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Lecture notes in computer science

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

Carmit Hazay, Gert Læssøe Mikkelsen, Tal Rabin, Tomas Toft

Published Jan 1, 2012• 88 citations
Publisher
DOI
10.1007/978-3-642-27954-6_20

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

Carmit Hazay, Gert Læssøe Mikkelsen, Tal Rabin +1 more

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 complete Paillier [Pai99] threshold encryption scheme in the two-party setting with security against malicious behavior. Furthermore, we describe how to extend our protocols to the multiparty setting with dishonest majority. 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.

•Jan 1, 2011•0 citations

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

Carmit Hazay, Gert Læssøe Mikkelsen, Tal Rabin +2 more

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.

Journal of Cryptology•Feb 5, 2018•76 citations
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 complete Paillier [Pai99] threshold encryption scheme in the two-party setting with security against malicious behavior. Furthermore, we describe how to extend our protocols to the multiparty setting with dishonest majority. 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.
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.