Efficient RSA key generation and threshold paillier in the two-party setting

Authors:
Carmit Hazay;Gert Læssøe Mikkelsen;Tal Rabin;Tomas Toft
Affiliations:
Department of Computer Science, Aarhus University, Denmark;The Alexandra Institute, Denmark;IBM T.J.Watson Research Center;Department of Computer Science, Aarhus University, Denmark
Venue:
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Year:
2012

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Abstract

The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first non-generic fully simulatable protocol for distributively generating an RSA composite with security against malicious behavior in the two party setting. Our second contribution is a complete Paillier [37] threshold encryption scheme in the two-party setting with security against malicious behavior. Our RSA key generation is comprised of the following: (i) a distributed protocol for generation of an RSA composite, and (ii) a biprimality test for verifying the validity of the generated composite. Our Paillier threshold encryption scheme uses the RSA composite as public key and is comprised of: (i) a distributed generation of the corresponding secret-key shares and, (ii) a distributed decryption protocol for decrypting according to Paillier.