Zvika Brakerski, Vinod Vaikuntanathan

We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption. Applying known results on LWE, the security of our scheme is based on the worst-case hardness of ``short vector problems'' on arbitrary lattices.

Our construction improves on previous works in two ... more >>>

Eli Ben-Sasson, iddo Ben-Tov, Ivan Bjerre Damgard, Yuval Ishai, Noga Ron-Zewi

Several well-known public key encryption schemes, including those of Alekhnovich (FOCS 2003), Regev (STOC 2005), and Gentry, Peikert and Vaikuntanathan (STOC 2008), rely on the conjectured intractability of inverting noisy linear encodings. These schemes are limited in that they either require the underlying field to grow with the security parameter, ... more >>>

Andrej Bogdanov, Miguel Cueto Noval, Charlotte Hoffmann, Alon Rosen

The continuous learning with errors (CLWE) problem was recently introduced by Bruna

et al. (STOC 2021). They showed that its hardness implies infeasibility of learning Gaussian

mixture models, while its tractability implies efficient Discrete Gaussian Sampling and thus

asymptotic improvements in worst-case lattice algorithms. No reduction between CLWE and

LWE ...
more >>>

Sagnik Saha, Nikolaj Schwartzbach, Prashant Nalini Vasudevan

In the average-case $k$-SUM problem, given $r$ integers chosen uniformly at random from $\{0,\ldots,M-1\}$, the objective is to find a set of $k$ numbers that sum to $0$ modulo $M$ (this set is called a ``solution''). In the related $k$-XOR problem, given $k$ uniformly random Boolean vectors of length $\log{M}$, ... more >>>

Yilei Chen, Jiatu Li

A recent line of research has introduced a systematic approach to explore the complexity of explicit construction problems through the use of meta problems, namely, the range avoidance problem (abbrev. Avoid) and the remote point problem (abbrev. RPP). The upper and lower bounds for these meta problems provide a unified ... more >>>