Security estimates and parameter choice for lattice based cryptography are described in

Lattice-Based Cryptography (

*Micciancio & Regev*, Post Quantum Cryptography, 2009)Better Key Sizes (and Attacks) for LWE-Based Encryption (

*Lindner & Peikert*, CT-RSA 2011)On the concrete hardness of Learning with Errors (Albrecht, Payer & Scott, ePrint 2015)

For recent work on the experimental evaluation of lattice reduction algorithms used in cryptanalysis see

BKZ 2.0: Better Lattice Security Estimates (

*Chen & Nguyen*, Asiacrypt 2011)Solving BDD by Enumeration: An Update (

*Liu & Nguyen*, CT-RSA 2013)

Test challenges for various lattice problems of interest in cryptography are given in the following pages:

Lazy Modulus Switching for the BKW Algorithm on LWE (

*Albrecht, Faugere, Fitzpatrick & Perret*, PKC 2014)On the Complexity of the BKW Algorithm against LWE (

*Albrecht, Cid, Faugere, Fitzpatrick & Perret*, DCC 2015)On the Efficacy of Solving LWE by Reduction to Unique-SVP (

*Albrecht, Fitzpatrick & Gopfert*, ICISC 2013)Better Algorithms for LWE and LWR (

*Duc, Tramer & Vaudenay*, Eurocrypt 2015)

New Algorithms for Learning in Presence of Errors (Arora & Ge, ICALP 2011)

Algebraic Algorithms for LWE (Albrecht, Cid, Faugere & Perret, ePrint 2014)

On the Complexity of the Arora-Ge Algorithm against LWE (

*Albrecht, Cid, Faugere, Fitzpatrick & Perret*, SCC 2012)