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

• 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
• ISSN: 0933-2790; 1432-1378
• DOI: 10.1007/s00145-017-9275-7

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.