Fast correlation attacks and multiple linear approximations

1997 ◽  
pp. 228-239 ◽  
Author(s):  
M. Salmasizadeh ◽  
L. Simpson ◽  
J. Dj. Golić ◽  
E. Dawson
Keyword(s):  
Linear Approximations ◽  
Correlation Attacks ◽  
Fast Correlation Attacks

scholarly journals Resistance of SNOW-V against Fast Correlation Attacks

2021 ◽  
pp. 378-410
Author(s):  
Xinxin Gong ◽  
Bin Zhang
Keyword(s):  
Linear Approximation ◽  
Mobile Communication ◽  
Time Complexity ◽  
Stream Ciphers ◽  
Design Document ◽  
Linear Approximations ◽  
Correlation Attack ◽  
Correlation Attacks ◽  
Memory Complexity ◽  
Fast Correlation Attacks

SNOW-V is a new member in the SNOW family of stream ciphers, hoping to be competitive in the 5G mobile communication system. In this paper, we study the resistance of SNOW-V against bitwise fast correlation attacks by constructing bitwise linear approximations. First, we propose and summarize some efficient algorithms using the slice-like techniques to compute the bitwise linear approximations of certain types of composition functions composed of basic operations like ⊞, ⊕, Permutation, and S-box, which have been widely used in word-oriented stream ciphers such as SNOW-like ciphers. Then, using these algorithms, we find a number of stronger linear approximations for the FSM of the two variants of SNOW-V given in the design document, i.e., SNOW-V σ0 and SNOW-V⊞8, ⊞8. For SNOW-V σ0, where there is no byte-wise permutation, we find some bitwise linear approximations of the FSM with the SEI (Squared Euclidean Imbalance) around 2−37.34 and mount a bitwise fast correlation attack with the time complexity 2251.93 and memory complexity 2244, given 2103.83 keystream outputs, which improves greatly the results in the design document. For SNOW-V⊞8, ⊞8, where both of the two 32-bit adders in the FSM are replaced by 8-bit adders, we find our best bitwise linear approximations of the FSM with the SEI 2−174.14, while the best byte-wise linear approximation in the design document of SNOW-V has the SEI 2−214.80. Finally, we study the security of a closer variant of SNOW-V, denoted by SNOW-V⊞32, ⊞8, where only the 32-bit adder used for updating the first register is replaced by the 8-bit adder, while everything else remains identical. For SNOW-V⊞32, ⊞8, we derive many mask tuples yielding the bitwise linear approximations of the FSM with the SEI larger than 2−184. Using these linear approximations, we mount a fast correlation attack with the time complexity 2377.01 and a memory complexity 2363, given 2253.73 keystream outputs. Note that neither of our attack threatens the security of SNOW-V. We hope our research could further help in understanding bitwise linear approximation attacks and also the structure of SNOW-like stream ciphers.

scholarly journals Fast Correlation Attacks on Grain-like Small State Stream Ciphers

2017 ◽  
pp. 58-81 ◽  
Author(s):  
Bin Zhang ◽  
Xinxin Gong ◽  
Willi Meier
Keyword(s):  
Internal State ◽  
Stream Ciphers ◽  
Small Scale ◽  
Secret Key ◽  
Small State ◽  
Key Recovery ◽  
Key Recovery Attack ◽  
Correlation Attacks ◽  
Fast Correlation Attacks

In this paper, we study the security of Grain-like small state stream ciphers by fast correlation attacks, which are commonly regarded as classical cryptanalytic methods against LFSR-based stream ciphers. We extend the cascaded structure adopted in such primitives in general and show how to restore the full internal state part-by-part if the non-linear combining function meets some characteristic. As a case study, we present a key recovery attack against Fruit, a tweaked version of Sprout that employs key-dependent state updating in the keystream generation phase. Our attack requires 262.8 Fruit encryptions and 222.3 keystream bits to determine the 80-bit secret key. Practical simulations on a small-scale version confirmed our results.

A survey on fast correlation attacks

2012 ◽  
Vol 4 (3-4) ◽  
pp. 173-202 ◽  
Author(s):  
Martin Ågren ◽  
Carl Löndahl ◽  
Martin Hell ◽  
Thomas Johansson
Keyword(s):  
Correlation Attacks ◽  
Fast Correlation Attacks
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