Abstract
We present a new construction of non-committing encryption schemes. Unlike the previous constructions of Canetti et al. (STOC ’96) and of Damgård and Nielsen (Crypto ’00), our construction achieves all of the following properties:
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Optimal round complexity. Our encryption scheme is a 2-round protocol, matching the round complexity of Canetti et al. and improving upon that in Damgård and Nielsen.
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Weaker assumptions. Our construction is based on trapdoor simulatable cryptosystems, a new primitive that we introduce as a relaxation of those used in previous works. We also show how to realize this primitive based on hardness of factoring.
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Improved efficiency. The amortized complexity of encrypting a single bit is O(1) public key operations on a constant-sized plaintext in the underlying cryptosystem.
As a result, we obtain the first non-committing public-key encryption schemes under hardness of factoring and worst-case lattice assumptions; previously, such schemes were only known under the CDH and RSA assumptions. Combined with existing work on secure multi-party computation, we obtain protocols for multi-party computation secure against a malicious adversary that may adaptively corrupt an arbitrary number of parties under weaker assumptions than were previously known. Specifically, we obtain the first adaptively secure multi-party protocols based on hardness of factoring in both the stand-alone setting and the UC setting with a common reference string.
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Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H. (2009). Improved Non-committing Encryption with Applications to Adaptively Secure Protocols. In: Matsui, M. (eds) Advances in Cryptology – ASIACRYPT 2009. ASIACRYPT 2009. Lecture Notes in Computer Science, vol 5912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10366-7_17
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