A unified method for finding impossible differentials of block cipher structures

Improvements for Finding Impossible Differentials of Block Cipher Structures

“…MIBS is a 16-subblock Feistel structure with substitution and permutation input: A differential pair (Δin, Δout) and the system S output: A boolean flag indicates if (Δin, Δout) is an impossible differential (1) is the × augmented matrix of S; (2) is the − 1 dimension variable vector; (3) N is the map of constraints of S; (4) flag←false; (5) index←true; (6) Initialize every variable in according to (Δin, Δout) and the constraints in N; (7) while index do (8) UpdateMatrix ( , ) // Update according to ; / * Transform into the reduced-row-echelon form by Gauss-Jordan Elimination * / (9) ReducedRowEchelon ( ); (10) if has no solution then (11) flag←true; (12) break; (13) else (14) index ← false; (15) count← 0; (16) for ← to 1 do (17) → V ← Row of ; (18) if the sum of the first − 1 elements of → V is 1 then (19) ← the index of the element 1 in → V ; (20) ← the last element of → V ; // the solution of the th variable in (21) / * update the variable vector with ( , ) and return true if there is no contradiction and return false otherwise. * / (22) ←UpdateVector ( , N, , ); (23) if is false then (24) flag ← true; (25) return flag; (26) else (27) index ← true; (28) end (29) end (30) end ( …”

“…However, these two differentials cannot meet in the middle since they can never be equal in the 2 Security and Communication Networks middle. The U method [12,13] and the UID method [14] both belong to this category. In the U method and the UID method, the adversary first represents the block cipher structure as a matrix; then given a differential pair (Δin, Δout), he calculates the -round intermediate difference from Δin forwardly and the ( − )-round intermediate difference from Δout backwardly by the matrix method.…”

“…We implement the method in java language and apply it to many block cipher structures, including Gen-CAST256 [15], Gen-Skipjack [23], Four-Cell [24], Gen-MARS [12], Gen-RC6 [23], SMS4 [14], Misty [25], MIBS [26], Camellia * [27], LBlock [28], E2 [29], and SNAKE [30] ones. For these block ciphers, we rediscover all known impossible differentials.…”

Development of the approach to proving the security of block ciphers to impossible differential attack

“…The importance of the analysis of BSC resistance to IDA is confirmed by a number of works [1][2][3][4][5][6][7][8][9][10][11]. However, using of the methods proposed in these works would be problematic for 512-or 1024-bit block BSCs which are often used today, for example, in hash algorithms.…”

Revised Unified Impossible Differential Cryptanalysis of ARIA

“…Unified Impossible Differential cryptanalysis (UID) [2] is inspired by the previous U-method, which is used to find the impossible differential characteristics for block cipher structures. Since UID makes a great performance in the problem of retrieving the impossible differential characteristics of block ciphers, we apply the UID method to ARIA.…”