Paul Kirchner

An Improved BKW Algorithm for LWE with Applications to Cryptography and Lattices

In this paper, we study the Learning With Errors problem and its binary variant, where secrets and errors are binary or taken in a small interval. We introduce a new variant of the Blum, Kalai and Wasserman algorithm, relying on a quantization step that generalizes and fine-tunes modulus switching. In general this new technique yields a significant gain in the constant in front of the exponent in the overall complexity. We illustrate this by solving p within half a day a LWE instance with dimension n = 128, modulus

Revisiting Lattice Attacks on Overstretched NTRU Parameters

q = n^2

Computing Generator in Cyclotomic Integer Rings

, Gaussian noise

Efficient and Provable White-Box Primitives

\alpha = 1/(\sqrt{n/\pi} \log^2 n)

Homomorphic Evaluation of Lattice-Based Symmetric Encryption Schemes

and binary secret, using

Fast Lattice-Based Encryption: Stretching Spring

2^{28}

Improved Generalized Birthday Attack.

samples, while the previous best result based on BKW claims a time complexity of

Comparison between Subfield and Straightforward Attacks on NTRU.

2^{74}

Computing Generator in Cyclotomic Integer Rings - A Subfield Algorithm for the Principal Ideal Problem in L |Δ𝕂| (½) and Application to the Cryptanalysis of a FHE Scheme.

with

Time-Memory Trade-Off for Lattice Enumeration in a Ball.

2^{60}