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.
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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 -