类Piccolo结构的差分安全性评估

doi:10.11959/j.issn.1000-436x.2022037

Abstract

Abstract:

In order to diversify the design of block cipher, Piccolo-like structure was proposed with principles of design.Security evaluation for Piccolo-like structure against differential cryptanalysis was deeply studied.By studying the input-output propagation characteristics of differential characteristics, the lower bound on the number of active round functions for arbitrary round Piccolo-like structure was given.The results show that, under the condition that the round functions are all bijective, there are at least l active round functions for l-round Piccolo-like structure if l≥6, and there are at least l-1 active round functions for l-round Piccolo-like structure if l is 1,2,3,4,5.

Key words: Piccolo-like structure, differential cryptanalysis, active round function

CLC Number:

TN918.1

Nianping WANG, Qing YIN. Differential security evaluation of Piccolo-like structure[J]. Journal on Communications, 2022, 43(2): 55-64.

Figures/Tables 9

块移位变换σ	活动指标为6的6轮差分特征的尾轮输出差分	活动指标为k-1（k=1,2,3,4,5）的k轮差分特征的首轮输入差分
(26043715)	3 13 16 17 1a 23 25 29 2b 30 31 32 33 35 3a 46 47	478 b c d e f4044
(62407351)	52 53 56 57 5b 61 64 65 67 6e 6f 71 74 75 76 77 7a	48 49 4c 4d 68 70 80 84 86 88
(37152604)	7b 7e 7f 89 8b 92 98 9a 9b 9d 9f a1 a3 a7 a9 ab b2	8c 8e 94 b0 c0 c4 c8 cc d0 d4
(73516240)	b5 b7 b8 b9 ba bb bd bf d9 db e6 e7 f6 f7 f9 fb	e0 e8 f0
(26513740)	3 13 16 1a 1b 23 25 27 29 30 31 32 33 36 39 45 47	478 b c d e f4044
(62157304)	52 54 56 57 5d 5f 61 63 65 67 6b 72 74 75 76 77 79	48 4a 4c 4e 58 70 80 84 85 88
(37402651)	7b 7d 7f 8a 8b 92 93 97 9a 9b a1 a8 a9 ab ae af b1	8c 8d a4 b0 c0 c4 c8 cc d0 d8
(73046215)	b6 b7 b8 b9 ba bb be bf d5 d7 ea eb f5 f7 fa fb	e0 e4 f0
(27043651)	3 13 16 17 1a 23 25 29 2b 30 31 32 33 35 3a 49 4b	478 b c d e f4044
(72406315)	52 58 5a 5b 5d 5f 61 63 67 69 6b 72 75 77 78 79 7a	46 48 4c 4e 54 70 80 84 88 89
(36152740)	7b 7d 7f 86 87 92 93 96 97 9b a1 a4 a5 a7 ae af b1	8c 8d a8 b0 c0 c4 c8 cc d0 d4
(63517204)	b4 b5 b6 b7 ba bb be bf d9 db e6 e7 f6 f7 f9 fb	e0 e8 f0
(27513604)	3 13 16 1a 1b 23 25 27 29 30 31 32 33 36 39 4a 4b	478 b c d e f4044
(72156340)	52 53 57 5a 5b 61 68 69 6b 6e 6f 71 76 77 78 79 7a	45 48 4c 4d 64 70 80 84 88 8a
(36402715)	7b 7e 7f 85 87 92 94 96 97 9d 9f a1 a3 a5 a7 ab b2	8c 8e 98 b0 c0 c4 c8 cc d0 d8
(63047251)	b4 b5 b6 b7 b9 bb bd bf d5 d7 ea eb f5 f7 fa fb	e0 e4 f0
(26057314)	3 13 15 19 1b 23 26 27 2a 30 31 32 33 35 3a 46 47	478 b c d e f4044
(62503741)	51 54 55 57 5e 5f 62 63 66 67 6b 71 74 75 76 77 7a	48 49 4c 4d 58 70 80 84 86 88
(73412650)	7b 7e 7f 89 8b 91 93 97 99 9b a2 a8 aa ab ad af b2	b5 b7 b8 b9 ba bb bd bf d6 d7
(37146205)	b5 b7 b8 b9 ba bb bd bf d6 d7 e9 eb f6 f7 f9 fb	e0 e4 f0
(26417350)	3 13 15 17 19 23 26 2a 2b 30 31 32 33 36 39 45 47	478 b c d e f4044
(62143705)	51 53 55 57 5b 62 64 66 67 6d 6f 72 74 75 76 77 79	48 4a 4c 4e 68 70 80 84 85 88
(73052614)	7b 7d 7f 8a 8b 91 98 99 9b 9e 9f a2 a3 a7 aa ab b1	8c 8d 94 b0 c0 c4 c8 cc d0 d4
(37506241)	b6 b7 b8 b9 ba bb be bf da db e5 e7 f5 f7 fa fb	e0 e8 f0
(27056341)	3 13 15 19 1b 23 26 27 2a 30 31 32 33 35 3a 49 4b	478 b c d e f4044
(72503614)	51 53 57 59 5b 62 68 6a 6b 6d 6f 72 75 77 78 79 7a	46 48 4c 4e 64 70 80 84 88 89
(63412705)	7b 7d 7f 86 87 91 94 95 97 9e 9f a2 a3 a6 a7 ab b1	8c 8d 98 b0 c0 c4 c8 cc d0 d8
(36147250)	b4 b5 b6 b7 ba bb be bf d6 d7 e9 eb f6 f7 f9 fb	e0 e4 f0
(27416305)	3 13 15 17 19 23 26 2a 2b 30 31 32 33 36 39 4a 4b	478 b c d e f4044
(72143650)	51 58 59 5b 5e 5f 62 63 67 6a 6b 71 76 77 78 79 7a	45 48 4c 4d 54 70 80 84 88 8a
(63052741)	7b 7e 7f 85 87 91 93 95 97 9b a2 a4 a6 a7 ad af b2	8c 8e a8 b0 c0 c4 c8 cc d0 d4
(36507214)	b4 b5 b6 b7 b9 bb bd bf da db e5 e7 f5 f7 fa fb	e0 e8 f0

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块移位变换σ	满足条件的3轮差分特征的尾轮输出差分
(26417350) (62143705) (73052614) (37506241)	(10001010)(10001110)(01000101)(01001101)(01100100)(11100100)(10011000)(11011000)
(26043715) (62407351) (37152604) (73516240)	(10000110)(10001110)(01001001)(01001101)(01101000)(11101000)(10010100)(11010100)
(26513740) (62157304) (37402651) (73046215)	(10000101)(10001101)(01001010)(01001110)(10100100)(11100100)(01011000)(11011000)
(27043651) (72406315) (36152740) (63517204)	(10000110)(10001110)(01001001)(01001101)(10100100)(11100100)(01011000)(11011000)
(27513604) (72156340) (36402715) (63047251)	(10000101)(10001101)(01001010)(01001110)(01101000)(11101000)(10010100)(11010100)
(26057314) (62503741) (73412650) (37146205)	(10001001)(10001101)(01000110)(01001110)(10101000)(11101000)(01010100)(11010100)
(72143650) (27416305) (63052741) (36507214)	(10001010)(10001110)(01000101)(01001101)(10101000)(11101000)(01010100)(11010100)
(27056341) (72503614) (63412705) (36147250)	(10001001)(10001101)(01000110)(01001110)(01100100)(11100100)(10011000)(11011000)

输入差分	6轮Piccolo结构的活动指标的最小值
00~0f	—	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7
10~1f	7	8	8	7	7	8	8	7	7	8	7	7	7	8	7	7
20~2f	7	8	8	7	7	7	8	7	7	8	8	7	7	7	8	7
30~3f	7	7	7	7	6	7	7	7	6	7	7	7	7	6	6	7
40~4f	7	7	7	6	7	6	6	6	6	7	7	6	6	6	6	6
50~5f	7	8	7	7	6	8	7	7	7	7	7	7	7	6	7	7
60~6f	7	8	8	7	6	7	8	7	7	7	7	7	7	7	7	7
70~7f	7	7	7	7	6	7	7	7	6	7	7	7	6	6	6	7
80~8f	7	7	7	6	6	7	7	6	7	6	6	6	6	6	6	6
90~9f	7	8	8	7	7	7	7	7	6	8	7	7	7	7	7	7
a0~af	7	7	8	7	7	7	7	7	6	7	8	7	7	7	6	7
b0~bf	7	7	7	7	6	7	7	7	6	7	7	7	6	6	6	7
c0~cf	7	7	7	7	6	7	7	6	6	7	7	6	6	7	7	6
d0~df	7	8	7	6	6	6	7	6	6	7	7	6	7	6	7	6
e0~ef	7	7	8	6	6	7	7	6	6	7	6	6	7	7	6	6
f0~ff	7	7	7	7	6	7	7	7	6	7	7	7	6	6	6	7

Differential security evaluation of Piccolo-like structure

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Figures/Tables 9

References 14

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变换1~8	变换9~16	变换17~24	变换25~32
(26043715)	(26513740)	(27043651)	(27513604)
(26057314)	(26417350)	(27056341)	(27416305)
(62503741)	(62143705)	(72503614)	(72143650)
(62407351)	(62157304)	(72406315)	(72156340)
(36402715)	(36152740)	(37402651)	(37152604)
(63052741)	(63412705)	(73052614)	(73412650)
(36507214)	(36147250)	(37506241)	(37146205)
(73046215)	(73516240)	(63047251)	(63517204)

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