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Hidenori KUWAKADO, Kenji KOYAMA, "Efficient Cryptosystems over Elliptic Curves Based on a Product of Form-Free Primes" in IEICE TRANSACTIONS on Fundamentals,
vol. E77-A, no. 8, pp. 1309-1318, August 1994, doi: .
Abstract: This paper proposes RSA-type cryptosystems over elliptic curves En(O, b) and En(a, O),where En(a, b): y2 x3+ax+b (mod n),and n is a product of from-free primes p and q. Although RSA cryptosystem is not secure against a low exponent attack, RSA-type cryptosystems over elliptic curves seems secure against a low multiplier attack. There are the KMOV cryptosystem and the Demytko cryptosystem that were previously proposed as RSA-type cryptosystems over elliptic curves. The KMOV cryptosystem uses form-restricted primes as p q 2(mod 3)or p q 3(mod 4), and encrypts/decrypts a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem, which is an extension of the KMOV cryptosystem, uses form-free primes, and encrypts/decrypts a log n-bit message over fixed elliptic curves by operating only a value of x coordinates. Our cryptosystems, which are other extensions fo the KMOV cryptosystem, encrypt/decrypt a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem and our cryptosystems have higher security than the KMOV cryptosystem because from-free primes hide two-bit information about prime factors. The encryption/decryption speed in one of our cryptosystems is about 1.25 times faster than that in the Demytko cryptosystem.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_8_1309/_p
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@ARTICLE{e77-a_8_1309,
author={Hidenori KUWAKADO, Kenji KOYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Efficient Cryptosystems over Elliptic Curves Based on a Product of Form-Free Primes},
year={1994},
volume={E77-A},
number={8},
pages={1309-1318},
abstract={This paper proposes RSA-type cryptosystems over elliptic curves En(O, b) and En(a, O),where En(a, b): y2 x3+ax+b (mod n),and n is a product of from-free primes p and q. Although RSA cryptosystem is not secure against a low exponent attack, RSA-type cryptosystems over elliptic curves seems secure against a low multiplier attack. There are the KMOV cryptosystem and the Demytko cryptosystem that were previously proposed as RSA-type cryptosystems over elliptic curves. The KMOV cryptosystem uses form-restricted primes as p q 2(mod 3)or p q 3(mod 4), and encrypts/decrypts a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem, which is an extension of the KMOV cryptosystem, uses form-free primes, and encrypts/decrypts a log n-bit message over fixed elliptic curves by operating only a value of x coordinates. Our cryptosystems, which are other extensions fo the KMOV cryptosystem, encrypt/decrypt a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem and our cryptosystems have higher security than the KMOV cryptosystem because from-free primes hide two-bit information about prime factors. The encryption/decryption speed in one of our cryptosystems is about 1.25 times faster than that in the Demytko cryptosystem.},
keywords={},
doi={},
ISSN={},
month={August},}
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TY - JOUR
TI - Efficient Cryptosystems over Elliptic Curves Based on a Product of Form-Free Primes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1309
EP - 1318
AU - Hidenori KUWAKADO
AU - Kenji KOYAMA
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 1994
AB - This paper proposes RSA-type cryptosystems over elliptic curves En(O, b) and En(a, O),where En(a, b): y2 x3+ax+b (mod n),and n is a product of from-free primes p and q. Although RSA cryptosystem is not secure against a low exponent attack, RSA-type cryptosystems over elliptic curves seems secure against a low multiplier attack. There are the KMOV cryptosystem and the Demytko cryptosystem that were previously proposed as RSA-type cryptosystems over elliptic curves. The KMOV cryptosystem uses form-restricted primes as p q 2(mod 3)or p q 3(mod 4), and encrypts/decrypts a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem, which is an extension of the KMOV cryptosystem, uses form-free primes, and encrypts/decrypts a log n-bit message over fixed elliptic curves by operating only a value of x coordinates. Our cryptosystems, which are other extensions fo the KMOV cryptosystem, encrypt/decrypt a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem and our cryptosystems have higher security than the KMOV cryptosystem because from-free primes hide two-bit information about prime factors. The encryption/decryption speed in one of our cryptosystems is about 1.25 times faster than that in the Demytko cryptosystem.
ER -
English
