1 IPA Hierocrypt-L1 Hierocrypt-L Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 2 Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-
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- ゆみか まつかた
- 7 years ago
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1 Hierocrypt-L1 : Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 Abstract: In this report, we address our security evaluation of Hierocrypt-L1. As a result, we found no critical security flaw during the limited period available for security evaluation. Hierocrypt-L1has not yet been evaluated enough even with our evaluation. Further evaluation results are necessary. We however show some evidences to consider Hierocrypt-L1to provide expected security at this moment. 1
2 1 IPA Hierocrypt-L1 Hierocrypt-L Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 2 Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 SPN S(ubstitution: ) S ( ) S S 8 / P(ermutation: ) MDS (maximum distance separation) Hierocrypt-L1 (8 ) Square, CRYPTON, Rijndael AES Rijndael ( ) S 1. ( MDSL MDSH) 2. S 3. 2
3 DES S MDSL, MDSH S 3 GF(2 k ) k ( 10 ) b 1,...,b k f(x) = k i=1 b i x k i k 1 GF(2) ( k 1 ) GF(2 k ) 1 1: GF(2 n ) n P(x) n P(x) 2 x 2 + x +1 6 x 6 + x +1 3 x 3 + x +1 7 x 7 + x +1 4 x 4 + x +1 8 x 8 + x 6 + x 5 + x +1 5 x 5 + x x 9 + x
4 [1]( pp.10 [ ( )] (5 t 7)) 3(32) 3(32) = W (t 1) 2(32) V (t) (32) 3(32) = W (t) 2(32) V (t) (32) 1 / [4] Hierocrypt-3 [2] Hierocrypt-L Feistel Feistel 4 Z ( 1) = K Z (0) = σ 0 (Z ( 1),G (0) ) Z (1) = σ(z (0),G (1) ) Z (2) = σ(z (1),G (2) ) Z (3) = σ(z (2),G (3) ) Z (4) = σ(z (3),G (4) ) Z (5) = Z (8 5) = Z (3) Z (6) = Z (8 6) = Z (2) Z (7) = Z (8 7) = Z (1) Z (t) (t) Z 3(32) 4(32) = P (32) 1 (W (t) (t) W 1(32) 2(32) ) P (16) 1 4
5 σ (Z (t 1) 1,Z (t 1) 2,Z (t 1) 3,Z (t 1) 4 ) := Z (t 1) (Z (t) 1,Z (t) 2,Z (t) 3,Z (t) 4 ) := Z (t) (W (t 1) 1,W (t 1) 2 ) := P (Z (t 1) 3,Z (t 1) 4 ) Z (t) 3 = M 5 (W (t 1) 1 ) G (t) Z (t) 4 = M B (W (t 1) 2 ) Z (t) 1 = Z (t 1) 2 Z (t) 2 = Z (t 1) 1 F σ (Z (t 1) 2 Z (t) 3 ) 1 2 F σ S Z1(t-1) Z2(t-1) Z3(t-1) Z4(t-1) P W1(t-1) V(t) M5 G(t) M5 W2(t-1) -1 Z1(t) Z2(t) Z3(t) Z4(t) 1: Intermediate keys generation (partial) M 5 M B P 16 σ σ 0 t Z t K Z 4.1: ) Z 3 Z 4 ( ) ( (GF(2 8 )) Z 3 Z 4 W 1,W 2 K i:j 128 K 32 i j K 1:1 K 1:2 K 1:3... K 4:8 := K 128 Z( 1) 3:1 = K 3:1 Z( 1) 3:2 = K 3:2 5
6 Z( 1) 3:3 = K 3:3 Z( 1) 3:4 = K 3:4 Z( 1) 4:1 = K 4:1 Z( 1) 4:2 = K 4:2 Z( 1) 4:3 = K 4:3 Z( 1) 4:4 = K 4:4 Z(0) 3,1 = K 3:1 K 3:3 G 0:1 Z(0) 3,2 = K 3:1 K 3:2 K 3:4 G 0:2 Z(0) 3,3 = K 3:1 K 3:2 K 3:3 G 0:3 Z(0) 3,4 = K 3:2 K 3:4 G 0:4 Z(0) 4,1 = K 4:2 K 4:4 Z(0) 4,2 = K 4:1 K 4:3 Z(0) 4,3 = K 4:1 K 4:2 K 4:4 Z(0) 4,4 = K 4:1 K 4:3 K 4:4 Z(1) 3,1 = K 3:2 K 4:1 G 0:1 G 0:3 G 1:1 Z(1) 3,2 = K 3:3 K 4:2 G 0:1 G 0:2 G 0:4 G 1:2 Z(1) 3,3 = K 3:1 K 3:4 K 4:3 G 0:1 G 0:2 G 0:3 G 1:3 Z(1) 3,4 = K 3:1 K 4:4 G 0:2 G 0:4 G 1:4 Z(1) 4,1 = K 3:1 G 0:2 G 0:4 Z(1) 4,2 = K 3:2 G 0:1 G 0:3 Z(1) 4,3 = K 3:2 K 3:3 K 4:1 G 0:2 G 0:3 G 0:4 Z(1) 4,4 = K 3:1 K 3:4 K 4:4 G 0:1 G 0:2 G 0:3 W (1)(= W (7)) 1,1 = K 3:1 K 3:2 K 4:1 G 0:1 G 0:2 G 0:3 G 0:4 G 1:1 W (1)(= W (7)) 1,2 = K 3:2 K 3:3 K 4:2 6
7 G 0:2 G 0:3 G 0:4 G 1:2 W (1)(= W (7)) 1,3 = K 3:1 K 3:2 K 3:3 K 3:4 K 4:1 K 4:3 G 0:1 G 0:4 G 1:3 W (1)(= W (7)) 1,4 = K 3:4 G 0:1 G 0:3 G 0:4 G 1:4 W (1)(= W (7)) 2,1 = K 3:2 K 3:3 K 3:4 K 4:1 K 4:3 G 0:1 G 0:2 G 1:3 W (1)(= W (7)) 2,2 = K 3:2 K 3:4 G 0:4 G 1:4 W (1)(= W (7)) 2,3 = K 3:1 K 3:3 G 0:1 G 1:1 W (1)(= W (7)) 2,4 = K 3:1 K 3:2 K 3:3 K 3:4 K 4:2 K 4:4 G 0:1 G 0:4 G 1:2 Z(2) 3,1 = K 3:3 K 3:4 K 4:3 G 0:2 G 0:3 G 1:1 G 1:3 G 2:1 3,2 = K 3:1 K 3:3 K 3:4 K 4:1 K 4:2 G 0:3 G 0:4 G 1:1 G 1:2 G 1:4 G 2:2 3,3 = K 3:2 K 3:4 K 4:2 K 4:3 G 0:4 G 1:1 G 1:2 G 1:3 G 2:3 3,4 = K 3:2 K 3:3 K 3:4 K 4:2 G 0:1 G 0:2 G 1:2 G 1:4 G 2:4 4,1 = K 3:1 K 3:3 K 4:2 K 4:4 G 0:1 G 1:2 G 1:4 4,2 = K 3:1 K 3:2 K 3:4 K 4:1 K 4:3 G 0:2 G 1:1 G 1:3 4,3 = K 3:1 K 3:2 K 3:4 K 4:1 K 4:2 K 4:3 K 4:4 G 0:2 G 1:2 G 1:3 G 1:4 4,4 = K 3:3 K 4:1 K 4:2 K 4:3 K 4:4 G 0:1 G 0:2 G 0:4 G 1:1 G 1:2 G 1:3 W (2)(= W (6)) 3,1 = K 3:1 K 3:4 K 4:2 K 4:3 K 4:4 G 0:1 G 0:2 G 0:3 G 1:1 G 1:2 G 1:3 G 1:4 G 2:1 3,2 = K 3:2 K 3:3 K 4:2 K 4:3 G 0:2 G 0:3 G 0:4 G 1:2 G 1:3 G 1:4 G 2:2 3,3 = K 3:1 K 4:1 K 4:4 G 0:2 G 0:4 G 1:1 G 1:4 G 2:3 3,4 = K 3:2 K 3:4 K 4:1 K 4:3 K 4:4 G 0:4 G 1:1 G 1:3 G 1:4 G 2:4 7
8 4,1 = K 3:3 K 4:1 K 4:2 G 0:1 G 0:2 G 0:4 G 1:1 G 1:2 G 2:3 4,2 = K 3:1 K 4:4 G 0:2 G 0:4 G 1:4 G 2:4 4,3 = K 3:2 K 4:1 G 0:1 G 0:3 G 1:1 G 2:1 4,4 = K 3:2 K 4:1 K 4:4 G 0:1 G 0:3 G 1:1 G 1:4 G 2:2 Z(3) 3,1 = K 3:4 K 4:1 K 4:2 K 4:3 G 0:1 G 0:3 G 0:4 G 1:2 G 1:3 G 2:1 G 2:3 G 3:1 3,2 = K 3:1 K 3:3 K 4:1 K 4:3 G 0:1 G 1:3 G 1:4 G 2:1 G 2:2 G 2:4 G 3:2 3,3 = K 3:2 K 3:3 K 3:4 K 4:1 G 0:1 G 0:2 G 1:4 G 2:1 G 2:2 G 2:3 G 3:3 3,4 = K 3:3 K 3:4 K 4:1 K 4:2 K 4:4 G 0:2 G 0:3 G 1:1 G 1:2 G 2:2 G 2:4 G 3:4 4,1 = K 3:1 K 3:2 K 4:1 G 0:1 G 0:2 G 0:3 G 0:4 G 1:1 G 2:2 G 2:4 4,2 = K 3:2 K 3:3 K 4:2 G 0:2 G 0:3 G 0:4 G 1:2 G 2:1 G 2:3 4,3 = K 3:1 K 3:2 K 3:3 K 4:2 G 0:3 G 1:2 G 2:2 G 2:3 G 2:4 4,4 = K 3:3 K 4:1 K 4:2 K 4:4 G 0:1 G 0:2 G 0:4 G 1:1 G 1:2 G 1:4 G 2:1 G 2:2 G 2:3 W (3)(= W (5)) 3,1 = K 3:1 K 3:2 K 3:4 K 4:2 K 4:3 G 0:2 G 1:1 G 1:2 G 1:3 G 2:1 G 2:2 G 2:3 G 2:4 G 3:1 3,2 = K 3:1 K 3:2 K 4:1 K 4:2 K 4:3 G 0:1 G 0:2 G 0:3 G 0:4 G 1:2 G 1:3 G 1:4 G 2:2 G 2:3 G 2:4 G 3:2 3,3 = K 3:1 K 3:4 K 4:1 K 4:2 G 0:1 G 0:2 G 0:3 G 1:2 G 1:4 G 2:1 G 2:4 G 3:3 3,4 = K 3:4 G 0:1 G 0:3 G 0:4 G 1:4 G 2:1 G 2:3 G 2:4 G 3:4 4,1 = K 3:2 K 3:4 K 4:2 G 0:4 G 1:1 G 1:2 G 1:4 G 2:1 G 2:2 G 3:3 4,2 = K 3:2 K 3:3 K 3:4 K 4:2 G 0:1 G 0:2 G 1:2 G 1:4 G 2:4 G 3:4 4,3 = K 3:3 K 3:4 K 4:3 8
9 G 0:2 G 0:3 G 1:1 G 1:3 G 2:1 G 3:1 4,4 = K 3:1 K 3:2 K 3:3 K 4:3 K 4:4 G 0:3 G 1:1 G 1:3 G 2:1 G 2:4 G 3:2 Z(4) 3,1 = K 3:2 K 4:1 K 4:3 G 0:1 G 0:3 G 1:1 G 1:3 G 1:4 G 2:2 G 2:3 G 3:1 G 3:3 G 4:1 3,2 = K 4:1 G 1:1 G 2:3 G 2:4 G 3:1 G 3:2 G 3:4 G 4:2 3,3 = K 3:1 K 4:2 G 0:2 G 0:4 G 1:1 G 1:2 G 2:4 G 3:1 G 3:2 G 3:3 G 4:3 3,4 = K 3:1 K 3:2 K 3:4 K 4:1 K 4:2 K 4:3 G 0:2 G 1:2 G 1:3 G 2:1 G 2:2 G 3:2 G 3:4 G 4:4 4,1 = K 3:1 K 3:4 K 4:2 K 4:3 K 4:4 G 0:1 G 0:2 G 0:3 G 1:1 G 1:2 G 1:3 G 1:4 G 2:1 G 3:2 G 3:4 4,2 = K 3:2 K 3:3 K 4:2 K 4:3 G 0:2 G 0:3 G 0:4 G 1:2 G 1:3 G 1:4 G 2:2 G 3:1 G 3:3 4,3 = K 3:1 K 3:2 K 4:3 K 4:4 G 0:1 G 0:2 G 0:3 G 0:4 G 1:3 G 2:2 G 3:2 G 3:3 G 3:4 4,4 = K 3:1 K 4:2 K 4:4 G 0:2 G 0:4 G 1:1 G 1:2 G 1:4 G 2:1 G 2:2 G 2:4 G 3:1 G 3:2 G 3:3 4.2 (1) (2) Hierocrypt-L1 4.2: (K (1),K (2),K (3),K (4) ) Z Z t, 1 t Z (t) t, 1 t 4 9
10 V (t) = F σ ( ) Z (t) 1 = 3 4 V (t) Z (t) 2 = 1 Z (t) 3 = 2 V (t) Z (t) 4 = 3 V (t) 4.3: (K (5),K (6),K (7) ) Z (t 1), 5 t 8 Z (t 1) Z (t 1) 1 = Z (t 1) 3 Z (t 1) 2 F σ (Z (t 1) 1 Z (t 1) 3 ) (1) 2 = M 5 (G (t 1) Z (t 1) 3 ) F σ (Z (t 1) 1 Z (t 1) 3 ) (2) 3 = M B (Z (t 1) 4 ) F σ (Z (t 1) 1 Z (t 1) 3 ) (3) 4 = Z (t 1) 1 M B (Z (t 1) 4 ) (4) x Y (t 1) Y (t 1) 4 = MB 1(K(t) 4 x) Y (t 1) 3 = M5 1 (x M 5 (G (t 1) ) ) Y (t 1) 2 = x Y ) Y (t 1) 1 = x Y (t 1) x x Y (t 1) Z (t 1) = Y (t 1) (1) (4) F σ (Y (t 1) 1 Y (t 1) 3 )=Y (t 1) Y Y F σ (1)F σ (2)x Y F σ (1) (4) Z 1 DES MISTY
11 SAFER+ 256 (minor flaw ) [5] Magenta [6] [7] Hierocrypt-L1 Z (t) = Z (8 t), 5 t 7, 1 t 4 Z (t 1),Z (t), 5 t 7 Z (t 1),Z (t) K (8 t) K (9 t) V (t) 1: V (t) = V (9 t), 5 t 7 4.4: 1 = K (9 t) 1 K (9 t) 2, 5 t 7 (5 t 7) K (9 t) 1 K (9 t) 2 = Z (9 t 1) 1 Z (9 t) 3 = Z (8 (9 t 1)) 1 Z (8 (9 t)) 3 = Z (t) 1 Z (t 1) 3 1 = Z (t) 1 Z (t 1) 3 4.5: 1 2 K (t 1) 4 = Z (t) 3 Z (t 1) 4, 2 t 4 11
12 (2 t 4) 1 = Z (t 1) 1 V (t) = Z (t) 2 2 = Z (t) 3 V (t) = Z (t) 3 Z (t) 2 Z (t 1) 1 4 = Z (t 1) 2 Z (t) 4 = Z (t) 1 Z (t) 4 K (t 1) 4 = Z (t 1) 1 Z (t 1) K (t 1) 4 = Z (t) 2 Z (t) 3 Z (t) 2 Z (t 1) 1 Z (t 1) 1 Z (t 1) 4 = Z (t) 3 Z (t 1) 4 Z 3 Z 4 (Z (2) 3 Z (1) 4 ) 1 = K 3:1 K 3:3 K 3:4 K 4:3 G 0:3 G 0:4 G 1:1 G 1:3 G 2:1 (Z (2) 3 Z (1) 4 ) 2 = K 3:1 K 3:2 K 3:3 K 3:4 K 4:1 K 4:2 G 0:1 G 0:4 G 1:1 G 1:2 G 1:4 G 2:2 (Z (2) 3 Z (1) 4 ) 3 = K 3:3 K 3:4 K 4:1 K 4:2 K 4:3 G 0:2 G 0:3 G 1:1 G 1:2 G 1:3 G 2:3 (Z (2) 3 Z (1) 4 ) 4 = K 3:1 K 3:2 K 3:3 K 4:2 K 4:4 G 0:3 G 1:2 G 1:4 G 2:4 (Z (3) 3 Z (2) 4 ) 1 = K 3:1 K 3:3 K 3:4 K 4:1 K 4:3 K 4:4 G 0:3 G 0:4 G 1:3 G 1:4 G 2:1 G 2:3 G 3:1 (Z (3) 3 Z (2) 4 ) 2 = K 3:2 K 3:3 K 3:4 G 0:1 G 0:2 G 1:1 G 1:4 G 2:1 G 2:2 G 2:4 G 3:2 (Z (3) 3 Z (2) 4 ) 3 = K 3:1 K 3:3 K 4:2 K 4:3 K 4:4 G 0:1 G 1:2 G 1:3 G 2:1 G 2:2 G 2:3 G 3:3 (Z (3) 3 Z (2) 4 ) 4 = K 3:4 K 4:3 G 0:1 G 0:3 G 0:4 G 1:3 G 2:2 G 2:4 G 3:4 (Z (4) 3 Z (3) 4 ) 1 = K 3:1 K 4:3 G 0:2 G 0:4 G 1:3 G 1:4 G 2:3 G 2:4 G 3:1 G 3:3 G 4:1 (Z (4) 3 Z (3) 4 ) 2 = K 3:2 K 3:3 K 4:1 K 4:2 G 0:2 G 0:3 G 0:4 G 1:1 G 1:2 G 2:1 G 2:4 G 3:1 G 3:2 G 3:4 G 4:2 (Z (4) 3 Z (3) 4 ) 3 = K 3:2 K 3:3 12
13 G 0:2 G 0:3 G 0:4 G 1:1 G 2:2 G 2:3 G 3:1 G 3:2 G 3:3 G 4:3 (Z (4) 3 Z (3) 4 ) 4 = K 3:1 K 3:2 K 3:3 K 3:4 K 4:3 K 4:4 G 0:1 G 0:4 G 1:1 G 1:3 G 1:4 G 2:3 G 3:2 G 3:4 G 4:4 t SPN ( ) F LOKI89 ( ) [8] DES [9] Hierocrypt-L1 DES F ( ) Hierocrypt-L1 1 ( P A K (1) A = P B K (1) B ) S ( A,K(t) B ) ( ) S SPN DES DES F P A,P B K (1) A,K (1) B 4.6: Z (1) A,Z (1) B Z (t) A,Z (t) B, 2 t 4 ( x ( ) 0 0 ) Case 1:( ) Case 2:( ) Z (0) = 000x, 000x, 000x, x0x0 Z (1) = 000x, 000x, 000x, x0x0 Z (2) = 000x, 000x, 000x, x0x0 Z (3) = 000x, 000x, 000x, x0x0 Z (4) = 000x, 000x, 000x, x0x0 Z (0) = 0000, 000x, 0000,x0xx Z (1) = 000x, 0000, 000x, 000x 13
14 Z (2) = 0000, 000x, 0000,x0xx Z (3) = 000x, 0000, 000x, 000x Z (4) = 0000, 000x, 0000,x0xx Case 3:( Case 2 ) Z (0) = 000x, 0000, 000x, 000x Z (1) = 0000, 000x, 0000,x0xx Z (2) = 000x, 0000, 000x, 000x Z (3) = 0000, 000x, 0000,x0xx Z (4) = 000x, 0000, 000x, 000x 5 Hierocrypt-L1 Hierocrypt-L1 SPN Square[10] Rijndael[11] CRYPTON [12] Square [10] truncated-differential[13] Hierocrypt-L1 Square truncated-differential Hierocrypt-L1 1. ( ) 2. S (8 ) 3. MDSL(GF(2 8 ) ) 4. MDSH( ) S GF(2 8 ) S S MDSL ( ) S MDSL S ( ) 5.1 Hierocrypt-L1 S S 2 14
15 S S Hierocrypt-L1 S s(x) =Add(Power(Perm(x))) Perm() GF(2 8 ) Power() Add() Add 0x11 x =0 S 7 s(perm 1 (x)) x ( GF(2 8 ) ) S S x 8 + x 6 + x 5 + x +1 GF(2 8 ) 10 GF(2 8 ) F (x) = 7 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
16 + 195 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 254 ( MDSH MDSL) GF(2 8 ) S GF(2 k ) GF(2 k ) S GF(2 k ),k <8 S 8 GF(2 k ) x (GF2) 8 y GF(2 k ) φ S φ n φ : x y =(y k 1 y k 2...y 0 ) y i = parity(x, mask i ) φ mask i φ d GF(2 k ) ( d ) GF(2 k ) f bias (φ,f) =#{x f(φ(x)) = φ(s(x))} 2 8 /2 k (5) GF(2 2 ) 8 GF(2 2 ) 0 mask0, mask GF(2 2 ) d ( 88/256=24/256+1/4 bias = 24/256)9 φ(x) φ(s(x)) dist 16
17 4 4 dist[a][b] φ(x) =a φ(s(x)) = b x mask = (7, 233),f(x) =x +3 dist = {10, 16, 10, 28, 12, 18, 24, 10, 24, 18, 12, 10, 18, 12, 18, 16) mask = (7, 233),f(x) =2x +3 dist = {10, 16, 10, 28, 12, 18, 24, 10, 24, 18, 12, 10, 18, 12, 18, 16) mask = (7, 238),f(x) =x +1 dist = {10, 28, 10, 16, 18, 16, 18, 12, 24, 10, 12, 18, 12, 10, 24, 18) mask = (7, 238),f(x) =3x +1 dist = {10, 28, 10, 16, 18, 16, 18, 12, 24, 10, 12, 18, 12, 10, 24, 18) mask = (121, 129), f(x) =x +3 dist = {12, 12, 12, 28, 14, 18, 20, 12, 16, 18, 16, 14, 22, 16, 16, 10) mask = (121, 248), f(x) =x +1 dist = {12, 28, 12, 12, 22, 10, 16, 16, 16, 14, 16, 18, 14, 12, 20, 18) mask = (129, 248), f(x) =x +1 dist = {12, 28, 12, 12, 22, 10, 16, 16, 14, 12, 18, 20, 16, 14, 18, 16) mask = (233, 238), f(x) =x +1 dist = {10, 28, 16, 10, 18, 16, 12, 18, 12, 10, 18, 24, 24, 10, 18, 12) mask = (233, 238), f(x) =2x +1 dist = {10, 28, 16, 10, 18, 16, 12, 18, 12, 10, 18, 24, 24, 10, 18, 12) ( 88/256=24/256+1/4)6 mask = (7, 233),f(x) =x 2 +3 dist = (10, 16, 10, 28, 12, 18, 24, 10, 24, 18, 12, 10, 18, 12, 18, 16) mask = (7, 238),f(x) =2x 2 +1 dist = (10, 28, 10, 16, 18, 16, 18, 12, 24, 10, 12, 18, 12, 10, 24, 18) 17
18 mask = (86, 147),f(x) =x 2 dist = (24, 12, 14, 14, 12, 24, 14, 14, 14, 14, 16, 20, 14, 14, 20, 16) mask = (86, 197),f(x) =2x 2 dist = (24, 14, 14, 12, 14, 16, 20, 14, 14, 20, 16, 14, 12, 14, 14, 24) mask = (147, 197),f(x) =3x 2 dist = (24, 14, 12, 14, 14, 16, 14, 20, 12, 14, 24, 14, 14, 20, 14, 16) mask = (233, 238),f(x) =3x 2 +1 dist = (10, 28, 16, 10, 18, 16, 12, 18, 12, 10, 18, 24, 24, 10, 18, 12) ( 94/256=30/256+1/4)6 mask = (7, 233, ),f(x) =x 3 +2x 2 +2x +3 dist = (10, 16, 10, 28, 12, 18, 24, 10, 24, 18, 12, 10, 18, 12, 18, 16) mask = (7, 233, ),f(x) =3x 3 +3x 2 +1x +3 dist = (10, 16, 10, 28, 12, 18, 24, 10, 24, 18, 12, 10, 18, 12, 18, 16) mask = (7, 238, ),f(x) =x 3 +3x 2 + x +1 dist = (10, 28, 10, 16, 18, 16, 18, 12, 24, 10, 12, 18, 12, 10, 24, 18) mask = (7, 238, ),f(x) =3x 3 + x 2 +3x +1 dist = (10, 28, 10, 16, 18, 16, 18, 12, 24, 10, 12, 18, 12, 10, 24, 18) mask = (233, 238, ),f(x) =x 3 +2x 2 + x +1 dist = (10, 28, 16, 10, 18, 16, 12, 18, 12, 10, 18, 24, 24, 10, 18, 12) GF(2 3 ) mask = (233, 238, ),f(x) =2x 3 + x 2 +2x +1 dist = (10, 28, 16, 10, 18, 16, 12, 18, 12, 10, 18, 24, 24, 10, 18, 12) 8 GF(2 3 ) 0 mask0, mask1, mask GF(2 3 ) d 18
19 ( 57/256=25/256+1/8)7 mask = (40, 99, 215),f(x) =2x +7 mask = (61, 83, 185),f(x) =3x +4 mask = (61, 185, 234), f(x) =5x +6 mask = (83, 110, 234), f(x) =7x +4 mask = (99, 180, 255), f(x) =2x +1 mask = (110, 132, 185), f(x) =7x +6 mask = (132, 215, 234), f(x) =3x +7 ( 58/256=26/256+1/8)2 mask = (1, 7, 222),f(x) =4x 2 +3 mask = (7, 217, 223),f(x) =x 2 +7 ( 66/256=34/256+1/8)5 mask = (7, 27, 238),f(x) =7x 3 +5x 2 + x +3 mask = (7, 238, 245),f(x) =3x 3 +7x 2 + x +5 mask = (27, 28, 245),f(x) =6x 3 +4x 2 + x +5 mask = (28, 233, 238),f(x) =x 3 + x 2 + x +2 mask = (233, 242, 245),f(x) =5x 3 +3x 2 + x +5 65/256 : mask = (7, 117, 238),f(x) =7x 4 +2x 3 +6x 2 +6x +1 62/256 : mask = (1, 54, 239),f(x) =7x 5 +6x 4 +6x 3 +2x 2 +3x +5 62/256 : mask = (1, 55, 238),f(x) =3x 5 +2x 4 +4x 3 +5x 2 +4x +3 62/256 : mask = (1, 60, 185),f(x) =x 5 +4x 3 + x 2 +7x +7 62/256 : mask = (1, 61, 185),f(x) =6x 5 +2x 4 + x 3 +4x +5 MDSL MDSH Hierocrypt-L1 MDSL MDSH MDSL 4 S MDSH 19
20 S ( φ) MDSH S ( )-(S )-(MDSH)-( )-(S ) MDSL (MDS ) 5.2 Hierocrypt-L1 S Hierocrypt-L1 S MDSH HDSL x 8 + x 6 + x 5 + x +1 S ( 256 ) S ( ) 5.1: S 256 n n 1 n S t 1. t GF(2 8 ) t =2, 3, 4 5 S S 20
21 S :S(67 16 )=67 16 S OFB : 30738= ( 16 ): 109( ) e ec 8d b b6 26 3d 3e f9 cb 14 9d f0 ea db b 33 c9 8a 4a 57 b1 d4 93 f8 8f 0a ce 35 ed dc cd cf 45 0d e9 4c bd a6 e3 76 b7 2b f7 1d 5f 0f b a4 0e 5d c0 ad 5c fb 4f 1e 19 7a 7d b fc 16 f5 0c d d f df a f1 15 2e ac d6 da e4 36 de 97 b (= 3 47) c e7 3a 72 cc 6e 9e c5 c7 f2 dd ba 90 2c 8c ef 2a 4d c 95 e6 28 b9 86 4b e b c4 eb d9 53 9a b3 f3 c2 a bf 05 8e 3f d8 a b 18 c6 e f 1f c d7 ae f4 a5 6d fa b4 bb ff a0 52 b5 54 7c d5 e1 31 5a d a7 be 7b 3b a c a 5e 51 9f 7e af 5b 08 bc fe aa ee 62 1a 2f 17 e8 24 c3 10 1c b2 e a2 47 fd ab f c ca 6c 3 92 d1 d Hierocrypt-L1 SPN Hierocrypt-L1 S Hierocrypt-L1 Hierocrypt-L1 21
22 [1] : Hierocrypt-L1, available at security/hierocrypt/. [2] : Hierocrypt-3, available at security/hierocrypt/. [3] Specification on a Block Cipher: Hierocrypt-L1, available at rdc/security/hierocrypt/. [4],,,,, Hierocrypt-3 Hierocrypt-L1 /, ISEC ,, [5] J. Kelsey, B. Schneier, Key Schedule Weakness in SAFER+, Second AES Candidate Conference, 1999, available at [6] E. Biham, A. Biryukov, N. Ferguson, L. Knudsen, B. Schneier, A. Shamir, Cryptanalysis of Magenta, Second AES Candidate Conference, 1999, available at [7] A. Biryukov, D. Wagner, Slide Attacks, Fast Software Encryption, 6th International Workshop, FSE 99, Proceedings, Lecture Notes in Computer Science Vol. 1636, Springer-Verlag, [8] L. Knudsen, Cryptanalysis of LOKI, Advances in Cryptology, ASIACRYPT 91, Lecture Notes in Computer Science Vol. 739, Springer-Verlag, [9] C. H. Meyer, S. M. Matyas, Cryptography: A New Dimension in Coputer Data Security, New York: John Wiley & Sons, [10] J. Daemen, L. Knudsen, V. Rijmen, The Block Cipher Square, Fast Software Encryption, 4th International Workshop, FSE 97, Proceedings, Lecture Notes in Computer Science Vol. 1267, Springer-Verlag, [11] J. Daemen, V. Rijmen, AES Proposal: Rijndael, available at kuleuven.ac.be/~rijmen/rijndael/index.html [12] C. H. Lim, A Revised Version of Crypton -Crypton V1.0, Fast Software Encryption, 6th International Workshop, FSE 99, Proceedings, Lecture Notes in Computer Science Vol. 1636, Springer-Verlag, [13] L. Knudsen, T. Berson, Truncated Differentials of SAFER, Fast Software Encryption, third International Workshop, Proceedings, Lecture Notes in Computer Science Vol. 1039, Springer-Verlag,
23 Z1(-1) Z2(-1) Z3(-1) Z4(-1) V(0) M5 G(0) MB Z1(0) Z2(0) Z3(0) Z4(0) Note: M5 = MB -1 V(1) P W1(0) M5 G(1) MB W2(0) Z1(1) Z2(1) Z3(1) Z4(1) Z1(7) Z2(7) Z3(7) Z4(7) W1(1) P W2(1) W1(7) P -1 W2(7) V(2) M5 G(2) MB V(7) MB G(6) M5 Z1(2) Z2(2) Z3(2) Z4(2) Z1(6) Z2(6) Z3(6) Z4(6) W1(2) P W2(2) W1(6) P -1 W2(6) V(3) M5 G(3) MB V(6) MB G(5) M5 Z1(3) Z2(3) Z3(3) Z4(3) Z1(5) Z2(5) Z3(5) Z4(5) W1(3) P W2(3) W1(5) P -1 W2(5) V(4) M5 G(4) MB V(5) MB G(4) M5 Z1(4) Z2(4) Z3(4) Z4(4) Z1(4) Z2(4) Z3(4) Z4(4) 2: Intermediate keys generation (whole structure) 23
24 2: Evaluated S box (Hierocrypt-L1) 0x07, 0xFC, 0x55, 0x70, 0x98, 0x8E, 0x84, 0x4E 0xBC, 0x75, 0xCE, 0x18, 0x02, 0xE9, 0x5D, 0x80 0x1C, 0x60, 0x78, 0x42, 0x9D, 0x2E, 0xF5, 0xE8 0xC6, 0x7A, 0x2F, 0xA4, 0xB2, 0x5F, 0x19, 0x87 0x0B, 0x9B, 0x9C, 0xD3, 0xC3, 0x77, 0x3D, 0x6F 0xB9, 0x2D, 0x4D, 0xF7, 0x8C, 0xA7, 0xAC, 0x17 0x3C, 0x5A, 0x41, 0xC9, 0x29, 0xED, 0xDE, 0x27 0x69, 0x30, 0x72, 0xA8, 0x95, 0x3E, 0xF9, 0xD8 0x21, 0x8B, 0x44, 0xD7, 0x11, 0x0D, 0x48, 0xFD 0x6A, 0x01, 0x57, 0xE5, 0xBD, 0x85, 0xEC, 0x1E 0x37, 0x9F, 0xB5, 0x9A, 0x7C, 0x09, 0xF1, 0xB1 0x94, 0x81, 0x82, 0x08, 0xFB, 0xC0, 0x51, 0x0F 0x61, 0x7F, 0x1A, 0x56, 0x96, 0x13, 0xC1, 0x67 0x99, 0x03, 0x5E, 0xB6, 0xCA, 0xFA, 0x9E, 0xDF 0xD6, 0x83, 0xCC, 0xA2, 0x12, 0x23, 0xB7, 0x65 0xD0, 0x39, 0x7D, 0x3B, 0xD5, 0xB0, 0xAF, 0x1F 0x06, 0xC8, 0x34, 0xC5, 0x1B, 0x79, 0x4B, 0x66 0xBF, 0x88, 0x4A, 0xC4, 0xEF, 0x58, 0x3F, 0x0A 0x2C, 0x73, 0xD1, 0xF8, 0x6B, 0xE6, 0x20, 0xB8 0x22, 0x43, 0xB3, 0x33, 0xE7, 0xF0, 0x71, 0x7E 0x52, 0x89, 0x47, 0x63, 0x0E, 0x6D, 0xE3, 0xBE 0x59, 0x64, 0xEE, 0xF6, 0x38, 0x5C, 0xF4, 0x5B 0x49, 0xD4, 0xE0, 0xF3, 0xBB, 0x54, 0x26, 0x2B 0x00, 0x86, 0x90, 0xFF, 0xFE, 0xA6, 0x7B, 0x05 0xAD, 0x68, 0xA1, 0x10, 0xEB, 0xC7, 0xE2, 0xF2 0x46, 0x8A, 0x6C, 0x14, 0x6E, 0xCF, 0x35, 0x45 0x50, 0xD2, 0x92, 0x74, 0x93, 0xE1, 0xDA, 0xAE 0xA9, 0x53, 0xE4, 0x40, 0xCD, 0xBA, 0x97, 0xA3 0x91, 0x31, 0x25, 0x76, 0x36, 0x32, 0x28, 0x3A 0x24, 0x4C, 0xDB, 0xD9, 0x8D, 0xDC, 0x62, 0x2A 0xEA, 0x15, 0xDD, 0xC2, 0xA5, 0x0C, 0x04, 0x1D 0x8F, 0xCB, 0xB4, 0x4F, 0x16, 0xAB, 0xAA, 0xA0 24
25 3: Partial interpolations of the S box terms/deg/points equation points x (56, 92, 93, 106, 158, 172, 227, 241) x+81 x 2 (4, 38, 107, 136, 165, 176, 209, 241, 255) x+191 x 2 (11, 14, 42, 62, 70, 100, 233, 243, 245) x+239 x 2 (13, 40, 53, 55, 174, 232, 235, 249, 255) x+34 x 2 (15, 122, 143, 170, 175, 210, 211, 219, 226) x+205 x 2 (21, 44, 98, 117, 175, 196, 228, 238, 247) x+139 x 2 (23, 63, 73, 122, 124, 131, 139, 150, 214) x+33 x 2 (24, 75, 99, 107, 111, 134, 150, 201, 231) x+124 x 2 (26, 60, 68, 113, 123, 133, 154, 199, 206) x+61 x 2 (32, 46, 111, 153, 188, 200, 209, 217, 245) x+16 x 2 (36, 53, 69, 78, 103, 120, 170, 242, 250) x+109 x 2 (40, 63, 92, 94, 96, 150, 175, 186, 192) x+211 x 2 (41, 71, 78, 121, 141, 143, 158, 171, 248) x+148 x 2 (65, 73, 77, 79, 112, 143, 153, 194, 225) x+101 x x 3 (21, 33, 35, 61, 77, 82, 90, 104, 171, 173, 190, 213, 246) 25
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