We show polynomial-time quantum algorithms for the following problems: The SIS, LWE, and EDCP problems in their standard forms are as hard solving lattice worst case. However, variants that we can solve not parameter regimes known to be worst-case problems. Still, no classical or were of SIS LWE consider. For EDCP, our algorithm slightly extends result Ivanyos et al. (2018). Our use existing re...

We give a simple proof that the decisional Learning With Errors (LWE) problem with binary secrets is at least as hard as the standard LWE problem (with unrestricted, uniformly random secrets). This proves that the binary-secret LWE distribution is pseudorandom, under standard worst-case complexity assumptions on lattice problems. Our results are similar to those proved by (Brakerski, Langlois, ...

Motivated by the need to have secure strong designate verifier signatures (SDVS) even in the presence of quantum computers, a post-quantum lattice-based SDVS scheme is proposed based on the hardness of the short integer solution problem (SIS) and the learning with errors problem (LWE). The proposed SDVS scheme utilizes the Bonsai trees and pre-image sample-able function primitives to generate t...

We propose a new unidirectional proxy re-encryption scheme based on the hardness of the LWE problem. Our construction is collusionsafe and does not require any trusted authority for the re-encryption key generation. We extend a recent trapdoor definition for a lattice of Micciancio and Peikert. Our proxy re-encryption scheme is provably CCA-1 secure in the selective model under the LWE assumption.

We provide for the first time an asymptotic comparison of all known algorithms for the search version of the Learning with Errors (LWE) problem. This includes an analysis of several lattice-based approaches as well as the combinatorial BKW algorithm. Our analysis of the lattice-based approaches defines a general framework, in which the algorithms of Babai, Lindner-Peikert and several pruning st...

The LWE problem has been widely used in many constructions for post-quantum cryptography due to its strong security reduction from the worst-case of lattice hard problems and its lightweight operations. The PKE schemes based on the LWE problem have a simple and fast decryption, but the encryption phase is rather slow due to large parameter size for the leftover hash lemma or expensive Gaussian ...

Multi-key Fully homomorphic encryption (MFHE) schemes allow computation on the encrypted data under different keys. However, traditional multi-key FHE based Learning with errors (LWE) have undesirable property that is number of keys has to be fixed in advance. A dynamic scheme most versatile variant which information about participants not required before key generation. To support further exte...

As an invited speaker of the ACISP 2017 conference, Dongxi Liu recently introduced a new lattice-based encryption scheme (joint work with Li, Kim and Nepal) designed for lightweight IoT applications, and announced plans to submit it to the NIST postquantum competition. The new scheme is based on a variant of standard LWE called Compact-LWE, but is claimed to achieve high security levels in cons...

Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with Errors and show that there exists an efficient quantum learning algorithm (with polynomial sample and time complexity) for the Learning with Errors problem whe...

We present novel variants of the dual-lattice attack against LWE in the presence of an unusually short secret. These variants are informed by recent progress in BKW-style algorithms for solving LWE. Applying them to parameter sets suggested by the homomorphic encryption libraries HElib and SEAL v2.0 yields revised security estimates. Our techniques scale the exponent of the dual-lattice attack ...