共通鍵ブロック暗号CLEFIAの安全性評価報告書
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- さあしゃ こびき
- 5 years ago
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1 CLEFIA
2 CLEFIA 2007 SONY [5] /192/256 4 Type-2 Feistel ,256 22,26 CLEFIA [1] [12] CLEFIA 2 S-box S 0,S 1 ) CLEFIA 2 truncate S 0,S 1 truncate Viterbi DSM(Difffusion Switching Mechanism) active S-box truncate 2 S-box DSM Viterbi 1 128,192, , , , , ,2 192, ,16,20 CLEFIA truncate 2 S-box S 0,S 1 ) truncate S 0,S 1 Viterbi truncate 2 S-box DSM Viterbi 128,192, , , [13] DSM truncate [13] DSM 1
3 , , ,2 192, ,16,21 CLEFIA CLEFIA , , , 2 155,2 220 CLEFIA S-box (=128 ) 1 (=32 ) 2 (=64 ) 1 SP Feistel m n XOR m 2n [8] CLEFIA CLEFIA ,256 11, , ,2 223 CLEFIA S-box (S 0,S 1 ) S 0 6 S 1 7 F i F i F i F i 3 6 7) 2 F i S-box GF (2 8 ) 2
4 128 4 Type2 Feistel Type2 Feistel 10 truncate ,192, CLEFIA 128 3
5 1 6 2 CLEFIA CLEFIA truncate active Sbox CLEFIA Sbox F i CLEFIA truncate truncate CLEFIA Sbox F i CLEFIA truncate CLEFIA XOR F CLEFIA
6 CLEFIA CLEFIA CLEFIA XOR (m, n) (6.16) F i S-box S 0 S F i F i F i S box F i S-box S 0 S 1 GF(2 8 ) GF N 8,10 DCP GF N 8,10 DCP GF N 8,10 DCP GF N 8, A : 70 5
7 1 CLEFIA SONY FSE CRYPTREC CLEFIA CLEFIA CLEFIA CLEFIA 6
8 2 CLEFIA CLEFIA 4-way Feistel 4( 8)-way Feistel CLEFIA CLEFIA CLEFIA 4 Feistel 1 F 0 F 1 2 F CLEFIA 128bit X (0) 0 X (0) 1 X (0) 2 X (0) 3 32bit 2r RK 0,, RK 2r 1 4 WK 0,, WK 3 128bit r bit F 2.2 F 0 F F 0 F 1 S 0 S 1 8 S-box 2 M 0 M 1 0x01 0x02 0x04 0x06 M 0 = 0x02 0x01 0x06 0x04 0x04 0x06 0x01 0x02, (2.1) 0x06 0x04 0x02 0x01 0x01 0x08 0x02 0x0a M 1 = 0x08 0x01 0x0a 0x02 0x02 0x0a 0x01 0x08. (2.2) 0x0a 0x02 0x08 0x01 M 0 M 1 5 DSM Diffusion Swiching Mechanism) S-box (M 0 M 1 ) 5 z 8 + z 4 + z 3 + z GF(2 8 ) 2.2 L CLEFIA 128bit r ,256bit 8 Feistel L bit r bit GF N 8,10 WK i (0 i < 4) 7
9 2.1: CLEFIA 2.2: F 0, F 1 8
10 RK j (0 j < 2r) K L 2.3: GF N 8,10 9
11 3 CLEFIA [1] CLEFIA (DSM) CLEFIA 2 S-box 2 128,192,256bit CLEFIA , , , , [14] f(x) x y DP f n x DP f ( x, y) = {x {0, 1}n f(x) f(x x) = y} 2 n (3.1) f(x) DP max DP max = max DP f ( x, y) (3.2) x 0, y f(x) R i x i x i+1 DCP max DCP max = R 1 max x 0 0 x 1,, x i=0 R DP fi ( x i, x i+1 ) (3.3) x0 x1 xr 10
12 3.1.3 truncate truncate truncate DCP T max bit 1bit active Sbox bit 8bit truncate,4 4 = ( 0, 1, 2, 3 ) (3.4) ( 3.1) ( 3.2) active = ( 0, 1, 2, 3) (3.5) = ( 0, 1, 2, 3) (3.6) truncate i = i i (3.7) truncate : truncate or1 Δ Δ Δ 3.1: Δ Δ Δ Δ Δ 0 Δ 0 Δ 3.2: 11
13 3.1.4 active Sbox Sbox active Sbox active Sbox t active Sbox as (t) active Sbox AS(=Σas (t) ) AS AS min 3.2 CLEFIA CLEFIA 8bit truncate Sbox 2 Sbox S 0, S 1 S 0 : DP max = (3.8) S 1 : DP max = (3.9) S 0, S 1 DP max 3.2, : S 0 : DP max x 0x97 0xE2 0xE3 0x32 0xC6 0xF3 0x8 y 0xA 0xD 0x1E 0x20 0x30 0x7D 0x7E 3.3: S 1 : DP max x 0xA6 0xBE 0xEA 0xA2 0xFB 0xA9 0x2 y 0x14 0x1 0x13 0x2 0x3 0xFF 0xE F i F i truncate DP F T max 2 Sbox (S 0 : DP = , S 1 : DP = ) S 0 DP = , 3.5 DP F T max ( ) AS 0 ( ) AS 0 ( ) AS 1 (AS 0, AS 0, AS 1 ) (2 4.67, , ) active Sbox F 0 ( )=0xB,( )=0x3 DP F T max (AS 0 = 2, AS 1 = 1) DP F T max (AS 0 = 1, AS 0 = 1, AS 1 = 1) (log 2 DP F T max ) 12
14 3.4: F0 [log2] 0x0 0x1 0x2 0x3 0x4 0x5 0x6 0x7 0x8 0x9 0xA 0xB 0xC 0xD 0xE 0xF 0x x x x x x x x x x xA xB xC xD xE xF : F1 [log2] 0x0 0x1 0x2 0x3 0x4 0x5 0x6 0x7 0x8 0x9 0xA 0xB 0xC 0xD 0xE 0xF 0x x x x x x x x x x xA xB xC xD xE xF
15 3.2.3 CLEFIA truncate Sbox DCP T max F i CLEFIA Viterbi Viterbi DCP T max 3.3 F 8 truncate X i X i active D i X i 4 D i (0 D i 4) 2 st(0) = ( X 0, X 1, X 2, X 3 ) (3.10) 0 t = 1 st(1) = ( X 2, X 3, X 4, X 5, D 0, D 1 ) (3.11) st(0) st(1) truncate D 0 D 1 DSM t = 2 st(2) = ( X 4, X 5, X 6, X 7, D 0, D 1, D 2, D 3 ) (3.12) D 2 D 3 DSM t 2 st(t) = ( X 2t, X 2t+1, X 2t+2, X 2t+3, (3.13) D 2t 4, D 2t 3, D 2t 2, D 2t 1 ) M(DSM) CLEFIA MDS viterbi M 0, M 1 M 0, M 1 (M 0 ), (M 1 ), (M 0 M 1 ) 5 (M 0 M 1 ) (M 0 ) (M 1 ) [1], p.24, 2.2 2,3 14
16 X 0 X1 F 0 F 1 X 2 X3 F 0 F 1 X 4 X 5 F 1 F 0 X 6 X 7 F 1 F 0 X 8 X 9 F 0 F 1 4 bit 3.3: 1 t = 2a 1(a 1) D 2t+2 + D 2t+1 + D 2t 2 5 (D 2t+1 0) D 2t+3 + D 2t + D 2t 1 5 (D 2t 0) t = 2a(a 1) D 2t+2 + D 2t + D 2t 2 5 (D 2t 0) D 2t+3 + D 2t+1 + D 2t 1 5 (D 2t+1 0) 2 t = 2a 1(a 2) D 2t+2 + D 2t+1 + D 2t 3 + D 2t 6 5 (D 2t+1 + D 2t 3 0) D 2t+3 + D 2t + D 2t 4 + D 2t 5 5 (D 2t + D 2t 4 0) t = 2a(a 2) D 2t+2 + D 2t + D 2t 4 + D 2t 6 5 (D 2t + D 2t 4 0) D 2t+3 + D 2t+1 + D 2t 3 + D 2t 5 5 (D 2t+1 + D 2t 3 0) 1 F F st(t) st(t + 1) st(t) truncate X 2t, X 2t+1, X 2t+2, X 2t DP F T max 3.1, st(5) = ( X 10, X 11, X 12, X 13, D 6, D 7, D 8, D 9 ) =(0xB,0x7,0x1,0xA,0x0,0x4,0x2,0x1) X 14 ( X 14 = F ( X 12 ) X 10 ) F ( X 12 ) F (0x4, 0x5, 0x6, 0x7, 0xC, 0xD, 0xE, 0xF) 8 2 (3.14) (0x5,0x6,0x7,0xC,0xD,0xE,0xF) 7 D 14 (D 12 + D 8 + D 6 ) = 2 (3.14) 15
17 3.6: DCP T max [log 2 ] r AS min bit CLEFIA DCP 18round T max = bit CLEFIA DCPT 22round max = bit CLEFIA DCPT 26round max = AS min log 2 (DCP T max ) S 0 DCP T max S 0 S 1 DCP T max active Sbox AS min Sbox CLEFIA 2 Sbox DSM Viterbi truncate truncate 1 Sbox 2 Sbox CLEFIA 16
18 3.7: 18 t F 1 ( X 0 X 1 ) = 0x01 2 ( X 2 X 3 ) = 0x00 3 ( X 4 X 5) = 0x01 4 ( X 6 X 7) = 0x0f 5 ( X 8 X 9) = 0xb1 6 ( X 10 X 11 ) = 0x67 7 ( X 12 X 13 ) = 0x0b 8 ( X 14 X 15 ) = 0x60 9 ( X 16 X 17 ) = 0x00 10 ( X 18 X 19 ) = 0x60 11 ( X 20 X 21 ) = 0x0b 12 ( X 22 X 23) = 0x6a 13 ( X 24 X 25) = 0xb5 14 ( X 26 X 27) = 0x07 15 ( X 28 X 29 ) = 0x05 16 ( X 30 X 31 ) = 0x00 17 ( X 32 X 33 ) = 0x05 18 ( X 34 X 35 ) = 0x07 17
19 4 CLEFIA S-box active S-box CLEFIA (DSM) CLEFIA 2 Sbox 4.1 n bit f(x) Γ x Γ y f(x) LP (Γ x, Γ y ) LP (Γ x, Γ y ) = (2 #{x {0, 1}n x Γ x = y Γ y } 2 n 1) 2 (4.1) # (x Γ x = y Γ y ) GF(2) LP max LP max LP max = max LP (Γx, Γy) (4.2) Γx,Γy 0 (4.2) f(x) R i Γ xi Γ xi+1 LCP max LP (Γ xi, Γ xi+1 ) LCP max = max Γ x0,γ x1,,γ xr Γ xi 0 R 1 i=0 LP (Γ xi, Γ xi+1 ) (4.3) Γ x0 Γ x1 Γ x2 Γ xr 18
20 4.2 truncate truncate bit 1bit 1bit 1 active 0 non-acive passive Sbox bit 8bit truncate 1 (4 ) 4 Γ Γ = (Γ 0, Γ 1, Γ 2, Γ 3 ), Γ i GF(2). (4.4) active Γ Γ 4.1 Γ Γ Γ 4.1 truncate Γ i XOR Γ = Γ Γ (4.5) Sbox Sbox active Sbox active Sbox Γ Γ' Γ Γ Γ 0 0 Γ Γ' ' 0 Γ Γ 4.1: Γ Γ Γ 4.2: 4.1: truncate XOR or1 4.3 CLEFIA Sbox CLEFIA S-box S 0 S 1 (4.2) S 0 LP max = S 1 LP max =
21 LP max = , LP S1 max = S 0 LP max (Γ x, Γ y ) S 1 LP max (Γ x, Γ y ) : S 0 (Γ x, Γ y ) (0x1,0xdd) (0x2,0x7c) (0x3,0x6a) (0x3,0xe6) (0x7,0x7f) (0xb,0xe7) (0x1c,0xac) (0x1d,0x80) (0x2a,0x7d) (0x2b,0xec) (0x35,0x6) (0x35,0x6c) (0x3e,0xa0) (0x40,0xd1) (0x49,0x6f) (0x4b,0xfe) (0x53,0x90) (0x54,0x49) (0x5c,0x7a) (0x5f,0xc1) (0x69,0xe2) (0x6d,0xa2) (0x75,0x9) (0x79,0xe0) (0x7f,0x2b) (0x81,0x59) (0x85,0x11) (0x8c,0xd2) (0x95,0x20) (0x9d,0xa8) (0xa1,0x90) (0xa8,0xc7) (0xa8,0xf1) (0xb4,0xc0) (0xb9,0x23) (0xc0,0x39) (0xc3,0x16) (0xc4,0xbe) (0xc9,0x50) (0xd8,0x31) (0xdd,0x2c) (0xe5,0x68) (0xe6,0x6e) (0xed,0x30) (0xee,0x5) (0xee,0x19) (0xef,0x55) (0xf5,0x38) (0xf7,0x66) (0xf7,0xb0) (0xfc,0x5f) (0xff,0x22) 4.3: S 1 (Γ x, Γ y ) (0x1,0x1) (0x1,0x10) (0x1,0x11) (0x1,0x88) (0x1,0x98) (0x2,0x3) (0x2,0x10) (0x2,0x13) (0x2,0x88) (0x2,0x9b) (0x3,0x2) (0x3,0x10) (0x3,0x8a) (0x3,0x98) (0x3,0x9a) (0x4,0xc) (0x4,0x42) (0x4,0x4e) (0x4,0xa0) (0x4,0xee) (0x5,0xd) (0x5,0x47) (0x5,0x4a) (0x5,0x64) (0x5,0x69) (0x6,0x9) (0x6,0x62) (0x6,0xb5) (0x6,0xbc) (0x6,0xde) (0x7,0x29) (0x7,0x30) (0x7,0xc9) (0x7,0xe0) (0x7,0xf9) (0x8,0x5c) (0x8,0x85) (0x8,0xa1) (0x8,0xd9) (0x8,0xfd) (0x9,0x44) (0x9,0x77) (0x9,0x84) (0x9,0xc0) (0x9,0xf3) (0xa,0x18) (0xa,0x2c) (0xa,0x34) (0xa,0xdd) (0xa,0xe9) (0xb,0x20) (0xb,0x28) (0xb,0x52) (0xb,0x72) (0xb,0x7a) (0xc,0x2) (0xc,0x10) (0xc,0x11) (0xc,0x12) (0xc,0x13) (0xd,0x1) (0xd,0x10) (0xd,0x8b) F i Sbox F i 4.4, 4.5 log 2 LP F max 0x03, 0x07 F i
22 F i S-box 21
23 4.4: F0 [log2] 0x0 0x1 0x2 0x3 0x4 0x5 0x6 0x7 0x8 0x9 0xA 0xB 0xC 0xD 0xE 0xF 0x x x x x x x x x x xA xB xC xD xE xF : F1 [log2] 0x0 0x1 0x2 0x3 0x4 0x5 0x6 0x7 0x8 0x9 0xA 0xB 0xC 0xD 0xE 0xF 0x x x x x x x x x x xA xB xC xD xE xF
24 4.3.3 CLEFIA truncate Sbox LCP T max F i truncate CLEFIA Viterbi Viterbi DCP T max 4.3 F 8 truncate Γx i,γy i Γx i active L i Γx i,γy i 4 L i 0 L i 4 2 st(0) = (Γy 0, Γy 1, Γy 2, Γy 3 ) (4.6) 0 t=1 st(1) = (L 0, L 1, L 2, L 3, Γy 2, Γy 3, Γy 4, Γy 5 ) (4.7) st(0) st(1) 4.2 truncate L 0, L 1, L 2, L 3 DSM t 1 st(t) = (L 2t 2, L 2t 1, L 2t, L 2t+1, Γy 2t, Γy 2t+1, Γy 2t+2, Γy 2t+3 ) (4.8) M 0, M 1 (DSM) CLEFIA 2 DSM Viterbi M 0, M 1 M 0, M 1 ( t M0 1 ),(t M1 1 ), ( t M0 1 t M1 1 ) (t M0 1 )=(M 0), ( t M1 1 )=(M 1),( t M0 1 t M1 1 )= (M 0 M 1 ) 5 ( t M0 1 t M1 1 ) (M 0 M 1 ) ( t M0 1 ) ( t M1 1 ),(M 0) (M 1 )
25 4.3: t = 2a 1(a 1) { = 0 L 2t 2 + L 2t + L 2t+2 5 { = 0 L 2t 1 + L 2t+1 + L 2t+3 5 t = 2a(a 1) { = 0 L 2t 2 + L 2t+1 + L 2t+2 5 { = 0 L 2t 1 + L 2t + L 2t+3 5 (4.9) (4.10) (4.11) (4.12) 4.1, bit CLEFIA LCPT 18round max = bitCLEFIA LCPT 22round max = bitCLEFIA LCPT 26round max = AS log 2 (LCP T max ) S 0 LCP T max S 0, S 1 LCP T max 2 active Sbox S 0 S 1 AS 0,AS 1,AS 4.7,4.8, 4.9,
26 4.6: active Sbox LCP T max ( AS AS AS 0 AS 1 LCP T max LCP T max CLEFIA 2 Sbox DSM 8bit truncate Viterbi truncate truncate 1 Sbox 2 Sbox CLEFIA 25
27 4.7: 12 t F 1 (Γy 0 Γy 1 )=0x07 2 (Γy 2 Γy 3 )=0x00 3 (Γy 4 Γy 5 )=0x07 4 (Γy 6 Γy 7 )=0xb0 5 (Γy 8 Γy 9 )=0x57 6 (Γy 10 Γy 11 )=0xfb 7 (Γy 12 Γy 13)=0x77 8 (Γy 14 Γy 15)=0x5f 9 (Γy 16 Γy 17)=0x0f 10 (Γy 18 Γy 19 )=0x0f 11 (Γy 20 Γy 21 )=0x00 12 (Γy 22 Γy 23 )=0x0f 4.8: 18 t F 1 (Γy 0 Γy 1)=0xb0 2 (Γy 2 Γy 3 )=0x00 3 (Γy 4 Γy 5 )=0xb0 4 (Γy 6 Γy 7 )=0x07 5 (Γy 8 Γy 9 )=0xba 6 (Γy 10 Γy 11 )=0x7f 7 (Γy 12 Γy 13 )=0xba 8 (Γy 14 Γy 15)=0x0b 9 (Γy 16 Γy 17)=0xb0 10 (Γy 18 Γy 19)=0x00 11 (Γy 20 Γy 21 )=0xb0 12 (Γy 22 Γy 23 )=0x07 13 (Γy 24 Γy 25 )=0xbb 14 (Γy 26 Γy 27 )=0x3f 15 (Γy 28 Γy 29 )=0x0f 16 (Γy 30 Γy 31 )=0x0f 17 (Γy 32 Γy 33)=0x00 18 (Γy 34 Γy 35)=0x0f 26
28 4.9: 22 t F 1 (Γy 0 Γy 1 )=0xb0 2 (Γy 2 Γy 3)=0x00 3 (Γy 4 Γy 5)=0xb0 4 (Γy 6 Γy 7)=0x07 5 (Γy 8 Γy 9 )=0xba 6 (Γy 10 Γy 11 )=0x7f 7 (Γy 12 Γy 13 )=0xbb 8 (Γy 14 Γy 15 )=0xfb 9 (Γy 16 Γy 17 )=0xab 10 (Γy 18 Γy 19 )=0xb0 11 (Γy 20 Γy 21)=0x0b 12 (Γy 22 Γy 23)=0x00 13 (Γy 24 Γy 25)=0x0b 14 (Γy 26 Γy 27)=0x70 15 (Γy 28 Γy 29 )=0xab 16 (Γy 30 Γy 31 )=0xf7 17 (Γy 32 Γy 33 )=0xbb 18 (Γy 34 Γy 35 )=0xaf 19 (Γy 36 Γy 37 )=0x0f 20 (Γy 38 Γy 39)=0x0f 21 (Γy 40 Γy 41)=0x00 22 (Γy 42 Γy 43)=0x0f 4.10: 26 t F 1 (Γy 0 Γy 1 )=0xf0 2 (Γy 2 Γy 3)=0x00 3 (Γy 4 Γy 5)=0xf0 4 (Γy 6 Γy 7)=0x0f 5 (Γy 8 Γy 9 )=0xfa 6 (Γy 10 Γy 11 )=0x77 7 (Γy 12 Γy 13 )=0x7f 8 (Γy 14 Γy 15 )=0x57 9 (Γy 16 Γy 17 )=0x07 10 (Γy 18 Γy 19 )=0x07 11 (Γy 20 Γy 21)=0x00 12 (Γy 22 Γy 23)=0x07 13 (Γy 24 Γy 25)=0x0e 14 (Γy 26 Γy 27 )=0x37 15 (Γy 28 Γy 29 )=0xbb 16 (Γy 30 Γy 31 )=0x0a 17 (Γy 32 Γy 33 )=0xb0 18 (Γy 34 Γy 35 )=0x00 19 (Γy 36 Γy 37 )=0xb0 20 (Γy 38 Γy 39)=0x07 21 (Γy 40 Γy 41)=0xbb 22 (Γy 42 Γy 43)=0x3f 23 (Γy 44 Γy 45)=0x0f 24 (Γy 46 Γy 47 )=0x0f 25 (Γy 48 Γy 49 )=0x00 26 (Γy 50 Γy 51 )=0x0f 27
29 5 CLEFIA CLEFIA [6] , , ,2 220 CLEFIA Feistel [7] Feistel F 5 Feistel HIGHT HIGHT CLEFIA F XOR ( ) XOR F F : Zero 0 Fix 0 Delta 0 (Zero ) Random (Zero ) Z F D R 28
30 XOR F 5.2 XOR x y = z x Z y D z D CLEFIA F S-box MDS F 1 F x y = F( x) 5.2 F x F y D 5.2: XOR F XOR y F Z F D R Z Z F D R Z x F F Z R R D D D R R R D R R R R R R F MDS : Zero 0 Fix 0 Delta 0 (Delta Fix) Delta2 0 (Delta2 = Fix Delta) Delta3 0 Random (Zero ) Delta2 Delta3 D2 D3 XOR F : XOR F x XOR y Z F D D2 D3 R F Z Z F D D2 D3 R Z F F Z D2 D R R D D D D2 R R R R D3 D2 D2 D R R R R D3 D3 D3 R R R R R D3 R R R R R R R R
31 [6] : Zero 0 Fix 0 Delta 0 (Delta Fix) Delta2 0 (Delta2 = Fix Delta) Delta3 0 (Delta3 = Delta Delta) Delta4 0 (Delta4 = Delta Delta2) Delta5 0 Random (Zero ) Delta4 Delta5 D4 D5 XOR F : XOR F XOR y F Z F D D2 D3 D4 D5 R x Z Z F D D2 D3 D4 D5 R Z F F Z D2 D R R R R D D D D2 D3 D4 R R R R D5 D2 D2 D D4 R R R R R D5 D3 D3 R R R R R R R D5 D4 D4 R R R R R R R D5 D5 D5 R R R R R R R D5 R R R R R R R R R R ( ) ( ) 2 F k Feistel α=(α 0, α 1,, α k 1 ) α a=(a 0, a 1,, a k 1 ) α r α (r) =(α (r) 0, α(r) 1,, α(r) k 1 ) α(r) a (r) =(a (r) 0, a(r) 1,, a (r) k 1 ) a i a (r) i (0 i k 1) α, α i, α (r), α (r) i, a, a i, a (r), a (r) i β, β i, β (r), β (r) i, b, b i, b (r), b (r) i 30
32 r e a (re) =(a (r e) 0, a (r e) 1, a (r e) 2, a (r e) 3 ) r d b (rd) =(b (r d) 0, b (r d) 1, b (r d) 2, b (r d) 3 ) ( ) b (r d) 0 = a (r e) 1 F 0 a (r e) 0 (5.1) b (r d) 1 = a (re) 2 (5.2) ( ) b (r d) 2 = a (r e) 3 F 1 a (r e) 2 (5.3) b (r d) 3 = a (re) 0 (5.4) (5.2) (5.4) (5.1) (5.3) ( ) a (re) 1 = b (r d) 0 F 0 b (r d) 3, (5.5) a (r e) 3 = b (r d) 2 F 1 ( b (r d) 1 ). (5.6) (5.1) (5.5) (5.3) (5.6) a (re) 1 = b (r d) 0 {Z, F } a (re) 3 = b (r d) 2 {Z, F } XOR F F 0 ( F 1 ( a (re) 0 a (r e) 2 ) = F 0 ( ) = F 1 ( b (r d) 3 b (r d) 1 ) = Z, (5.7) ) = Z, (5.8) a (re) 0 b (r d) 3 a (re) 2 b (r d) 1 Z (5.7) (5.8) (r e + r d + 1) 0 0 r e a (re) =(a (r e) 0, a (r e) 1, a (r e) 2, a (r e) 3 ) r d b (rd) =(b (r d) 0, b (r d) 1, b (r d) 2, b (r d) 3 ) (a (re) i )(0 i 3) 1 (r e + r d ) b (r d) i Step1 a=(a 0, a 1, a 2, a 3 ) { (Z, Z, Z, F), (Z, Z, F, Z),, (F, F, F, F)} XOR F Step2 b=(b 0, b 1, b 2,b 3 ) { (Z, Z, Z, F), (Z, Z, F, Z),, (F, F, F, F)} XOR F Step3 31
33 5.2 CLEFIA F CLEFIA (Z, Z, Z, F) (Z, Z, Z, F) (Z, F, Z, Z) (Z, F, Z, Z) 9 (Z, Z, Z, F) (Z, Z, Z, F) F MDS 5.1: 9 (Z, Z, Z, F) (Z, Z, Z, F) (Z, F, Z, Z) (Z, F, Z, Z) CLEFIA 32
34 6 CLEFIA ( ) 10, 11,12 CLEFIA [15] n ( m bit) XOR ( ) (m, n) (m, n) [16] CLEFIA 33
35 6.1 CLEFIA CLEFIA bit 10 CLEFIA bit CLEFIA Daemen SQUARE [9] AES [10] X GF(2) n K GF(2) s Y GF(2) m Y = E(X; K) E(X; K) X i (i) V (i) E(X; K) = α V (i) E(X α; K) (6.1) V (i) GF(2) n i V (i) α (i) V (i) (i) 1 E(X; K) X N { (N) E(X; K) = const (6.2) (N+1) E(X; K) = 0 const X i {0, 1} j (0 i < 2 j ) 2 j j X i Y i X i 5 Constant : i 0, i 1 ; X i0 = X i1 All : i 0, i 1 ; i 0 i 1 X i0 X i1 Even/odd : i 0, i 1 ; Y i0 = Y i1 (mod 2) Balance : X i = 0 Unknown : i Constant C All A Even/odd E Balance B Unknown U 34
36 2 E : GF(2) n GF(2) s GF(2) n Y GF(2) n C A E B n 0 R E R X GF(2) n (R 1) Y (R 1) (X) GF(2) m Y (R 1) (X) = E (R 1) (X; K 1, K 2,, K (R 1) ) (6.3) K i GF(2) s i C GF(2) n R K R Y (R 1) Ẽ( ) : GF(2)n GF(2) s GF(2) m Y (R 1) (X) = Ẽ(C(X); K R) (6.4) E (R 1) ( ) 1 2 (N) Y (R 1) (X) = 0 (6.5) (6.4) (6.5) Ẽ(C(X α); K R ) = 0 (6.6) a V (N) (6.6) (6.6) K R 1 2 m K R CLEFIA [12] 6 [11] 8 ( C, A, C, C ) 6r ( B, U, U, U ), ( C, C, C, A ) 6r ( U, U, B, U ), ( A 0, C, A 1, A 2 ) 8r ( B, U, U, U ), ( A 0, A 1, A 2, C ) 8r ( U, U, B, U ). A 0 A 1 A 2 All 96bit F SP m 2n 4 Type-2 Feistel 6 8 [8] m S-box n S-box ( C, A, C, C ) 6r ( B, U, B, U ), ( C, C, C, A ) 6r ( B, U, B, U ), ( A 0, A 1, C, A 2 ) 8r ( B, U, B, U ), ( C, A 0, A 1, A 2 ) 8r ( B, U, B, U ). 35
37 CLEFIA 4 Type-2 Feistel 1 F F SP CLEFIA 6 Type-2 Feistel CLEFIA 128bit X 4 X i GF(2) 32 (1 i 4) 1 8bit 4 X ij GF(2) 8 (1 j 4) X = (X 1, X 2, X 3, X 4 ), X i = (X i1, X i2, X i3, X i4 ) GF N 8, CLEFIA (d 1) ( (C C C C) (A C C C) (C C C C) (C C C C) ) 5r ( (U U U U) (U U U U) (B B B B) (U U U U) ) (d 2) ( (C C C C) (C C C C) (C C C C) (A C C C) ) 5r ( (B B B B) (U U U U) (U U U U) (U U U U) ) (A C C C) (C A C C), (C C A C) (C C C A) CLEFIA (d 1) (d 2) 8 5 (d 3) ( (C C C C) (A C C C) (C C C C) (A C C C) ) 5r ( (B B B B) (U U U U) (B B B B) (U U U U) ) CLEFIA (d 4) (EEEE) (d 4) ( (C C C C) (A A A A) (C C C C) (C C C C) ) 6r ( (B B B B) (U U U U) (B B B B) (U U U U) ) 36
38 (d 5) ( (C C C C) (C C C C) (C C C C) (A A A A) ) 6r ( (B B B B) (U U U U) (B B B B) (U U U U) ) (I) ( (A A A A) (A A A A) (C C C C) (A A A A) ) 8r ( (B B B B) (U U U U) (B B B B) (U U U U) ) (II) ( (C C C C) (A A A A) (A A A A) (A A A A) ) 8r ( (B B B B) (U U U U) (B B B B) (U U U U) ) 6.1: 6 CLEFIA CLEFIA B [8] 37
39 6.1.3 CLEFIA CLEFIA 8 (I) (II) CLEFIA (I) CLEFIA 9 [12] 10 CLEFIA 9 F 0 M M0 1 M 0 M0 1 = M 0 6.2: 10 CLEFIA i C (i) = (C (i) 0, C(i) 1, C(i) 2, C(i) 3 ) 6.2 (6.6) ( ) ) F0 (F 1 C (10) 2 ; RK 19 C (10) 3 ; RK 16 C (10) 0 = 0, (6.7) ( ) ) F1 (F 0 C (10) 0 ; RK 18 C (10) 1 ; RK 17 C (10) 2 = 0, (6.8) 38
40 RK 16 = WK 3 RK 16 RK 17 = WK 2 RK 17 (6.7) 64bit RK 16=RK 16(0) RK 16(1) RK 16(2) RK 16(3) RK C (10) XOR M 1 0 Y = Y 0 Y 1 Y 2 Y 3 2. ( A 0, A 1, C, A 2 ) 2 96 C (10) 2 C (10) 3 64bit LIST(C (10) 2, C (10) 3 ) = LIST(C (10) 2 ) LIST(C (10) 3 ) 3. l (10) C LIST(C (10) 2 ) l (10) 2 C LIST(C (10) 3 ) RK 19 3 X i (0 i 3) 8bit LIST(X i ) l C (10) 3 ) F 1 (l (10) C ; RK 19 = X, (6.9) 2 X = X 0 X 1 X 2 X l Xi LIST(X i ) RK 16(i) ( ) Sj l Xi RK 16(i) = Y i (0 i 3) (6.10) RK 16 RK 19 j i 0 1 (6.8) RK 17 RK 18 (6.10) 8bit 4 ( 2 8) 4 = 2 32 (6.9) 64bit RK 16 RK 19 3(> ) XOR S-box F 1 2 Y LIST(C (10) 2, C (10) 3 ) = 2 97 F bit RK 19 64bit LIST(C (10) 2, C (10) 3 ) X X 8bit LIST(X i ) (0 i 3) LIST(X i ) 8bit RK 16(i) 232 ( ) 2 96 F 64bit F CLEFIA 20 F F = (6.8) = bit 10 CLEFIA 64bit LIST(C (10) 2, C (10) 3 ) 32bit LIST(X) bit 39
41 11/12 11/12 10 LIST(C (10) 2, C (10) 3 ) LIST(X i ) RK 19 RK 16(i) 11/ bit 96 5(> ), 7(> 32 ) 11/12 CLEFIA , bit CLEFIA : CLEFIA ,192, , RK B B CLEFIA CLEFIA 6 8 CLEFIA 128bit 10 CLEFIA bit CLEFIA CLEFIA 128bit /256bit CLEFIA 40
42 6.2 XOR (m, n) (m, n) (m, n) n ( m bit) XOR ( ) XOR (m, n) m < 2n m = 2n (m, n) (m, n) Type-2 Feistel [8] (m, n) (m, n) (m, n) 6.3 (m, n) (m 2, n 1) bit m x i u i g i (i = 0, 1, 2,, n 1) X = x 0 x 1 x n 1 (m, n) ( ) (m, n) y u i XOR ( ) g i u i 2 m 1 i=0 u i = 0. (6.11) u i y x i = 0, 1, 2,, 2 m 1 u i ( ) f i (u) ( f i (u) = 2 m ) X = 0, 1, 2,, 2 mn 1 y f y (y) ( f y (y) = 2 mn ) f i (u) mod2 f (2) i (u) mod2 f i (u) f (2) i (u) (m, n) (m 2, n 1) [ 1] m < 2n f y (y) y [ 2] m = 2n (f y (0) + f y (y)) y f y (τ) f y (τ) = 2 m 1 2 m 1 u 0=0 u 1=0 2 m 1 u n 2=0 f 0 (u 0 )f 1 (u 1 ) f n 2 (u n 2 ) f n 1 (u 0 u 1 u n 2 τ). (6.12) f i (u) φ i (t) f i (u) φ i (t) H 2 m H 2 m H 1 2m (6.12) f y (τ) = H 1 2 m { φ0 (t)φ 1 (t) φ n 2 (t)φ n 1 (t) }. (6.13) 41
43 X x 0 x 1 x n-1 m m m g 0 g 1 g n-1 m m m u 0 u 1 u n-1 m y 6.3: (m, n). H 2 m, H 1 2m ( ) f (2) i (u) f i (u) g i f (2) i (u) 2 m, 2 m m 1 H 2 m H 2 mf (2) i = 0, f (2) i = (f (2) i (0), f (2) i (1),, f (2) i (2 m 1)) t. (6.14) ( ) t (6.14) XOR (6.14) H 2 mf i = ( ), f i = (f i (0), f i (1),, f i (2 m 1)) t. (6.15) (6.15) φ i (t) = H 2 mf i (u) ( ) φ i (t) 4. (6.16) (6.13) H 1 2 m = 1 2 m H f y (τ) 4 n /2 m = 2 2n m m < 2n f y (τ) τ ( 1 ) 2 y =
44 f y (0) + f y (τ) f y (0) + f y (τ) = 2 m 1 2 m 1 u 0=0 u 1=0 f y (0) + f y (τ) = u 0 U(τ) u 1 U(τ) 2 m 1 u n 2=0 f 0 (u 0 )f 1 (u 1 ) f n 2 (u n 2 ) {f n 1 (u 0 u 1 u n 2 ) +f n 1 (u 0 u 1 u n 2 τ) }. (6.17) u n 2 U(τ) {f 0 (u 0 ) + f 0 (u 0 τ)} {f 1 (u 1 ) + (f 1 (u 1 τ)} {f n 2 (u n 2 ) + f n 2 (u n 2 τ)} {f n 1 (u 0 u 1 u n 2 ) +f n 1 (u 0 u 1 u n 2 τ) }. (6.18) U = {0, 1, 2,, 2 m 1} τ U(τ) {U(τ), U(τ) τ} = U F i (u) = (f i (u) + f i (u τ)) (u u τ) φ Fi (t) = H 2 m 1F i (u) (6.16) φ Fi (t) f y (0) + f y (τ) φ Fi (t) 4. (6.19) f y (0) + f y (τ) = 1 2 m 1 H 2 m 1φ(t), φ(t) = φ F0 (t)φ F1 (t) φ Fn 1 (t). (6.20) 1 0 (6.22) x=0 (6.19) φ(t) 4 n f y (0) + f y (τ) 4 n /2 m 1 = 2 2n m+1 m 2n f y (0) + f y (τ) τ ( 2 ) GF(2) m 2 p i (x) (i = 0, 1) (x GF(2) m, p i (x) R) p i (x) P i (t) = H 2 m p i (x) (t GF(2) m, P i (t) R) H 2 m P i (t) = x p i (x)( 1) x t. (6.21) 43
45 H 1 2 m p i (x) = 1 2 m P i (t)( 1) x t. (6.22) p 0 (x) p 1 (x) q(τ ) q(τ ) t q(τ ) = p 0 (x) p 1 (x) = x p 0 (x)p 1 (x τ ). (6.23) q(τ ) Q(t) Q(t) Q(t) = τ = τ q(τ )( 1) τ t p 0 (x)p 1 (x τ )( 1) τ t. (6.24) x (6.24) σ = x τ Q(t) = p 0 (x)p 1 (σ)( 1) (x σ) t σ x = p 0 (x)p 1 (σ)( 1) x t σ t. (6.25) σ x (-1) 0 = 1 (6.25) ( 1) x t σ t = ( 1) x t ( 1) σ t (6.25) Q(t) = p 0 (x)( 1) x t p 1 (σ)( 1) σ t σ x = p 0 (x)( 1) x t p 1 (σ)( 1) σ t x σ = P 0 (t) P 1 (t). (6.26) (6.22) (6.26) (6.23) q(τ ) i = 0, 1, 2, (6.16) (6.16) H H 1 H 1 = 1, [ H 2 m = H 2 m 1 H 2 m 1 H 2 m 1 H 2 m 1 ], H 1 2 = 1 m 2 m H 2m, (1 m N). (6.27) H H 2 m m m 1 H 2 m 2 m H 2 m ( H 2 m
46 ) φ = H 2 m f i φ 0 φ 0 2 m ( 2 m 1 u=0 f i (u) = 2 m. f i (u) f i ) 1 φ 1 2 m m 1 2 φ 1 = f i (2u) f i (2u + 1). (6.28) u=0 1 2 (6.15) (6.28) u=0 φ 1 = ( 2 m 1 + 2a ) ( 2 m 1 2a ) = 4a, (a Z). (6.29) φ 1 φ (6.29) 4 (6.16) 45
47 7 S-box S 0 S 1 GF(2 8 ) CLEFIA 7.1 F 0 F 0 F 1 F 1 P 0 3 F 0 P 1 F 1 3 F i S-box 7 ( 6 ) : CLEFIA 46
48 7.1 F i S-box S 0 S bit S-box: GF(2) 8 GF(2) 8 x i, y i GF(2) (i = 0, 1, 2,, 7) y i S 0 6 S 1 7 S i 7.1, y 0 y , 7.2 (i )/2 7.1, 7.2 S 0 y i 6 S 1 y i 7 S 0 y 1 S 1 y 3 S 0 y 6 S 1 y 4 7.2: 8bit S-box 47
49 7.1: S 0 y0 y1 y2 y3 y4 y5 y6 y C 6 /2= C 5 /2= C 4 /2= C 3 /2= C 2 /2= C 1 /2= C 0 /2= : S 1 y0 y1 y2 y3 y4 y5 y6 y C 7 /2= C 6 /2= C 5 /2= C 4 /2= C 3 /2= C 2 /2= C 1 /2= C 0 /2= F i F S box F i 4 4MDS F i 32 (i=0,1) F i 2 F i CLEFIA 2 F i 7.3 x i (i = 0, 1, 2,, 63) y i (i = 0, 1, 2,, 31) XOR 48
50 7.3: F i F i 32 7 (i = 0,1) XOR (i = 0,1) 2 F i = F i 7.3 x i (i = 32, 33,, 63) 2 F i x i (i = 0, 1,, 31) y i (i = 0, 1,, 31) y i x i (i = 0, 1,, 31) 31 y i x i (i = 32, 33,, 63) 7 F i S box 7.3 y i x i (i = 32, 33,, 63) 32 2 F i ( 7.4) x i, y i, z i 1 x 0 = (x 00, x 01,, x 07 ) x 1, x 2, x 3 x 0 z 0 z 0 x 0j 7 z 1, z 2, z 3 x 0j 7 x 1, x 2, x 3 z i (i = 0, 1, 2, 3) x ij (i = 0, 1, 2, 3, j = 0, 1,, 7) 7 4 = 28 MDS y i
51 7.4: 32 2 F i F (X; K) X N X,K (N+1) F (X; K)=0 deg X {F (X; K)}=N (N) F (X; K)=const F i x i (i = 0, 1, 2, 3) x ij (j = 0, 1,, 7) x i (i = 0, 1, 2, 3) x i0 x i1 x i2 x i3 x i4 x i5 x i6 x i C 28 4 x i (i = 0, 1, 2, 3) 7 ( 8 C 7 ) 4 = y i (i = 0, 1,, 31) y i (i = 0, 1,, 31) , (x 0, x 1, x 2, x 3 ) 32 (x 0, x 1,, ) x 1 7 x 0 x 2 x 3 x 4 x 5 x 6 x 7 x 7 [1] 28 x 28 [2,11,18,24] x 2, x 11, x 18, x x 28 [2,11,18,24] F DEF 7BDD 28 y i (i = 0, 1, 2,,31) 1, 0 1 MDS (36) 2 =
52 F i F 0 F F i 28 x i 8 8 x 28 [14,18,22,26] 7.3: 28 F y i (i = 31, 30,, 1, 0) x 28 [2,11,18,24] DFEFDF7F x 28 [1,13,23,31] BFFBFEFE x 28 [5,10,19,29] FBDFF7FB x 28 [5,13,17,26] FBFBFBDF x 28 [5,10,17,26] FBDFBFDF x 28 [1,10,17,26] BFDFBFDF x 28 [1,9,19,24] BFBFEF7F x 28 [14,18,22,26] FFFDDDDF : 28 F y i (i = 31, 30,, 1, 0) x 28 [2,11,18,24] DFEFDF7F x 28 [1,13,23,31] BFFBFEFE x 28 [5,10,19,29] FBDFF7FB x 28 [5,13,17,26] FBFBFBDF x 28 [5,10,17,26] FBDFBFDF x 28 [1,10,17,26] BFDFBFDF x 28 [1,9,19,24] BFBFEF7F x 28 [14,18,22,26] FFFDDDDF F i F i
53 7.5: 26 F y i (i = 31, 30,, 1, 0) x 26 [6,11,16,21,26,30] FDEF7BDD x 26 [3,7,11,16,20,27] EEEF77EF x 26 [2,6,12,18,21,26] DDF7DBDF x 26 [4,14,21,25,27,30] F7FDFBAD x 26 [1,2,9,17,21,29] 9FBFBBFB x 26 [1,4,8,11,23,29] B76FFEFB x 26 [3,8,15,20,23,31] EF7EF6FE x 26 [1,6,7,10,24,28] BCDFFF : 27 F y i (i = 31, 30,, 1, 0) x 27 [5,10,16,23,27] FBDF7EEF x 27 [4,9,15,21,30] F7BEFBFD x 27 [2,10,23,26,29] DFDFFEDB x 27 [6,8,13,20,27] FD7BF7EF x 27 [4,7,12,21,24] F6F7FB7F x 27 [1,9,16,20,26] BFBF77DF x 27 [4,12,18,23,25] F7F7DEBF x 27 [1,2,3,15,16] 8FFE7FFF : 26 F y i (i = 31, 30,, 1, 0) x 26 [6,11,16,21,26,30] FDEF7BDD x 26 [3,7,11,16,20,27] EEEF77EF x 26 [2,6,12,18,21,26] DDF7DBDF x 26 [4,14,21,25,27,30] F7FDFBAD x 26 [1,2,9,17,21,29] 9FBFBBFB x 26 [1,4,8,11,23,29] B76FFEFB x 26 [3,8,15,20,23,31] EF7EF6FE EFEEEF x 26 [0,4,11,19,23,27] x 26 [1,6,7,10,24,28] BCDFFF
54 7.8: 27 F y i (i = 31, 30,, 1, 0) x 27 [5,10,16,23,27] FBDF7EEF x 27 [4,9,15,21,30] F7BEFBFD x 27 [2,10,23,26,29] DFDFFEDB x 27 [6,8,13,20,27] FD7BF7EF x 27 [4,7,12,21,24] F6F7FB7F x 27 [1,9,16,20,26] BFBF77DF x 27 [4,12,18,23,25] F7F7DEBF x 27 [1,2,3,15,16] 8FFE7FFF , y i (i = 0, 1,, 31)
55 7.9: 31 F y i (i = 31, 30,, 1, 0) [0] 7FFFFFFF [1] BFFFFFFF [2] DFFFFFFF [3] EFFFFFFF [4] F7FFFFFF [5] FBFFFFFF [6] FDFFFFFF [7] FEFFFFFF [8] FF7FFFFF [9] FFBFFFFF [10] FFDFFFFF [11] FFEFFFFF [12] FFF7FFFF [13] FFFBFFFF [14] FFFDFFFF [15] FFFEFFFF [16] FFFF7FFF [17] FFFFBFFF [18] FFFFDFFF [19] FFFFEFFF [20] FFFFF7FF [21] FFFFFBFF [22] FFFFFDFF [23] FFFFFEFF [24] FFFFFF7F [25] FFFFFFBF [26] FFFFFFDF [27] FFFFFFEF [28] FFFFFFF [29] FFFFFFFB [30] FFFFFFFD [31] FFFFFFFE
56 7.10: 31 F y i (i = 31, 30,, 1, 0) [0] 7FFFFFFF [1] BFFFFFFF [2] DFFFFFFF [3] EFFFFFFF [4] F7FFFFFF [5] FBFFFFFF [6] FDFFFFFF [7] FEFFFFFF [8] FF7FFFFF [9] FFBFFFFF [10] FFDFFFFF [11] FFEFFFFF [12] FFF7FFFF [13] FFFBFFFF [14] FFFDFFFF [15] FFFEFFFF [16] FFFF7FFF [17] FFFFBFFF [18] FFFFDFFF [19] FFFFEFFF [20] FFFFF7FF [21] FFFFFBFF [22] FFFFFDFF [23] FFFFFEFF [24] FFFFFF7F [25] FFFFFFBF [26] FFFFFFDF [27] FFFFFFEF [28] FFFFFFF [29] FFFFFFFB [30] FFFFFFFD [31] FFFFFFFE
57 7.4 S-box S 0 S 1 GF(2 8 ) CLEFIA S-box S 0 S 1 GF(2 8 ) [1] 7.11, 7.12 S-box S i (i = 0, 1): GF(2 8 ) GF(2 8 ) y = S i (x) y x 244 (i = 0), 252 (i = 1) 7.13, 7.14 GF(2 8 ) cp(x): 0x11b (= x 8 + x 4 + x 3 + x + 1) S (x 255, x 254, x 253, x 251, x 247, x 239, x 223, x 191, x 127 ) [1] [1] 7.11: S a.b.c.d.e.f d1 c6 2f fb 95 6d 82 ea 0e b0 a8 1c d0 4b 92 5c ee 85 b1 c4 0a 76 3d 63 f9 17 af 2. bf a f7 7a ce e4 83 9d 5b 4c d d 2e e8 d4 9b 0f 13 3c c0 71 aa b6 f5 4. a4 be fd 8c da 78 e1 cf 6b cc dd eb 54 b3 8f 4e 16 fa 22 a d6 2a c1 6c ae ef b 1d f2 b4 7. e9 c7 9f 4a fe 7c d3 a2 bd b 8. cd e e dc b b7 a9 48 ff 66 8a f1 6a a7 40 c2 b9 2c db 1f e ed a. fc 1b a0 04 b8 8d e e ca 21 df 47 b. 15 f3 ba 7f a6 69 c8 4d 87 3b 9c 01 e0 de c. 7b 0c 68 1e 80 b2 5a e7 ad d5 23 f4 46 3f 91 c9 d. 6e bb 0d 18 d9 96 f0 5f 41 ac 27 c5 e3 3a e. 81 6f 07 a3 79 f6 2d 38 1a 44 5e b5 d2 ec cb 90 f. 9a 36 e5 29 c3 4f ab f8 10 d7 bc 02 7d 8e 56
58 7.12: S a.b.c.d.e.f 0. 6c da c3 e9 4e 9d 0a 3d b8 36 b c d9 1. bf f b7 9c e5 dc 9e f 98 2c b eb cd b3 92 e e b e6 19 d2 0e c7 3f 2a 8e a1 bc 2b c8 c5 0f 5b f3 87 8b 4. fb f5 de 20 c6 a7 84 ce d c9 a4 ef d 9b 31 e8 3e 0d d7 80 ff 69 8a ba 0b 73 5c 6. 6e f a3 16 d fa aa 5e 7. cf ea ed b 63 c0 c1 46 1e df a c ec dd 83 1f 9. 9a c a d ca 6f a. 7e 6a b6 71 a d1 45 8c 23 1c f0 ee 89 ad b. 7a 4b c2 2f db 5a 4d d f4 cb b1 4a a8 c. b a d5 10 4c 72 cc 00 f9 e0 fd e2 fe ae d. f8 5f ab f1 1b d6 be a6 57 b9 af f2 e. d bb 68 9f c 7f 8d 1a 88 bd ac f. f7 e a2 fc 6d b2 6b 03 e1 2e 7d d 57
59 7.13: S 0 cp(x) 11b d b d f d f b b d f a a b bd c cf d dd e f f f
60 7.14: S 1 cp(x) 11b d b d f d f b b d f a a b bd c cf d dd e f f f
61 Type2 Feistel Type2 Feistel ,192, CLEFIA
62 8.1 (DCP) DCP /256bit GF N 8,10 ( ) 32bit k i (i = 0, 1,, 7) l i (i = 0, 1,, 7) k 0 = k 0 l 0 = l 0 x j y j (j = 0, 1,, 39) F i (i = 0, 1) x j = x j (j = 0, 1, 2, 3, 4) DCP DCP 8.1 DCP 128bit GF N 4,12 GF N 4,12 DCP 3.6 GF N 4,12 DCP (DCP ) < 2 128bit 2 S-box (S 0, S 1 ) k 0 k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 0 x 0 y 0 x 10 y 10 x 20 y 20 x 30 y 30 x 0 x 5 y 5 x 15 y 15 x 25 y 25 x 35 y 35 x 1 y 1 x 11 y 11 x 21 y 21 y 31 x 1 x 6 y 6 x 16 y 16 x 26 y 26 x 36 y 36 x 2 y 2 x 12 y 12 x 22 y 22 x 32 y 32 x 2 x 7 y 7 x 17 y 17 x 27 y 27 x 37 y 37 x 3 y 3 x 13 y 13 x 23 y 23 x 33 y 33 x 3 x 8 y 8 x 18 y 18 x 28 y 28 x 38 y 38 x 4 y 4 x 14 y 14 x 24 y 24 x 34 y 34 x 4 x 9 y 9 x 19 y 19 x 29 y 29 x 39 y 39 l 0 l 1 l 2 l 3 l 4 l 5 l 6 l 7 l 0 8.1: GF N 8, GF N 8,10 DCP DCP 8bit truncation DSM DCP Vterbi 61
63 F i F i k i l i 2 F i x i ( 8 ) 2 F i x i ( 8 ) ( x i, x i+10, x i+20, x i+30, x i+5, x i+15, x i+25, x i+35, x i+1, x i+11, x i+21, x i+31, x i+6, x i+16, x i+26, x i+36 ) x i 0 0xf 16 x i (= ) GF N 8,10 DCP GF N 8,10 DCP 8.1 ( x 0, x 1, x 2, x 3, x 4 ) 5 (DCP ) ( x 0, x 1, x 2, x 3, x 4) x i = x i (i = 0, 1, 2, 3, 4) 8.2 Step0: ( x 0, x 1, x 2, x 3, x 4 ), k 1 Step5: ( x 5, x 6, x 7, x 8, x 9 ) x 0 = x 1 =0 f=0, f=1 Step1: (f, k 1 + x 0, x 1, x 2, x 3, x 4, x 5 = y 0 k 1 ) : DP( x 1 y 1 ) Step2: ( x 1, x 2, x 3, x 4, x 5, x 6 = y 1 x 5 ) Step3: ( x 2, x 3, x 4, x 5, x 6, x 7 = y 2 x 6 ) Step4: ( x 3, x 4, x 5, x 6, x 7, x 8 = y 3 x 7 ) Step5: ( x 5, x 6, x 7, x 8, x 9 = y 4 x 8 ) : DP( x 0 y 0 ) DSM : f=1 k 1 + x 0 + x 1 + x 6 5 : DP( x 2 y 2 ) DSM : x 1 0 or x 2 0 x 1 + x 2 + x 5 + x 7 5 : DP( x 3 y 3 ) DSM : x 2 0 or x 3 0 x 2 + x 3 + x 6 + x 8 5 : DP( x 4 y 4 ) DSM : x 3 0 or x 4 0 x 3 + x 4 + x 7 + x 9 5 : DP( x 9 y 9 ) Step6: ( x 5, x 6, x 7, x 8 ), x 10 : DP( x 5 y 5 ) Step7: ( x 5, x 6, x 7, x 8, x 10, x 11 = y 5 x 10 ) : DP( x 6 y 6 ) DSM : x 5 0 or x 6 0 x 5 + x 6 + x 10 + x 12 5 Step8: ( x 6, x 7, x 8, x 10, x 11, x 12 = y 6 x 11 ) : DP( x 7 y 7 ) DSM : x 6 0 or x 7 0 x 6 + x 7 + x 11 + x 13 5 Step9: ( x 7, x 8, x 10, x 11, x 12, x 13 = y 7 x 12 ) : DP( x 8 y 8 ) DSM : x 7 0 or x 8 0 x 7 + x 8 + x 12 + x 14 5 Step10: ( x 10, x 11, x 12, x 13, x 14 = y 8 x 13 ) Step10=Step0 Step0 k 1 = k 3 4 ( x 0, x 1, x 2, x 3, x 4 ) 8.2: GF N 8,10 DCP. Step0 ( x 0, x 1, x 2, x 3, x 4 ) k 1 x 5 Step1 62
64 2 f f 1 f f f f f 0 2 f f 0 2 f f f 1 f 0 2 f 0 f f 1 f 2 f 0 8.3: GF N 8,10 DCP. DP ( x 0 y 0 ) Step2 f k 1 + x 0 (5 5 ) Step1 Step2 x 6 DP ( x 1 y 1 ) DSM ( x 0 0 or x 1 0) k 1 + x 0 + x 1 + x 6 5. (8.1) Step1 Step2 (8.1) Step Step40 ( x 0, x 1, x 2, x 3, x 4) Step Step (= ) k i l i ( 2 20 ) ( ) 1 DCP 8.2 1/ GF N 8,10 DCP 8.3 GF N 8,10 DCP ( ) truncated 16 63
65 DCP S-box S 0 17 Active S 1 12 Active 192/256bit (5 ) DSM SONY [13] 8.3 ( ) x 2 + x 3 + x 4 + x 6 + x 9 5 (8.2) 8.3 (8.2) 4 (8.2) x 9 = 8( 1) x 9 = a( 2) DCP DSM [13] bit 64
66 Type2 Feistel Type2 Feistel GF N 8,10 GF N 8, GF N 8, GF N 8,10 (k 1) ( (C C C C) (A C C C) (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) ) 9r ( (U U U U) (U U U U) (B B B B) (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) ) (k 2) ( (C C C C) (C C C C) (C C C C) (A C C C) (C C C C) (C C C C) (C C C C) (C C C C) ) 9r ( (U U U U) (U U U U) (U U U U) (U U U U) (B B B B) (U U U U) (U U U U) (U U U U) ) (k 3) ( (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (A C C C) (C C C C) (C C C C) ) 9r ( (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) (B B B B) (U U U U) ) (k 4) ( (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (A C C C) ) 9r ( (B B B B) (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) ) (A C C C) (C A C C), (C C A C) (C C C A) GF N 8,10 (k 5) 8.4 (k 5) ( (C C C C) (A A A A) (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) ) 10r ( (B B B B) (U U U U) (B B B B) (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) ) (k 6) ( (C C C C) (C C C C) (C C C C) (A A A A) (C C C C) (C C C C) (C C C C) (C C C C) ) 10r ( (U U U U) (U U U U) (B B B B) (U U U U) (B B B B) (U U U U) (U U U U) (U U U U) ) (k 7) ( (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (A A A A) (C C C C) (C C C C) ) 10r ( (U U U U) (U U U U) (U U U U) (U U U U) (B B B B) (U U U U) (B B B B) (U U U U) ) (k 8) ( (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (C C C C) (A A A A) ) 10r ( (B B B B) (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) (B B B B) (U U U U) ) 65
67 8.4: 10 GF N 8,10 66
68 8 Type-2 Feistel (III) ( (A A A A) (A A A A) (C C C C) (C C C C) (C C C C) (A A A A) (A A A A) (A A A A) ) 14r ( (B B B B) (U U U U) (B B B B) (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) ) (VI) ( (A A A A) (A A A A) (A A A A) (A A A A) (C C C C) (C C C C) (C C C C) (A A A A) ) 14r ( (U U U U) (U U U U) (B B B B) (U U U U) (B B B B) (U U U U) (U U U U) (U U U U) ) (V) ( (C C C C) (A A A A) (A A A A) (A A A A) (A A A A) (A A A A) (C C C C) (C C C C) ) 14r ( (U U U U) (U U U U) (U U U U) (U U U U) (B B B B) (U U U U) (B B B B) (U U U U) ) (VI) ( (C C C C) (C C C C) (C C C C) (A A A A) (A A A A) (A A A A) (A A A A) (A A A A) ) 14r ( (B B B B) (U U U U) (U U U U) (U U U U) (U U U U) (U U U U) (B B B B) (U U U U) ) F SP m 2n l Type-2 Feistel l 4 l + 2 l 2 B l/2 (3l/2 + 2) l 67
69 [1], 128 CLEFIA Version 1.0, , [2] A.Biryukov and D.Khovratovich, Related-Key Cryptanalysis of the Full AES-192 and AES- 256, ASIACRYPT 2009, LNCS 5912, pp. 1-18, [3], (2001 ) CRYPTREC Report 2001, [4] / /, (Telecommunications Advancement Organization of Japan), pp , June [5] T. Shirai, K. Shibutani, T. Akishita, S. Moriai, and T. Iwata, The 128-bit Blockcipher CLEFIA, FSE 2007, LNCS 4593, pp , Springer-Verlag, [6] CLEFIA vol.108, no38, ISEC2008-3, pp15-22, [7] Feistel SCIS2007-4A2-2, [8] Feistel A vol.j93-a, No.4, pp , 2010 [9] J. Daemen, L.R. Knudsen, and V. Rijmen, The block cipher SQUARE, FSE 97, LNCS 1267, pp , Springer-Verlag, [10] N. Ferguson, J. Kelsey, S. Lucks, B. Schneier, M. Stay, D. Wagner, and D. Whiting, Improved Cryptanalysis of Rijndael, in Proceedings of Fast Software Encryption-FSE2000, vol.1987 of Lecture Notes in Computer Science, pp , Springer, [11] K. Hwang, W. Lee, S. Lee, and J. Lim, Saturation attacks on reduced round Skipjack, FSE2002, LNCS 2365, pp , Springer-Verlag, [12] Sony Corporation, The 128-bit blockcipher CLEFIA, security and performance evaluations, revision 1.0, June 1(2007), Products/cryptography/clefia/. [13],, CLEFIA. SCIS2011, 2B1-2, (2011.1). 68
70 [14],,, CLEFIA,SCIS2011, 2B1-3, (2011.1). [15],,,, CLEFIA, SCIS2011, 2B1-4, (2011.1). [16],, XOR, SCIS2011, 3B2-1, (2011.1) 69
71 A : 1,, : CLEFIA, SCIS 2011, 2B1-3, (2011.1) 2,,, : CLEFIA, SCIS 2011, 2B1-4, (2011.1) 3, : XOR, SCIS 2011, 3B2-1, (2011.1) 70
72 All rights are reserved and copyright of this manuscript belongs to the authors. This manuscript has been published without reviewing and editing as received from the authors: posting the manuscript to SCIS 2011 does not prevent future submissions to any journals or conferences with proceedings. SCIS 2011 The 2011 Symposium on Cryptography and Information Security Kokura, Japan, Jan , 2011 The Institute of Electronics, Information and Communication Engineers CLEFIA Differential characteristic property of CLEFIA Naoto Kobayashi Yasutaka Igarashi Toshinobu Kaneko CLEFIA FSE2007 SONY [1] [2] CLEFIA (DSM) CLEFIA 2 Sbox 2 128,192,256bit CLEFIA , , , , CLEFIA (MDS) viterbi 1 CLEFIA FSE2007 SONY CLEFIA [2] CLEFIA (DSM) CLEFIA 2 Sbox 2 2 CLEFIA [4] 2.1 CLEFIA 32bit 4 r Feistel r 128,192,256bit 18,22,26 P,C 128 i P (i) C (i) P=P (i),c=c (i) P (i) 32 4 P {i,0},p {i,1},p {i,2},p {i,3} C (i) 32 4, , Department of Electrical Engineering, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, JAPAN, j @ed.noda.tus.ac.jp, yasutaka@rs.noda.tus.ac.jp, kaneko@ee.noda.tus.ac.jp C {i,0},c {i,1},c {i,2},c {i,3} WK i (0 i < 4) 32 RK i (0 i < 2r) 32 ENC r 1 Step1. T 0 T 1 T 2 T 3 P {0,0} (P {0,1} WK 0 ) P {0,2} (P {0,3} WK 1 ) Step2. i = 0 r 1 : Step2.1 T 1 T 1 F 0 (RK 2i,T0 ) T 3 T 3 F 1 (RK 2i+1,T 2 ) Step2.2 T 0 T 1 T 2 T 3 T 1 T 2 T 3 T 0 Step3. C {r,0} C {r,1} C {r,2} C {r,3} F T 3 T 0 WK 2 T 1 T 2 WK S 0,S 1 8 Sbox M 0,M MDS k i (i = 0,1,2,3) Rk i = k 0 k 1 k 2 k 3 ( ) F 0 1 F 1 F 0 S 0 S 1 M 0 M 1 1 t a a 71 1
1 IPA Hierocrypt-L1 Hierocrypt-L Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-L1 2 Hierocrypt-L1 Hierocrypt-L1 Hierocrypt-
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
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CLEFIA Sony s s Lightweight Block Cipher Shiho Moriai Sony Corporation 1 目次 ソニーにおける暗号技術 ソニーのブロック暗号 :CLEFIA 設計の背景 アルゴリズム仕様 設計方針 実装性能評価 まとめ 2 ソニーにおける暗号技術 暗号 / 情報セキュリティ技術搭載製品の増加 各種暗号アルゴリズム 著作権保護 機器認証 電子マネー
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