By Song Y. Yan
RSA is a public-key cryptographic approach, and is the main well-known and widely-used cryptographic approach in ultra-modern electronic international. Cryptanalytic assaults on RSA, a qualified ebook, covers just about all significant identified cryptanalytic assaults and defenses of the RSA cryptographic approach and its versions.
Since RSA relies seriously on computational complexity thought and quantity concept, historical past details on complexity conception and quantity thought is gifted first. this is often by way of an account of the RSA cryptographic process and its variants.
Cryptanalytic assaults on RSAis designed for a certified viewers composed of practitioners and researchers in undefined. This e-book can also be compatible as a reference or secondary textual content publication for complex point scholars in laptop science.
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Additional info for Cryptanalytic Attacks on RSA
So, for all practical purposes, we could just simply use a combined test of a probabilistic such as Miller-Rabin or Maple isprime) and an elliptic curve test such as ECPP as follows. 9 (Practical primality testing). Given a random odd positive integer n, this algorithm will make a combined use of probabilistic tests and elliptic curve tests to determine whether or not n is prime:  (Primality Testing – Probabilistic Testing) Use a combination of the strong pseudoprimality test and the Lucas pseudoprimality test to determine if n is a probable prime.
Proof. 16) to show gcd(Fn+2 , Fn+1 ) = F2 = 1, since Fn+2 = Fn+1 · 1 + Fn , Fn+1 = Fn · 1 + Fn−1 , .. F4 = F3 · 1 + F2 , F3 = F2 · 2 + 0. 3 Efficient Number-Theoretic Algorithms 21 of digits of b. 16) has the form rj = rj+1 qj+1 + rj+2 except the last one which is of the form rn−1 = rn qn . Note that each of the quotient q1 , q2 , · · · , qn−1 ≥ 1 and qn ≥ 2. Therefore rn ≥ 1 = F2 rn−1 ≥ 2rn ≥ 2F2 ≥ 2 = F3 rn−2 ≥ rn−1 + rn ≥ F3 + F2 = F4 rn−3 ≥ rn−2 + rn−1 ≥ F4 + F3 = F5 r2 .. ≥ r3 + r4 ≥ Fn−1 + Fn−2 = Fn b = r1 ≥ r2 + r3 ≥ Fn + Fn−1 = Fn+1 .
There are thousands of theorems about prime numbers, only this theorem is called the Prime Number Theorem. According to the prime number theorem, the probability of a randomly chosen number N to be prime is about 1/ ln N . In August 2002 Agrawal, Kayal and Saxena  proposed a deterministic polynomial-time test (AKS test for short) for primality, relying on no unproved assumptions. It is not a great surprise that such a test exists, since Dixon  predicated in 1984 that “the prospect for a polynomial-time algorithm for proving primality seems fairly good, but it may turn out that, on the contrary, factoring is NP-hard”.
Cryptanalytic Attacks on RSA by Song Y. Yan