an:07214302
Zbl 1448.94243
Ferradi, Houda; G??raud, R??mi; Guilley, Sylvain; Naccache, David; Tibouchi, Mehdi
Recovering secrets from prefix-dependent leakage
EN
J. Math. Cryptol. 14, 15-24 (2020).
00450255
2020
j
94A62 11T71
Galton-Watson process; discrete logarithm problem; cryptanalysis
Summary: We discuss how to recover a secret bitstring given partial information obtained during a computation over that string, assuming the computation is a deterministic algorithm processing the secret bits sequentially. That abstract situation models certain types of side-channel attacks against discrete logarithm and RSA-based cryptosystems, where the adversary obtains information not on the secret exponent directly, but instead on the group or ring element that varies at each step of the exponentiation algorithm.
Our main result shows that for a leakage of a single bit per iteration, under suitable statistical independence assumptions, one can recover the whole secret bitstring in polynomial time. We also discuss how to cope with imperfect leakage, extend the model to \(k\)-bit leaks, and show how our algorithm yields attacks on popular cryptosystems such as (EC)DSA.