Florian Göpfert

Discrete Ziggurat: A Time-Memory Trade-Off for Sampling from a Gaussian Distribution over the Integers

Several lattice-based cryptosystems require to sample from a discrete Gaussian distribution over the integers. Existing methods to sample from such a distribution either need large amounts of memory or they are very slow. In this paper we explore a different method that allows for a flexible time-memory trade-off, offering developers freedom in choosing how much space they can spare to store precomputed values. We prove that the generated distribution is close enough to a discrete Gaussian to be used in lattice-based cryptography. Moreover, we report on an implementation of the method and compare its performance to existing methods from the literature. We show that for large standard deviations, the Ziggurat algorithm outperforms all existing methods.

On the Efficacy of Solving LWE by Reduction to Unique-SVP

We present a study of the concrete complexity of solving instances of the unique shortest vector problem (uSVP). In particular, we study the complexity of solving the Learning with Errors (LWE) problem by reducing the Bounded-Distance Decoding (BDD) problem to uSVP and attempting to solve such instances using the ‘embedding’ approach. We experimentally derive a model for the success of the approach, compare to alternative methods and demonstrate that for the LWE instances considered in this work, reducing to uSVP and solving via embedding compares favorably to other approaches.

On the Hardness of LWE with Binary Error: Revisiting the Hybrid Lattice-Reduction and Meet-in-the-Middle Attack

The security of many cryptographic schemes has been based on special instances of the Learning with Errors LWE problem, e.g., Ring-LWE, LWE with binary secret, or LWE with ternary error. However, recent results show that some subclasses are weaker than expected. In this work we show that LWE with binary error, introduced by Micciancio and Peikert, is one such subclass. We achieve this by applying the Howgrave-Graham attack on NTRU, which is a combination of lattice techniques and a Meet-in-the-Middle approach, to this setting. We show that the attack outperforms all other currently existing algorithms for several natural parameter sets. For instance, for the parameter set

High-Speed Signatures from Standard Lattices

n=256

Revisiting the Expected Cost of Solving uSVP and Applications to LWE

,

Estimation of the hardness of the learning with errors problem with a restricted number of samples

m=512