卫星电话GMR-2流密码算法碰撞特性分析

doi:10.11959/j.issn.1000-436x.2018026

Abstract

Abstract:

A collision property analysis of the GMR-2 cipher used in the satellite phone was presented.By using the F-component as a bridge,the link between the difference of the key byte and the collision of the output ofFas well as the link between the collision of the output of F and the collision of keystream byte were analyzed,which finally revealed the relationship between the difference of the original key byte and the keystream collision.The theoretical analysis showed that for a random frame number,a special chosen key pair could lead to a keystream collision with a high probability,when the key pair has only one byte difference in which the most significant 4 bit of the difference was equal to the last significant 4 bit.The experimental result shows that the keystream collision probability is 2^?8.248,which is far higher than the ideal collision probability 2^?120.This proves once again,that there exists serious potential security hazards in the GMR-2 cipher.

Key words: satellite phones, stream cipher, GMR-2, collision analysis

CLC Number:

TN918

Ruilin LI,Jiao HU,Chaojing TANG. Collision analysis of the GMR-2 cipher used in the satellite phone[J]. Journal on Communications, 2018, 39(2): 88-95.

Figures/Tables 9

Δα	$I N_{τ_{1} (α)} (Δ α, Δ τ_{1} (α))$	$N_{τ_{1} (α)} (Δ α, Δ τ_{1} (α))$	$\Pr_{τ_{1} (α)} (Δ α \to Δ τ_{1} (α))$
0	0~15	16	1
8	5,6,13,14	4	0.25
9	3,10	2	0.125
11	2,9	2	0.125
12	4,7,8,11	4	0.25
13	1,12	2	0.125
15	0,15	2	0.125
其他	?	0	0

c	Pr ₁(c)	$P r_{1} (c)^{*}$	$P r_{2} (c)^{*}$	$P r_{2} (c)^{} - P r_{1} (c)^{}$
0	2^?8.544	2^?8.456	2^?8.455	2^?19.488
1	2^?9.077	2^?8.996	2^?8.994	2^?18.899
2	2^?8.544	2^?8.456	2^?8.455	2^?19.488
3	2^?9.077	2^?9.000	2^?8.998	2^?19.209
4	2^?9.077	2^?8.940	2^?8.938	2^?18.950
5	2^?8.544	2^?8.492	2^?8.491	2^?19.508
6	2^?8.544	2^?8.454	2^?8.453	2^?19.536
7	2^?6.817	2^?6.795	2^?6.791	2^?15.230
平均值	2^?8.314	2^?8.250	2^?8.248	2^?17.719

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符号	含义
⊕	异或，即按比特模2加
ΔX	2 bit序列的异或差分，即ΔX =X⊕X^?
Δ a→Δb	差分Δa能产生差分Δb
X \|\|Y	2 bit序列的级联
Γ	Γ={δ‖δ:δ∈{0x1,0x2,…,0xf}}

α	τ ₁(α)	τ ₂(τ₁(α))
(0,0,0,0),(1,1,1,1)	2	6
(0,0,0,1),(1,1,0,0)	5	3
(0,0,1,0),(1,0,0,1)	0	4
(0,0,1,1),(1,0,1,0)	6	2
(0,1,0,0),(1,0,0,0)	3	7
(0,1,0,1),(1,1,0,1)	7	1
(0,1,1,0),(1,1,1,0)	4	4
(0,1,1,1),(1,0,1,1)	1	5
(0,0,0,1),(1,1,0,0)	5	3

δ	c=0	c=	c=2	c=3	c=4	c=5	c=6	c=7
8	1	1	1	1	0.5	1	1	0.5
9	1	1	1	1	1	1	0	1
11	0	1	1	1	1	1	1	1
12	1	0.5	1	0.5	1	1	1	1
13	1	1	1	1	1	0	1	1
15	1	1	0	1	1	1	1	1
其他	0	0	0	0	0	0	0	0

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Collision analysis of the GMR-2 cipher used in the satellite phone

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