7 May 2013
Kristin E. Lauter
An arithmetic intersection formula for denominators of Igusa class polynomials
Kristin Lauter Bianca Viray
In this paper we prove an explicit formula for an arithmetic intersection number on the Siegel moduli space of abelian surfaces, generalizing the work of Bruinier-Yang and Yang. These intersection numbers allow one to compute...
received 30 Oct 2012
Full Cryptanalysis of LPS and Morgenstern Hash Function
Christophe Petit Kristin Lauter Jean-Jacques Quisquater
Collisions in the LPS cryptographic hash function of Charles, Goren and Lauter have been found by Zémor and Tillich, but it was not clear whether computing preimages was also easy for this hash function. We present a...
received 15 Apr 2008
Computing genus 2 curves from invariants on the Hilbert moduli space
Kristin Lauter Tonghai Yang
We give a new method for generating genus 2 curves over a finite field with a given number of points on the Jacobian of the curve. We define two new invariants for genus 2 curves as values of modular functions on the Hilbert...
received 17 May 2010
Denis Charles
Computing endomorphism rings of Jacobians of genus 2 curves over finite fields
David Freeman Kristin Lauter
We present probabilistic algorithms which, given a genus 2 curve C defined over a finite field and a quartic CM field K, determine whether the endomorphism ring of the Jacobian J of C is the full ring of integers in K. In...
last revised 30 May 2007
Signatures for Network Coding
Denis Charles Kamal Jain Kristin Lauter
This paper presents a practical digital signature scheme to be used in conjunction with network coding. Our scheme simultaneously provides authentication and detects malicious nodes that intentionally corrupt content on the...
last revised 16 Feb 2006
Supersingular isogeny graphs and endomorphism rings: reductions and solutions
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
Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms
Martin Roetteler Michael Naehrig Krysta M. Svore Kristin E. Lauter
Asiacrypt 2017
Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms
Martin Roetteler Michael Naehrig Krysta M. Svore Kristin Lauter
We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic...
last revised 30 Oct 2017
Genus 2 Curves with Complex Multiplication
Eyal Z. Goren Kristin E. Lauter
Genus 2 curves are useful in cryptography for both discrete-log based and pairing-based systems, but a method is required to compute genus 2 curves with Jacobian with a given number of points. Currently, all known methods...
received 23 Mar 2010
On the quaternion $\ell$-isogeny path problem
David Kohel Kristin Lauter Christophe Petit Jean-Pierre Tignol
Let $\cO$ be a maximal order in a definite quaternion algebra over $\mathbb{Q}$ of prime discriminant $p$, and $\ell$ a small prime. We describe a probabilistic algorithm, which for a given left $\cO$-ideal, computes a...
received 4 Jun 2014
EuroCrypt 2015 - Sofia, Bulgaria
Eurocrypt 2015 26 - 30 April 2015 Sofia, Bulgaria EUROCRYPT 2015 Home Event Program Invited talks Call for papers Paper submission Accepted papers Proceedings Rump Session Social Events Registration Practical info Venue Hotels...
Constructing Abelian Surfaces for Cryptography via Rosenhain Invariants
Craig Costello Alyson Deines-Schartz Kristin Lauter Tonghai Yang
This paper presents an algorithm to construct cryptographically strong genus 2 curves and their Kummer surfaces via Rosenhain invariants and related Kummer parameters. The most common version of the complex multiplication...
received 3 Jun 2014
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