Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting

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...

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Bibliographic Details
Published in:	Journal of cryptology Vol. 32; no. 2; pp. 265 - 323
Main Authors:	Hazay, Carmit, Mikkelsen, Gert Læssøe, Rabin, Tal, Toft, Tomas, Nicolosi, Angelo Agatino
Format:	Journal Article
Language:	English
Published:	New York Springer US 15-04-2019 Springer Nature B.V
Subjects:	Coding and Information Theory Combinatorics Communications Engineering Computational Mathematics and Numerical Analysis Computer Science Cryptography Data encryption Distributed generation Encryption Networks Probability Theory and Stochastic Processes Protocol Public Key Infrastructure Security Threshold encryption scheme Paillier Secure two-party computation RSA generation
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Summary:	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. Our second contribution is a complete Paillier (in: EUROCRYPT, pp 223–238, 1999 ) threshold encryption scheme in the two-party setting with security against malicious attacks. We further describe how to extend our protocols to the multiparty setting with dishonest majority. Our RSA key generation protocol is comprised of the following subprotocols: ( 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 for the public key and is comprised of the following subprotocols: ( i ) a distributed generation of the corresponding secret key shares and ( ii ) a distributed decryption protocol for decrypting according to Paillier.
ISSN:	0933-2790 1432-1378
DOI:	10.1007/s00145-017-9275-7