Robustness of the Learning with Errors Assumption

Abstract

Abstract: Starting with the work of Ishai-Sahai-Wagner and Micali-Reyzin, a new goal has been set within the theory of cryptography community, to design cryptographic primitives that are secure against large classes of side-channel attacks. Recently, many works have focused on designing various cryptographic primitives that are robust (retain security) even when the secret key is “leaky”, under various intractability assumptions. In this work we propose to take a step back and ask a more basic question: which of our cryptographic assumptions (rather than cryptographic schemes) are robust in presence of leakage of their underlying secrets? Our main result is that the hardness of the learning with error (LWE) problem implies its hardness with leaky secrets. More generally, we show that the standard LWE assumption implies that LWE is secure even if the secret is taken from an arbitrary distribution with sufficient entropy, and even in the presence of hard-to-invert auxiliary inputs. We exhibit various applications of this result. 1. Under the standard LWE assumption, we construct a symmetric-key encryption scheme that is robust to secret key leakage, and more generally maintains security even if the secret key is taken from an arbitrary distribution with sufficient entropy (and even in the presence of hard-to-invert auxiliary inputs).