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Since cryptosystem based on the problem of factoring the composite number *N* can be attacked with *P*-1 and *P*+1 methods, it is required that *P*-1 and *P*+1 should be difficult to be factored into many small primes, where we assume that the *P* is a factor of *N*. In this paper, first, we consider the distribution of secure primes against both *P*-1 and *P*+1 methods. Second, we propose two efficient algorithms for generating secure primes against both *P*-1 and *P*+1 methods by extending the trial division method.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.10 pp.2161-2166

- Publication Date
- 1999/10/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)

- Category
- Security

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Yoshizo SATO, Yasuyuki MURAKAMI, Masao KASAHARA, "New Methods of Generating Primes Secure against Both P-1 and P+1 Methods" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 10, pp. 2161-2166, October 1999, doi: .

Abstract: Since cryptosystem based on the problem of factoring the composite number *N* can be attacked with *P*-1 and *P*+1 methods, it is required that *P*-1 and *P*+1 should be difficult to be factored into many small primes, where we assume that the *P* is a factor of *N*. In this paper, first, we consider the distribution of secure primes against both *P*-1 and *P*+1 methods. Second, we propose two efficient algorithms for generating secure primes against both *P*-1 and *P*+1 methods by extending the trial division method.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_10_2161/_p

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@ARTICLE{e82-a_10_2161,

author={Yoshizo SATO, Yasuyuki MURAKAMI, Masao KASAHARA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={New Methods of Generating Primes Secure against Both P-1 and P+1 Methods},

year={1999},

volume={E82-A},

number={10},

pages={2161-2166},

abstract={Since cryptosystem based on the problem of factoring the composite number *N* can be attacked with *P*-1 and *P*+1 methods, it is required that *P*-1 and *P*+1 should be difficult to be factored into many small primes, where we assume that the *P* is a factor of *N*. In this paper, first, we consider the distribution of secure primes against both *P*-1 and *P*+1 methods. Second, we propose two efficient algorithms for generating secure primes against both *P*-1 and *P*+1 methods by extending the trial division method.},

keywords={},

doi={},

ISSN={},

month={October},}

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TY - JOUR

TI - New Methods of Generating Primes Secure against Both P-1 and P+1 Methods

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2161

EP - 2166

AU - Yoshizo SATO

AU - Yasuyuki MURAKAMI

AU - Masao KASAHARA

PY - 1999

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E82-A

IS - 10

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - October 1999

AB - Since cryptosystem based on the problem of factoring the composite number *N* can be attacked with *P*-1 and *P*+1 methods, it is required that *P*-1 and *P*+1 should be difficult to be factored into many small primes, where we assume that the *P* is a factor of *N*. In this paper, first, we consider the distribution of secure primes against both *P*-1 and *P*+1 methods. Second, we propose two efficient algorithms for generating secure primes against both *P*-1 and *P*+1 methods by extending the trial division method.

ER -