Constant weight strings in constant time: a building block for code-based post-quantum cryptosystems

Abstract

Code based cryptosystems often need to encode either a message or a random bitstring into one of fixed length and fixed (Hamming) weight. The lack of an efficient and reliable bijective map presents a problem in building constructions around the said cryptosystems to attain security against active attackers. We present an efficiently computable, bijective function which yields the desired mapping. Furthermore, we delineate how the said function can be computed in constant time. We experimentally validate the effectiveness and efficiency of our approach, comparing it against the current state of the art solutions, achieving three to four orders of magnitude improvements in computation time, and validate its constant runtime.