International Association
for Cryptologic Research

The slightly subexponential algorithm of Blum, Kalai and Wasserman (BKW) provides a basis for assessing LPN/LWE security. However, its huge memory consumption strongly limits its practical applicability, thereby preventing precise security estimates for cryptographic LPN/LWE instantiations.We provide the first time-memory trade-offs for the BKW algorithm. For instance, we show how to solve LPN in dimension k in time $$2^{\frac{4}{3} \frac{k}{\log k} }$$ and memory $$2^{\frac{2}{3} \frac{k}{\log k} }$$. Using the Dissection technique due to Dinur et al. (Crypto ’12) and a novel, slight generalization thereof, we obtain fine-grained trade-offs for any available (subexponential) memory while the running time remains subexponential.Reducing the memory consumption of BKW below its running time also allows us to propose a first quantum version QBKW for the BKW algorithm.

Key-encapsulation mechanisms (KEMs) are a common stepping stone for constructing public-key encryption. Secure KEMs can be built from diverse assumptions, including ones related to integer factorization, discrete logarithms, error correcting codes, or lattices. In light of the recent NIST call for post-quantum secure PKE, the zoo of KEMs that are believed to be secure continues to grow. Yet, on the question of which is the most secure KEM opinions are divided. While using the best candidate might actually not seem necessary to survive everyday life situations, placing a wrong bet can actually be devastating, should the employed KEM eventually turn out to be vulnerable.We introduce KEM combiners as a way to garner trust from different KEM constructions, rather than relying on a single one: We present efficient black-box constructions that, given any set of ‘ingredient’ KEMs, yield a new KEM that is (CCA) secure as long as at least one of the ingredient KEMs is.As building blocks our constructions use cryptographic hash functions and blockciphers. Some corresponding security proofs require idealized models for these primitives, others get along on standard assumptions.