We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.

Most lattice-based cryptographic schemes which enjoy a security proof suffer from huge key sizes and heavy computations. This is also true for the simpler case of identification protocols. Recent progress on ideal lattices has significantly improved the efficiency, and made it possible to implement practical lattice-based cryptography on constrained devices like FPGAs and smart phones. However,...

We construct a simple fully homomorphic encryption scheme, using only elementary modular arithmetic. We use Gentry’s technique to construct fully homomorphic scheme from a “bootstrappable” somewhat homomorphic scheme. However, instead of using ideal lattices over a polynomial ring, our bootstrappable encryption scheme merely uses addition and multiplication over the integers. The main appeal of...

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

We introduce a lattice-based group signature scheme that provides several noticeable improvements over the contemporary ones: simpler construction, weaker hardness assumptions, and shorter sizes of keys and signatures. Moreover, our scheme can be transformed into the ring setting, resulting in a scheme based on ideal lattices, in which the public key and signature both have bitsize Õ(n·logN), f...

We prove that the theory of EXPTIME degrees with respect to polynomial time Turing and many-one reducibility is undecidable. To do so we use a coding method based on ideal lattices of Boolean algebras which was introduced in Nies 12]. The method can be applied in fact to all time classes given by a time constructible function which dominates all polynomials. By a similar method, we construct an...

The security of many lattice-based cryptographic schemes relies on the hardness of finding short vectors in integral lattices. We propose a new variant of the parallel Gauss sieve algorithm to compute such short vectors. It combines favorable properties of previous approaches resulting in reduced run time and memory requirement per node. Our publicly available implementation outperforms all pre...

In this paper, we analyze the security of cryptosystems using short generators over ideal lattices such as candidate multilinear maps by Garg, Gentry and Halevi and fully homomorphic encryption by Smart and Vercauteren. Our approach is based on a recent work by Cramer, Ducas, Peikert and Regev on analysis of recovering a short generator of an ideal in the q-th cyclotomic field for a prime power...

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

We describe plausible lattice-based constructions with properties that approximate the soughtafter multilinear maps in hard-discrete-logarithm groups, and show an example application of such multi-linear maps that can be realized using our approximation. The security of our constructions relies on seemingly hard problems in ideal lattices, which can be viewed as extensions of the assumed hardne...