Journal of Cryptology, volume 32, issue 2, pages 265-323

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

Carmit Hazay ¹

Gert Læssøe Mikkelsen ²

Tal Rabin ³

Tomas Toft ⁴

Angelo Agatino Nicolosi ⁵

Hide authors affiliations Show authors affiliations: 5 affiliations

Faculty of Engineering, Bar-Ilan University, Ramat Gan, Israel |

The Alexandra Institute, Aarhus, Denmark |

IBM T.J. Watson Research Center, Yorktown heights, USA |

⁴

Partisia, Aarhus N, Denmark |

⁵

YanchWare, Brædstrup, Denmark |

Publication type: Journal Article

Publication date: 2018-02-05

Springer Nature

Journal: Journal of Cryptology

SJR: 1.433

CiteScore: 7.1

Impact factor: 2.3

ISSN: 09332790, 14321378

DOI: 10.1007/s00145-017-9275-7

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Computer Science Applications

Applied Mathematics

Software

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. 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.

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Hazay C. et al. Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting // Journal of Cryptology. 2018. Vol. 32. No. 2. pp. 265-323.

GOST all authors (up to 50) Copy

Hazay C., Mikkelsen G. L., Rabin T., Toft T., Nicolosi A. A. Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting // Journal of Cryptology. 2018. Vol. 32. No. 2. pp. 265-323.

RIS |

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RIS Copy

TY - JOUR

DO - 10.1007/s00145-017-9275-7

UR - https://doi.org/10.1007/s00145-017-9275-7

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

T2 - Journal of Cryptology

AU - Hazay, Carmit

AU - Mikkelsen, Gert Læssøe

AU - Rabin, Tal

AU - Toft, Tomas

AU - Nicolosi, Angelo Agatino

PY - 2018

DA - 2018/02/05

PB - Springer Nature

SP - 265-323

IS - 2

VL - 32

SN - 0933-2790

SN - 1432-1378

ER -

BibTex |

Cite this

BibTex (up to 50 authors) Copy

@article{2018_Hazay,

author = {Carmit Hazay and Gert Læssøe Mikkelsen and Tal Rabin and Tomas Toft and Angelo Agatino Nicolosi},

title = {Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting},

journal = {Journal of Cryptology},

year = {2018},

volume = {32},

publisher = {Springer Nature},

month = {feb},

url = {https://doi.org/10.1007/s00145-017-9275-7},

number = {2},

pages = {265--323},

doi = {10.1007/s00145-017-9275-7}

}

MLA

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MLA Copy

Hazay, Carmit, et al. “Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting.” Journal of Cryptology, vol. 32, no. 2, Feb. 2018, pp. 265-323. https://doi.org/10.1007/s00145-017-9275-7.

Found error?

Publisher

Springer Nature

Journal

Journal of Cryptology

SJR

1.433

CiteScore

7.1

Impact factor

2.3

ISSN

09332790 (Print)

14321378 (Electronic)