On error distributions in ring-based LWE
نویسندگان
چکیده
منابع مشابه
On error distributions in ring-based LWE
Since its introduction in 2010 by Lyubashevsky, Peikert and Regev, the ring learning with errors problem (ring-LWE) has become a popular building block for cryptographic primitives, due to its great versatility and its hardness proof consisting of a (quantum) reduction from ideal lattice problems. But, for a given modulus q and degree n number field K, generating ring-LWE samples can be perceiv...
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We develop a statistical framework to analyse the Ring-LWE processes of A Toolkit for Ring-LWE Cryptography (Eurocrypt 2013) and similar processes. We consider the δ-subgaussian random variables used in the Toolkit and elsewhere in the literature, and we give a simple and complete characterisation of such random variables. We then apply our results to the homomorphic cryptosystem provided as an...
متن کاملOn the tightness of the error bound in Ring-LWE
Since its introduction in 2010 by Lyubashevsky, Peikert and Regev, the Ring Learning With Errors problem (Ring-LWE) has been widely used as a building block for cryptographic primitives, due to its great versatility and its hardness proof consisting of a (quantum) reduction to ideal lattice problems. This reduction assumes a lower bound on the width of the error distribution that is often viola...
متن کاملRing-LWE Ciphertext Compression and Error Correction
Some lattice-based public key cryptosystems allow one to transform ciphertext from one lattice or ring representation to another e ciently and without knowledge of public and private keys. In this work we explore this lattice transformation property from cryptographic engineering viewpoint. We apply ciphertext transformation to compress Ring-LWE ciphertexts and to enable e cient decryption on a...
متن کاملLarge Modulus Ring-LWE ≥ Module-LWE
We present a reduction from the module learning with errors problem (MLWE) in dimension d and with modulus q to the ring learning with errors problem (RLWE) with modulus q. Our reduction increases the LWE error rate α by a quadratic factor in the ring dimension n and a square root in the module rank d for power-of-two cyclotomics. Since, on the other hand, MLWE is at least as hard as RLWE, we c...
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2016
ISSN: 1461-1570
DOI: 10.1112/s1461157016000280