### Abstract

We propose a public-key primitive modulo p^{k}q based on the RSA primitive. The decryption process of the proposed scheme is faster than those of two variants of PKCS #1 version 2.1, namely the RSA cryptosystem using Chinese remainder theorem (CRT) and the Multi-Prime RSA. The message M of the proposed scheme is decrypted from M mod p^{k} and M mod q using the CRT, where we apply the Hensel lifting to calculate M mod p^{k} from M mod p that requires only quadratic complexity O((log_{2} p)^{2}). Moreover, we propose a trick that avoids modular inversions used for the Hensel lifting, and thus the proposed algorithm can be computed without modular inversion. We implemented in software both the proposed scheme with 1024-bit modulus p^{2}g and the 1024-bit Multi-Prime RSA for modulus p _{1}p_{2}p_{3}, where p, q, p_{1}, p _{2}, p_{3} are 342bits. The improvements of the proposed scheme over the Multi-Prime RSA are as follows: The key generation is about 49% faster, the decryption time is about 42% faster, and the total secret key size is 33% smaller.

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

Pages (from-to) | 94-101 |

Number of pages | 8 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E87-A |

Issue number | 1 |

Publication status | Published - Jan 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics

### Cite this

^{k}q Using Hensel Lifting.

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E87-A*(1), 94-101.

**A Fast RSA-Type Public-Key Primitive Modulo p ^{k}q Using Hensel Lifting.** / Takagi, Tsuyoshi.

Research output: Contribution to journal › Article

^{k}q Using Hensel Lifting',

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E87-A, no. 1, pp. 94-101.

^{k}q Using Hensel Lifting. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. 2004 Jan 1;E87-A(1):94-101.

}

TY - JOUR

T1 - A Fast RSA-Type Public-Key Primitive Modulo pkq Using Hensel Lifting

AU - Takagi, Tsuyoshi

PY - 2004/1/1

Y1 - 2004/1/1

N2 - We propose a public-key primitive modulo pkq based on the RSA primitive. The decryption process of the proposed scheme is faster than those of two variants of PKCS #1 version 2.1, namely the RSA cryptosystem using Chinese remainder theorem (CRT) and the Multi-Prime RSA. The message M of the proposed scheme is decrypted from M mod pk and M mod q using the CRT, where we apply the Hensel lifting to calculate M mod pk from M mod p that requires only quadratic complexity O((log2 p)2). Moreover, we propose a trick that avoids modular inversions used for the Hensel lifting, and thus the proposed algorithm can be computed without modular inversion. We implemented in software both the proposed scheme with 1024-bit modulus p2g and the 1024-bit Multi-Prime RSA for modulus p 1p2p3, where p, q, p1, p 2, p3 are 342bits. The improvements of the proposed scheme over the Multi-Prime RSA are as follows: The key generation is about 49% faster, the decryption time is about 42% faster, and the total secret key size is 33% smaller.

AB - We propose a public-key primitive modulo pkq based on the RSA primitive. The decryption process of the proposed scheme is faster than those of two variants of PKCS #1 version 2.1, namely the RSA cryptosystem using Chinese remainder theorem (CRT) and the Multi-Prime RSA. The message M of the proposed scheme is decrypted from M mod pk and M mod q using the CRT, where we apply the Hensel lifting to calculate M mod pk from M mod p that requires only quadratic complexity O((log2 p)2). Moreover, we propose a trick that avoids modular inversions used for the Hensel lifting, and thus the proposed algorithm can be computed without modular inversion. We implemented in software both the proposed scheme with 1024-bit modulus p2g and the 1024-bit Multi-Prime RSA for modulus p 1p2p3, where p, q, p1, p 2, p3 are 342bits. The improvements of the proposed scheme over the Multi-Prime RSA are as follows: The key generation is about 49% faster, the decryption time is about 42% faster, and the total secret key size is 33% smaller.

UR - http://www.scopus.com/inward/record.url?scp=0842267122&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0842267122&partnerID=8YFLogxK

M3 - Article

VL - E87-A

SP - 94

EP - 101

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 1

ER -