Browsing by Subject "Cryptanalysis"
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Item Open Access Exploiting linearity of modular multiplication(Springer, 2020) Yıldırım, Hamdi MuratThe XOR Open image in new window and the addition ⊞⊞ operations have been widely used as building blocks for many cryptographic primitives. These operations and the multiplication ⊙⊙ operation are successively used in the design of IDEA and the MESH block ciphers. This work presents several interesting algebraic properties of the multiplication operation. By fixing one operand, we obtain vector valued function ggZggZ on Zn2Z2n, associated with ⊙⊙. In this paper we show that the nonlinearity of ggZggZ remains the same under some transformations of Z and moreover we give an upper bound for the nonlinearity of ggZggZ when Z is a power of 2. Under weak-key assumptions, we furthermore present a list of new linear relations for 1-round IDEA cipher, some of directly derived and others algorithmically generated using these relations and known ones. We extend the largest linear weak key class for IDEA cipher with size 223223 to derive such a class with sizes 224224. Under the independent key subblocks (subkeys) and weak-key assumptions we derive many linear relations for IDEA cipher using linear relations for 1-round IDEA cipher.Item Open Access The Shannon cipher system with a guessing wiretapper(Institute of Electrical and Electronics Engineers, 1999-09) Merhav, N.; Arikan, E.The Shannon theory of cipher systems is combined with recent work on guessing values of random variables. The security of encryption systems is measured in terms of moments of the number of guesses needed for the wiretapper to uncover the plaintext given the cryptogram. While the encrypter aims at maximizing the guessing effort, the wiretapper strives to minimize it, e.g., by ordering guesses according to descending order of posterior probabilities of plaintexts given the cryptogram. For a memoryless plaintext source and a given key rate, a singleletter characterization is given for the highest achievable guessing exponent function, that is, the exponential rate of the th moment of the number of guesses as a function of the plaintext message length. Moreover, we demonstrate asymptotically optimal strategies for both encryption and guessing, which are universal in the sense of being independent of the statistics of the source. The guessing exponent is then investigated as a function of the key rate and related to the large-deviations guessing performance.