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

TO CRYPTOGRAPHY workout publication 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 information A C.I.P. Catalogue list for this publication is obtainable from the Library of Congress. A CLASSICAL advent TO CRYPTOGRAPHY workout booklet via 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 is probably not translated or copied in entire or partly with out the written permission of the writer (Springer Science+Business Media, Inc., 233 Spring road, manhattan, long island 10013, USA), apart from short excerpts in reference to reports or scholarly research. Use in reference to any type of details garage and retrieval, digital model, software program, or through related or diverse technique now comprehend or hereafter built is forbidden. The use during this book of alternate names, logos, provider marks and related phrases, whether the should not pointed out as such, isn't really to be taken as an expression of opinion to whether or now not they're topic to proprietary rights. revealed within the us of a

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6 Check whether the assumption is true or false now for this variant of A5/1. 7 Compare the lower bounds obtained in questions 3 and 5, and briefly discuss the security strength of A511 and its variant. 8. We assume that the three initial values of the LFSRs are chosen independently and uniformly at random. 1 For i = 1,2,3, what is the probability that Ri is shifted at the first clock? What is the probability that it is not shifted? 2 What is the probability that exactly two LFSRs are shifted at the first clock?

7 A keystream generator should avoid generating the same keystream under several keys. These kind of keys are called "weak keys". Although we only computed lower bounds on the number of weak keys for both A511 and its variant, the huge difference between the two bounds (222 for the real A511 against 262 for its variant) suggests that the variant is much weaker. 51 Conventional Cryptography Solution 14 *A Variant of A511 II 1 Let Ti denote the value of the clocking tap of Ri just before it is clocked, for i = 1,2,3.

4). lie lie. Note that two independent keys are used here, one in the CBC mode, the other in the CFB mode. , that the block length is larger than the key length) and that all the IV 's are known to the adversary. For simplicity, we denote Eki and Dki by Ei and Di respectively. 3. 4. 4. 5. We are going to mount a chosen plaintext attack against it. The plaintext P we choose, is the concatenation of three n-bit blocks such that P = (A, A, B) (where A, B E (0, lIn denote arbitrary blocks of n bits).