The Learning with Errors (LWE) problem has become a central building block of modern cryptographic constructions. This work collects and presents hardness results for concrete instances of LWE. Inâ€¦ (More)

Achieving fully homomorphic encryption was a longstanding open problem in cryptography until it was resolved by Gentry in 2009. Soon after, several homomorphic encryption schemes were proposed. Theâ€¦ (More)

Traditional encryption schemes, both symmetric and asymmetric, were not designed to respect the algebraic structure of the plaintext and ciphertext spaces. Many schemes, such as Elgamal (resp. e.g.â€¦ (More)

The security of many cryptographic schemes has been based on special instances of the Learning with Errors (LWE) problem, e.g., Ring-LWE, LWE with binary secret, or LWE with ternary error. However,â€¦ (More)

In most RLWE-based homomorphic encryption schemes the native plaintext elements are polynomials in a rting Zt[x]/(x+1), where n is a power of 2, and t an integer modulus. For performing integer orâ€¦ (More)

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 Î´-subgaussian random variables usedâ€¦ (More)

Traditional encryption schemes, both symmetric and asymmetric, were not designed to respect the algebraic structure of the plaintext and ciphertext spaces. Many schemes, such as ElGamal (resp. e.g.â€¦ (More)