By Sean Murphy, Matthew J.B. Robshaw (auth.), Moti Yung (eds.)
Crypto 2002, the twenty second Annual Crypto convention, used to be subsidized through IACR, the foreign organization for Cryptologic examine, in cooperation with the IEEE desktop Society Technical Committee on defense and privateness and the pc technology division of the collage of California at Santa Barbara. it truly is released as Vol. 2442 of the Lecture Notes in machine technology (LNCS) of Springer Verlag. be aware that 2002, 22 and 2442 are all palindromes... (Don’t nod!) Theconferencereceived175submissions,ofwhich40wereaccepted;twos- missionsweremergedintoasinglepaper,yieldingthetotalof39papersaccepted for presentation within the technical application of the convention. during this complaints quantity you are going to ?nd the revised types of the 39 papers that have been offered on the convention. The submissions signify the present nation of labor within the cryptographic neighborhood around the world, overlaying all parts of cryptologic study. in reality, many top quality works (that absolutely should be released in different places) couldn't be approved. this is often end result of the aggressive nature of the convention and the demanding activity of choosing a software. I desire to thank the authors of all submitted papers. certainly, it's the authors of all papers who've made this convention attainable, whether or now not their papers have been authorised. The convention software used to be additionally immensely bene?ted by way of plenary talks.
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Extra info for Advances in Cryptology — CRYPTO 2002: 22nd Annual International Cryptology Conference Santa Barbara, California, USA, August 18–22, 2002 Proceedings
FIPS 197. 26 November 2001. 22. J. Patarin. Hidden ﬁeld equations (HFE) and isomorphisms of polynomials (IP): Two new families of asymmetric algorithms. In U. Maurer, editor, Proceedings of Eurocrypt ’96, LNCS 1070, pages 33–48, Springer-Verlag, 1996. 23. R. Schroeppel. Second round comments to NIST. gov/encryption/aes/, 2000. 24. R. Wernsdorf. The round functions of Rijndael generate the alternating group. In V. Rijmen, editor, Proceedings of Fast Software Encryption, LNCS, Springer– Verlag, to appear.
Then we get: Cb  ⊕ Cb  = EK (M0  ⊕ Cb ) ⊕ S1 ⊕EK (M0  ⊕ EK (M0  ⊕ Cb )) ⊕ S2 26 Antoine Joux, Gwena¨elle Martinet, and Fr´ed´eric Valette Furthermore, we have: C  ⊕ C  = EK (M  ⊕ C ) ⊕ S1 ⊕EK (M  ⊕ EK (M  ⊕ C ) ⊕ S2 = EK (C  ⊕ M0  ⊕ Cb  ⊕ C ) ⊕ S1 ⊕EK (M  ⊕ EK (C  ⊕ M0  ⊕ Cb  ⊕ C ) ⊕ S2 = EK (M0  ⊕ Cb ) ⊕ S1 ⊕EK (M0  ⊕ EK (M0  ⊕ Cb )) ⊕ S2 Now, we have proved above that S1 ⊕ S2 = S1 ⊕ S2 . Consequently, if b = 0, we always have Cb  ⊕ Cb  = C ⊕ C.
The main idea is to used deterministic relations veriﬁed by the masks. Indeed, even though the values used for diﬀerent blocks are pairwise independent, by construction they satisfy some relations. For every set of masks S = (S0 , S1 , . . , S −1 ) and every pair of indices (i, j), Si ⊕ Sj is a constant. To prove this claim we have to look at the mask generation. We have: Si = M × (< 2i >, < r >) and Sj = M × (< 2j >, < r >) Thus we get: Si ⊕ Sj = M × (< 2i > ⊕ < 2j >, < r > ⊕ < r >) = M × (< 2i > ⊕ < 2j >, < 0 >) Then the vector Si ⊕ Sj is independent of r and only depends on some columns of the secret matrix M .
Advances in Cryptology — CRYPTO 2002: 22nd Annual International Cryptology Conference Santa Barbara, California, USA, August 18–22, 2002 Proceedings by Sean Murphy, Matthew J.B. Robshaw (auth.), Moti Yung (eds.)