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Devoted toProf. Dr. Dr.h.c. Herbert Zeitler at the party of his eightieth birthdayProf. Dr. Dr.h.c. Helmut Karzel at the celebration of his seventy fifth birthdayProf. Dr. Dr.h.c Grozio Stanilov at the get together of his seventieth birthdayVarna (Bulgaria), September 5-10, 2003
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To specify such variables, we define U, V as U = {i|1 ≤ i ≤ k, xi depends on xt }, V = {j|1 ≤ j ≤ l, yj depends on xt }. -S. Cho et al. Let α = #U + #V. Note that α ≥ βd by the definition of the branch number. By defining U c = {1, · · · , k} − U, V c = {1, · · · , l} − V, we have that k l DP Si (ai , xi ) DP Sj (yj , bj ) i=1 (x1 ,··· ,xk ,0,··· ,0)∈BL (γa ,γb ) j=1 ≤ DP Si (ai , xi ))( ( x1 ,··· ,xt−1 i∈U c where Φt = obtain that i∈U DP Si (ai , xi ))( DP Si (ai , xi ))( ( xt xt ( i∈U j∈V DP Sj (yj , bj ))Φt .
2259, Springer-Verlag, pp. 112-128, 2001. 11. L. Keliher, Refined Anlaysis of Bounds Related to Linear and Differential Cryptanalysis for the AES, Fourth Conference on the Advanced Encryption Standard (AES4). 12. D. Kwon, J. Kim, S. H. Sung, Y. H. Song, Y. Yeom, E-J. Yoon, S, Lee, J. Lee, S. Chee, D. Han, and J. Hong, New block cipher: ARIA, ICISC 2003, LNCS 2971, pp. 432-445, 2004. 13. M. Matsui, Linear cryptanalysis method for DES cipher, Advance in CryptologyEurocrypt’93, LNCS Vol. 765, Springer-Verlag, pp.
The running time is 200,000 hours on a single Sun Ultra 5. Park et al. [15, 16] proposed a method for upper bounding on the MDP and MLHP for AES-like structures. 075 × 2−106 , respectively. Although the method of Park et al. [15, 16] produces good upper bounds for AES-like structures, it does not apply to other SPNs (for example ARIA). To find upper bounds on the MDP and MLHP for SPNs, one first finds upper bounds for 2-round and then use a recursive technique for 3 or more rounds. Thus it is very important to find effective upper bounds for 2-round SPNs.