## Abstract

RSA is a popular public key algorithm. Its private key operation is modular exponentiation with a composite 2k-bit modulus that is the product of two kbit primes. Computing 2k-bit modular exponentiation can be sped up four fold with the Chinese Remainder Theorem (CRT), requiring two k-bit modular exponentiations (plus recombination). Multi-prime RSA is the generalization to the case where the modulus is a product of r ≥ 3 primes of (roughly) equal bit-length, 2k/r. Here, CRT trades 2k-bit modular exponentiation with r modular exponentiations, with 2k/r-bit moduli (plus recombination). This paper discusses multi-prime RSA with key lengths (=2k) of 2048/3072/4096 bits, and r = 3 or r = 4 primes. With these parameters, the security of multi-prime RSA is comparable to that of classical RSA. We show how to optimize multi-prime RSA on modern processors, by parallelizing r modular exponentiations and leveraging “vector” instructions, achieving performance gains of up to 5.07x.

Original language | English |
---|---|

Title of host publication | Information Technology |

Subtitle of host publication | New Generations - 13th International Conference on Information Technology |

Editors | Shahram Latifi |

Publisher | Springer Verlag |

Pages | 237-245 |

Number of pages | 9 |

ISBN (Print) | 9783319324661 |

DOIs | |

State | Published - 2016 |

Event | 13th International Conference on Information Technology- New Generations, ITNG 2016 - Las Vegas, United States Duration: 4 Apr 2016 → 6 Apr 2016 |

### Publication series

Name | Advances in Intelligent Systems and Computing |
---|---|

Volume | 448 |

ISSN (Print) | 2194-5357 |

### Conference

Conference | 13th International Conference on Information Technology- New Generations, ITNG 2016 |
---|---|

Country/Territory | United States |

City | Las Vegas |

Period | 4/04/16 → 6/04/16 |

### Bibliographical note

Publisher Copyright:© Springer International Publishing Switzerland 2016.

## Keywords

- AVX2
- AVX512
- Haswell broadwell skylake
- Multi-prime RSA
- RSA

## ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science (all)