Abstract
We put forward two new measures of security for threshold schemes secure in the adaptive adversary model: security under concurrent composition; and security without the assumption of reliable erasure. Using novel constructions and analytical tools, in both these settings, we exhibit efficient secure threshold protocols for a variety of cryptographic applications. In particular, based on the recent scheme by Cramer-Shoup, we construct adaptively secure threshold cryptosystems secure against adaptive chosen ciphertext attack under the DDH intractability assumption. Our techniques are also applicable to other cryptosystems and signature schemes, like RSA, DSS, and ElGamal. Our techniques include the first efficient implementation, for a wide but special class of protocols, of secure channels in erasure-free adaptive model.
Of independent interest, we present the notion of a committed proof.
This extended abstract is a concise presentation of two independent results by Lysyanskaya [Lys00] and Jarecki and Lysyanskaya [JL00]. Lysyanskaya [Lys00] introduces the concurrent model, presents the notion of a committed proof, and constructs threshold schemes secure against the adaptive adversary in the concurrent model; Jarecki and Lysyanskaya [JL00] introduce the erasure-free model, and present threshold schemes secure against the adaptive adversary in this model, including the efficient implementation of secure channels.
Part of this research was carried out while the author was visiting IBM Zurich Research Laboratory.
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Jarecki, S., Lysyanskaya, A. (2000). Adaptively Secure Threshold Cryptography: Introducing Concurrency, Removing Erasures. In: Preneel, B. (eds) Advances in Cryptology — EUROCRYPT 2000. EUROCRYPT 2000. Lecture Notes in Computer Science, vol 1807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45539-6_16
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