Welcome to the resource topic for 2022/1193
Title:
Knowledge Encryption and Its Applications to Simulatable Protocols With Low Round-Complexity
Authors: Yi Deng, Xinxuan Zhang
Abstract:We introduce a new notion of public key encryption, knowledge encryption, for which its ciphertexts can be reduced to the public-key, i.e., any algorithm that can break the ciphertext indistinguishability can be used to extract the (partial) secret key. We show that knowledge encryption can be built solely on any two-round oblivious transfer with game-based security, which are known based on various standard (polynomial-hardness) assumptions, such as the DDH, the Quadratic(N^{th}) Residuosity or the LWE assumption.
We use knowledge encryption to construct the first three-round (weakly) simulatable oblivious transfer. This protocol satisfies (fully) simulatable security for the receiver, and weakly simulatable security ((T, \epsilon)-simulatability) for the sender in the following sense: for any polynomial T and any inverse polynomial \epsilon, there exists an efficient simulator such that the distinguishing gap of any distinguisher of size less than T is at most \epsilon.
Equipped with these tools, we construct a variety of fundamental cryptographic protocols with low round-complexity, assuming only the existence of two-round oblivious transfer with game-based security. These protocols include three-round delayed-input weak zero knowledge argument, three-round weakly secure two-party computation, three-round concurrent weak zero knowledge in the BPK model, and a two-round commitment with weak security under selective opening attack. These results improve upon the assumptions required by the previous constructions. Furthermore, all our protocols enjoy the above (T, \epsilon)-simulatability (stronger than the distinguisher-dependent simulatability), and are
quasi-polynomial time simulatable under the same (polynomial hardness) assumption.
ePrint: https://eprint.iacr.org/2022/1193
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