The performance of error correcting codes in discrete and continuous fuzzy pairing protocols

In fuzzy pairing, two parties compare two bit strings which are supposed to be similar, but almost never identical. So A and B engage in a protocol to verify whether d(sA, sB) is less than some threshold T; if not, the parties abort and authentication failed. Here d() is to be taken as the Hamming distance. One standard protocol is the code-offset method: A computes a random vector x such that sA − x is a code word of some pre-agreed error-correcting x. Together they verify whether the code and sends x to B, who decodes sB − two decoded codewords are the same. A common secret key can be obtained subsequently, We cast this problem in a different context, in which A and B want to compare continuous signals, instead of discrete bit strings. We test the code offset method for four classes of error-correcting codes: Reed-Solomon (RS) Codes, Low Density Parity Check (LDPC) Codes, Repeat-Accumulate Codes (RAC) and Low Density Lattice Codes (LDLC). For similar error correction capability our results show that RS codes perform slowly, while LDPC and RAC which very similar are both really fast. LDLC has the best correction capabilities, but are slower because of their mathematical complexity. Our results can be generalized to fuzzy extractors.