Creating a Challenge for Ideal Lattices

Lattice-based cryptography is one of the candidates in the area of post-quantum cryptography. Cryptographic schemes with security reductions to hard lattice problems (like the Shortest Vector Problem SVP) offer an alternative to recent number theory-based schemes. In order to guarantee asymptotic efficiency, most lattice-based schemes are instantiated using polynomial rings over integers. These lattices are called ideal lattices. It is assumed that the hardness of lattice problems in lattices over integer rings remains the same as in regular lattices. In order to prove or disprove this assumption, we instantiate random ideal lattices that allow to test algorithms that solve SVP and its approximate version. The Ideal Lattice Challenge allows online submission of short vectors to enter a hall of fame for full comparison. We adjoin a set of first experiments and a first comparison of ideal and regular lattices.

[1]  Johannes A. Buchmann,et al.  Density of Ideal Lattices , 2009, Algorithms and Number Theory.

[2]  Phong Q. Nguyen,et al.  BKZ 2.0: Better Lattice Security Estimates , 2011, ASIACRYPT.

[3]  Richard Lindner,et al.  Explicit Hard Instances of the Shortest Vector Problem , 2008, PQCrypto.

[4]  Chen-Mou Cheng,et al.  Extreme Enumeration on GPU and in Clouds - - How Many Dollars You Need to Break SVP Challenges - , 2011, CHES.

[5]  U. Fincke,et al.  Improved methods for calculating vectors of short length in a lattice , 1985 .

[6]  Craig Gentry,et al.  Fully homomorphic encryption using ideal lattices , 2009, STOC '09.

[7]  Nicolas Gama,et al.  Lattice Enumeration Using Extreme Pruning , 2010, EUROCRYPT.

[8]  Ravi Kannan,et al.  Improved algorithms for integer programming and related lattice problems , 1983, STOC.

[9]  Daniele Micciancio,et al.  Faster exponential time algorithms for the shortest vector problem , 2010, SODA '10.

[10]  Phong Q. Nguyen,et al.  The LLL Algorithm - Survey and Applications , 2009, Information Security and Cryptography.

[11]  Damien Stehlé,et al.  Algorithms for the Shortest and Closest Lattice Vector Problems , 2011, IWCC.

[12]  Nicolas Gama,et al.  Predicting Lattice Reduction , 2008, EUROCRYPT.

[13]  Daniel Goldstein,et al.  On the equidistribution of Hecke points , 2003 .

[14]  Frederik Vercauteren,et al.  Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes , 2010, Public Key Cryptography.

[15]  Daniele Micciancio,et al.  A Deterministic Single Exponential Time Algorithm for Most Lattice Problems based on Voronoi Cell Computations ( Extended Abstract ) , 2009 .

[16]  Phong Q. Nguyen,et al.  Sieve algorithms for the shortest vector problem are practical , 2008, J. Math. Cryptol..

[17]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[18]  Claus-Peter Schnorr,et al.  Lattice basis reduction: Improved practical algorithms and solving subset sum problems , 1991, FCT.

[19]  Ravi Kumar,et al.  A sieve algorithm for the shortest lattice vector problem , 2001, STOC '01.

[20]  Michael Schneider,et al.  Computing shortest lattice vectors on special hardware , 2011 .