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

TO CRYPTOGRAPHY workout e-book Thomas Baignkres EPFL, Switzerland Pascal Junod EPFL, Switzerland Yi Lu EPFL, Switzerland Jean Monnerat EPFL, Switzerland Serge Vaudenay EPFL, Switzerland Springer - Thomas Baignbres Pascal Junod EPFL - I&C - LASEC Lausanne, Switzerland Lausanne, Switzerland Yi Lu Jean Monnerat EPFL - I&C - LASEC EPFL-I&C-LASEC Lausanne, Switzerland Lausanne, Switzerland Serge Vaudenay Lausanne, Switzerland Library of Congress Cataloging-in-Publication info A C.I.P. Catalogue list for this publication is obtainable from the Library of Congress. A CLASSICAL creation TO CRYPTOGRAPHY workout publication through Thomas Baignkres, Palcal Junod, Yi Lu, Jean Monnerat and Serge Vaudenay ISBN- 10: 0-387-27934-2 e-ISBN-10: 0-387-28835-X ISBN- thirteen: 978-0-387-27934-3 e-ISBN- thirteen: 978-0-387-28835-2 published on acid-free paper. O 2006 Springer Science+Business Media, Inc. All rights reserved. This paintings will not be translated or copied in complete or partially with out the written permission of the writer (Springer Science+Business Media, Inc., 233 Spring road, manhattan, manhattan 10013, USA), apart from short excerpts in reference to studies or scholarly research. Use in reference to any kind of details garage and retrieval, digital variation, software program, or by way of related or varied technique now comprehend or hereafter built is forbidden. The use during this book of alternate names, logos, provider marks and related phrases, no matter if the usually are not pointed out as such, isn't to be taken as an expression of opinion as to if or no longer they're topic to proprietary rights. revealed within the us of a

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4 Find a relation between kl, k3, IV1, IV2, PI, P2 and A. Similarly, find a relation between kl, k3, IV1, P3,Pq,A, and B. 5 Deduce a (smart) attack that recovers kl and k3. Once this is done, how can k2 be recovered? Compute the complexity of the attack. 5. 6. Attacking the OFBlCBClECB mode of operation 28 EXERCISE BOOK Exercise 12 Attacks on Encryption Modes II We use the notations of the previous exercise. 7 for two plaintext blocks). For this attack, we mount a chosen-ciphertext attack. Moreover, the adversary will have the ability to choose the value of IV2 (the values of IV1 and IV3 are only known and fixed).

The plaintext is the input of the first block cipher and the ciphertext is the output of the last block cipher. 2). lie lie. + What is the complexity (in terms of number of encryptions) of the exhaustive key search of Algorithm 2 on the block cipher? What is the complexity of a similar exhaustive key search on a cascade of L block ciphers? Give the name of an attack which reduces this complexity for the specific case where L = 2. Recall its complexity. Algorithm 2 Exhaustive key search algorithm Input: a plaintext/ciphertext pair (P,C) such that C = Ek(P) Output: key candidate(s) for k Processing: 1: for each possible key K do 2: if C = EK (P)then 3: display K 4: end if 5: end for We now wonder how many (wrong) keys are displayed by Algorithm 2.

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?