By Thomas Baignères, Pascal Junod, Yi Lu, Jean Monnerat, Serge Vaudenay

This significant other workout and answer booklet to A Classical advent to Cryptography: functions for Communications Security incorporates a rigorously revised model of educating fabric. It was once utilized by the authors or given as examinations to undergraduate and graduate-level scholars of the Cryptography and defense Lecture at EPFL from 2000 to mid-2005.

A Classical creation to Cryptography workout publication for A Classical creation to Cryptography: purposes for Communications safeguard covers a majority of the topics that make up today's cryptology, resembling symmetric or public-key cryptography, cryptographic protocols, layout, cryptanalysis, and implementation of cryptosystems. workouts don't require a wide historical past in arithmetic, because the most vital notions are brought and mentioned in lots of of the exercises.

The authors anticipate the readers to be pleased with uncomplicated evidence of discrete chance conception, discrete arithmetic, calculus, algebra, in addition to computing device technological know-how. Following the version of A Classical creation to Cryptography: purposes for Communications safeguard, workouts concerning the extra complex components of the textbook are marked with a celeb.

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**Extra resources for A Classical Introduction to Cryptography Exercise Book**

**Example text**

A circuit implementing the recurrence formula of the LFSR Solution 10 *Attacks on Cascade Ciphers 1 The time complexity is 2e. A cascade of L block ciphers can be viewed as a block cipher of key length L . l (as the L keys are independent), so that the time complexity would be 2L'e. When L = 2 the meet-in-the-middle attack reduces the time complexity from 22e down to 2 . 2e = 2e+1. In that case, the storage complexity is 2e. 2 As in Solution 6, we can prove that Pr[C*(x) = y] = 2Tn. Assuming that EK roughly behaves like a random permutation when K is randomly chosen among all possible wrong keys, we estimate Pr[EK(P) = C] x 2-n.

N ) ) to the oracle is P ~ [= Eki]. The cryptanalyst iteratively queries the oracle with randomly selected keys, in an independent way, until he finds the right one. Note that, as the queries are independent, the complexity could in principle be infinite (we say that the algorithm is memoryless). The strategy of the cryptanalyst is to select a distribution for his queries. , when K is uniformly distributed). How do you improve the attack? 2 If the a priori distribution of the keys is not uniform (but known by the adversary), what is the best memoryless algorithm for finding the key with the oracle?

2 Let C* : (0, l)n + (0, lIn denote a uniformly distributed random permutation. Let x and y be some fixed elements of (0, l I n . What is the probability that C*(x) = y? 2. A cascade of L block ciphers 24 EXERCISE BOOK variable. Assuming that EK roughly behaves like C*, compute an estimation of the amount of wrong keys displayed by Algorithm 2. How many wrong keys are displayed for a similar algorithm on a cascade of L ciphers? Assume that the adversary knows t plaintext/ciphertext pairs, all corresponding to the same key k .