Analysis and design of stream ciphers
Analysis and design of stream ciphers
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Difference Sets and Hyperovals
Designs, Codes and Cryptography
Multiplicative Difference Sets via Additive Characters
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Shift Register Sequences
Some Cryptographic Properties of Exponential Functions
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Binary pseudorandom sequences of period 2n-1 with ideal autocorrelation
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Transform domain analysis of DES
IEEE Transactions on Information Theory
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Welch-Gong (WG) transformation sequences are binary sequences of period 2n - 1 with 2-level auto correlation. These sequences were discovered by Golomb, Gong and Gaal in 1998 and verified for 5 ≤ n ≤ 20. Later on, No, Chung and Yun found another way to construct the WG sequences and verified their result for 5 ≤ n ≤ 23. Dillon first proved this result for odd n in 1998, and finally, Dobbertin and Dillon proved it for even n in 1999. In this paper, we investigate a two-faced property of the WG transformation sequences for application in stream ciphers and pseudo-random number generators. One is to present randomness or unpredictability of the WG transformation sequences. The other is to exhibit the security property of the WG transformations regarded as Boolean functions. It is shown that the WG transformation sequences, in addition to the known 2-level auto correlation, have three-level cross correlation with m-sequences, large linear ! span increasing exponentially with n and efficient implementation. Thus this is the first type of pseudo-random sequences with good correlation and statistic properties, large linear span and efficient implementation. When the WG transformation are regarded as Boolean functions, it is proved that they have high nonlinearity. A criterion for whether the WG transformations regarded as Boolean functions are r-resilient is derived. It is shown that the WG transformations regarded as Boolean functions have large linear span (this concept will be defined in this paper) and high degree.