Efficient Cryptosystems over Elliptic Curves Based on a Product of Form-Free Primes (Special Section on Information Theory and Its Applications)
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概要
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This paper proposes RSA-type cryptosystems over elliptic curves E_n(0,b) and E_n(a,0), where E_n(a,b):y^2≡x^3+ax+b(mod n), and n is a product of form-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≡(mod 3) or p≡q≡3(mod 4), and encrypts/decrypts a 2 log 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 of the KMOV cryptosystem, encrypt/decrypt a 2 log 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 form-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.
- 社団法人電子情報通信学会の論文
- 1994-08-25
著者
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KOYAMA Kenji
NTT Communication Science Laboratories
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Kuwakado Hidenori
Ntt Communication Science Laboratories
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