Abstract
Threshold cryptosystems and signature schemes give ways to distribute trust throughout a group and increase the availability of cryptographic systems. A standard approach in designing these protocols is to base them upon existing single-server systems having the desired properties.
Two recent (single-server) signature schemes, one due to Gennaro et al., the other to Cramer and Shoup, have been developed which are provably secure using only standard number-theoretic hardness assumptions. Catalano et al. proposed a statically secure threshold implementation of these schemes. We improve their protocol to make it secure against an adaptive adversary, thus providing a threshold signature scheme with stronger security properties than any previously known.
As a tool, we also develop an adaptively secure, erasure-free threshold version of the Paillier cryptosystem.
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Lysyanskaya, A., Peikert, C. (2001). Adaptive Security in the Threshold Setting: From Cryptosystems to Signature Schemes. In: Boyd, C. (eds) Advances in Cryptology — ASIACRYPT 2001. ASIACRYPT 2001. Lecture Notes in Computer Science, vol 2248. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45682-1_20
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DOI: https://doi.org/10.1007/3-540-45682-1_20
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