In the multi-user with corruptions (muc) setting there are n >1 users, and the goal is to prove that, even in the face of an adversary that adaptively corrupts users to expose their keys, un-corrupted users retain security. This can be considered for many primitives including signatures and encryption. Proofs of muc security, while possible, generally suffer a factor n loss in tightness, which can be large. This paper gives new proofs where this factor is reduced to the number c of corruptions, which in practice is much smaller than n. We refer to this as corruption-parametrized muc (cp-muc) security. We give a general result showing it for a class of games that we call local. We apply this to get cp-muc security for signature schemes (including ones in standards and in TLS 1.3) and some forms of public-key and symmetric encryption. Then we give dedicated cp-muc security proofs for some important schemes whose underlying games are not local, including the Hashed ElGamal and Fujisaki-Okamoto KEMs and authenticated key exchange. Finally, we give negative results to show optimality of our bounds.
International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT)
2024-12-11
2025-01-09