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

TY - JOUR

T1 - Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting

AU - Hazay, Carmit

AU - Mikkelsen, Gert Læssøe

AU - Rabin, Tal

AU - Toft, Tomas

AU - Nicolosi, Angelo Agatino

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Paillier

KW - RSA generation

KW - Secure two-party computation

KW - Threshold encryption scheme

UR - https://www.scopus.com/pages/publications/85044934853

U2 - 10.1007/s00145-017-9275-7

DO - 10.1007/s00145-017-9275-7

M3 - Journal article

AN - SCOPUS:85044934853

SN - 0933-2790

VL - 32

SP - 265

EP - 323

JO - Journal of Cryptology

JF - Journal of Cryptology

IS - 2

ER -