A Theoretical Analysis of the Structure of HC-128

HC-128 is an eSTREAM finalist and no practical attack on this cipher is known. We show that the knowledge of any one of the two internal state arrays of HC-128 along with the knowledge of 2048 keystream words is sufficient to construct the other state array completely in 242 time complexity. Though our analysis does not lead to any attack on HC-128, it reveals a structural insight into the cipher. In the process, we theoretically establish certain combinatorial properties of HC-128 keystream generation algorithm. Our work may be considered as the first step towards a possible state recovery of HC-128. We also suggest a modification to HC-128 that takes care of the recently known cryptanalytic results with little reduction in speed.

[1]  Yunyi Liu,et al.  The Key and IV Setup of the Stream Ciphers HC-256 and HC-128 , 2009, 2009 International Conference on Networks Security, Wireless Communications and Trusted Computing.

[2]  Alan M. Frieze,et al.  The Size of the Largest Strongly Connected Component of a Random Digraph with a Given Degree Sequence , 2004, Combinatorics, Probability and Computing.

[3]  Amr M. Youssef,et al.  Differential Fault Analysis of HC-128 , 2010, AFRICACRYPT.

[4]  Vincent Rijmen,et al.  Analysis Methods for (Alleged) RC4 , 1998, ASIACRYPT.

[5]  A. I. SALTYKOV,et al.  The number of components in a random bipartite graph , 1995 .

[6]  Bruce A. Reed,et al.  The Size of the Giant Component of a Random Graph with a Given Degree Sequence , 1998, Combinatorics, Probability and Computing.

[7]  Martijn Stam.  Beyond Uniformity: Better Security/Efficiency Tradeoffs for Compression Functions , 2008, CRYPTO.

[8]  J. Hansen,et al.  Large components of bipartite random mappings , 2000 .

[9]  Alexander Maximov,et al.  New State Recovery Attack on RC4 , 2008, CRYPTO.

[10]  Hongjun Wu.  A New Stream Cipher HC-256 , 2004, FSE.

[11]  Kazuo Ohta,et al.  Advances in Cryptology — ASIACRYPT’98 , 2002, Lecture Notes in Computer Science.

[12]  Tanja Lange,et al.  Progress in Cryptology - AFRICACRYPT 2010, Third International Conference on Cryptology in Africa, Stellenbosch, South Africa, May 3-6, 2010. Proceedings , 2010, AFRICACRYPT.

[13]  Gerhard Goos,et al.  Fast Software Encryption , 2001, Lecture Notes in Computer Science.

[14]  Subhamoy Maitra,et al.  Some observations on HC-128 , 2011, Des. Codes Cryptogr..

[15]  I. B. KALUGIN,et al.  The number of components of a random bipartite graph , 1991 .