کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6884584 | 1444318 | 2018 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Cryptanalysis of RSA-type cryptosystems based on Lucas sequences, Gaussian integers and elliptic curves
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
شبکه های کامپیوتری و ارتباطات
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چکیده انگلیسی
In this paper, we apply the continued fraction method to launch an attack on the three RSA-type cryptosystems when the private exponent d is sufficiently small. The first cryptosystem, proposed by Kuwakado, Koyama and Tsuruoka in 1995, is a scheme based on singular cubic curves y2=x3+bx2(modN) where N=pq is an RSA modulus. The second cryptosystem, proposed by Elkamchouchi, Elshenawy and Shaban in 2002, is an extension of the RSA scheme to the field of Gaussian integers using a modulus N=PQ where P and Q are Gaussian primes such that p=|P| and q=|Q| are ordinary primes. The third cryptosystem, proposed by Castagnos in 2007, is a scheme over quadratic field quotients with an RSA modulus N=pq based on Lucas sequences. In the three cryptosystems, the public exponent e is an integer satisfying the key equation edâk(p2â1)(q2â1)=1. Our attack is applicable to primes p and q of arbitrary sizes and we do not require the usual assumption that p and q have the same bit size. Thus, this is an extension of our recent result presented at ACISP 2016 conference. Our experiments demonstrate that for a 513-bit prime p and 511-bit prime q, our method works for values of d of up to 520 bits.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Information Security and Applications - Volume 40, June 2018, Pages 193-198
Journal: Journal of Information Security and Applications - Volume 40, June 2018, Pages 193-198
نویسندگان
Martin Bunder, Abderrahmane Nitaj, Willy Susilo, Joseph Tonien,