Download Cryptanalytic Attacks on RSA by Song Y. Yan PDF

By Song Y. Yan

RSA is a public-key cryptographic process, and is the main recognized and widely-used cryptographic method in modern day electronic international. Cryptanalytic assaults on RSA, a qualified publication, covers just about all significant identified cryptanalytic assaults and defenses of the RSA cryptographic process and its editions.

Since RSA relies seriously on computational complexity conception and quantity thought, history info on complexity idea and quantity conception is gifted first. this is often via an account of the RSA cryptographic procedure and its variants.

Cryptanalytic assaults on RSAis designed for a certified viewers composed of practitioners and researchers in undefined. This publication is usually compatible as a reference or secondary textual content ebook for complex point scholars in computing device science.

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6. Solve 803x ≡ 22 (mod 154). Notice first that 803x ≡ 22 (mod 154) ⇐⇒ 803x − 154y = 22. 3, we get: q 5 4 1 2 u1 1 0 1 -4 5 ↑ x u2 0 1 -5 21 -26 u3 803 154 33 22 11 ↑ d Since d | b, and d = 11 and x = 5, the congruence has exactly 11 solutions x + iN/d for i = 0, 1, 2, · · · , d − 1, namely, x = {5, 19, 33, 47, 61, 75, 89, 103, 117, 131, 145}. 7. The complexity of extended Euclid’s algorithm is in P. 14) 1 q1 + q2 + 1 .. 6 again. If we only take the values of the q column, ignoring all other values in other columns, we get: 28 1.

If i < j, set y ≡ y 2 (mod N ) and return to [3]. [5] Terminate the algorithm and output “N is definitely not prime”. 17. The Miller-Rabin test runs in expected time O((log N )3 ), and if the generalized Riemann hypothesis is true then the test can be run deterministically in time O((log N )5 ). Proof. Let b < N be a positive integer. Then the primality of N can be determined in expected time O((log N )3 ), since only O(log N ) modular exponentiations may be needed and each of them takes O((log N )2 ) bit operations, resulting O(log N ) · O((log N )2 ) = O((log N )3 ).

3] (Exit) Terminate the algorithm. 4 Intractable Number-Theoretic Problems One of the most important features of number theory is that problems in number theory are easy to state but often very hard to solve. The following are just some of the problems that are still unsolved to date: 42 1. 13. 13), Goldbach (1690–1764) conjectured that every even integer greater than 4 is the sum of two prime numbers, such as 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7. 14 = 3+11, 16 = 3+13 = 5+11, 18 = 5 + 13 = 7 + 11, etc.

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