Read e-book online Probabilistic and Statistical Methods in Cryptology: An PDF

By Daniel Neuenschwander (auth.)

ISBN-10: 3540220011

ISBN-13: 9783540220015

ISBN-10: 3540259422

ISBN-13: 9783540259428

Cryptology these days is among the most vital parts of utilized arithmetic, development on deep effects and techniques from quite a few components of arithmetic. this article is dedicated to the examine of stochastic features of cryptology.

Besides classical subject matters from cryptology, the writer provides chapters on probabilistic best quantity checks, factorization with quantum desktops, random-number turbines, pseudo-random-number turbines, info thought, and the birthday paradox and meet-in-the-middle attack.

In the sunshine of the great literature on stochastic effects correct for cryptology, this e-book is meant as a call for participation and creation for college students, researchers, and practitioners to probabilistic and statistical concerns in cryptology.

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Additional resources for Probabilistic and Statistical Methods in Cryptology: An Introduction by Selected Topics

Example text

Now the Extended Riemann Hypothesis is the conjecture that all zeroes of Lχ with real part in ]0, 1] have in fact real part 1/2. g. Odlyzko (2001)). n) for all 0 < h ≤ e}, where e := ν2 (n − 1) (as defined before). Also here, properties (i)-(iii) of primality sequences are easily verified. We must again prove (iv). n) for some 0 < h ≤ e}. 3. Assume n is a composite odd integer with prime factorization t n = i=1 pki i (pi distinct primes). If we write n − 1 = 2e u (u odd), pi − 1 = µi 2 ui (ui odd), and µ := min{µ1 , µ2 , .

4 *Bit Security of RSA 31 Hence by the uniform distribution of a and b on ZZn∗ it follows that the λt,i = (2−1 + i)at−1 + bx are also uniformly distributed and thus ε ε P (Wi,t = w) ≥ P ( n < At,i x < n − n) 4 4 ε ≥ 1− . 2 Now we want to show P( t = Lsb(at x) | j = Lsb(aj x)(0 ≤ j ≤ t − 1)) ≥ 1 − 1 . 19) Consider the events E1,i := {A1 (n, e, Aet,i y) = Lsb(At,i x)} and ε ε E2,i := { n < At,i x < n − n}. 4 4 It follows that P (E1,i ) ≥ 12 + ε and P (E2,i ) = 1 − ε/2. Consider the indicator random variables Ii := 1( E1,i ∩ E2,i ).

4 *Bit Security of RSA Denote by Lsb(x) the least significant bit of the natural number x (represented in its binary expansion). n) represented as an element of {0, 1, . . , n − 1}. As before, let p, q be distinct odd primes, n := pq. Assume the RSA exponent e is relatively prime to ϕ(n). The following theorem says that if a polynomialtime algorithm for calculating the least significant bit of the plaintext x exists, then a polynomial-time algorithm for calculating the whole of x also exists. 7 and also Delfs, Knebl (2002), 7.

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Probabilistic and Statistical Methods in Cryptology: An Introduction by Selected Topics by Daniel Neuenschwander (auth.)


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