On the Number of Trace-One Elements in Polynomial Bases for $$\mathbb{F}_{2^n}$$
Designs, Codes and Cryptography
WG: A family of stream ciphers with designed randomness properties
Information Sciences: an International Journal
New constructions for resilient and highly nonlinear boolean functions
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
Resynchronization attacks on WG and LEX
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
Cryptanalysis of WG-7: a lightweight stream cipher
Cryptography and Communications
Resilience to distinguishing attacks on WG-7 cipher and their generalizations
Cryptography and Communications
Optimal parameters for the WG stream cipher family
Cryptography and Communications
| Hi-index | 754.84 |
Welch-Gong (WG) transformation sequences are binary sequences of period 2n - 1 with two-level autocorrelation. These sequences were discovered by Golomb, Gong, and Gaal (1998) and they verified the validity of their construction for 5 ⩽ n ⩽ 20. Later, No, Chung, and Yun (1998) found another way to construct the WG sequences and verified their result for 5 ⩽ n ⩽ 20. Dillon (1998) first proved this result for odd n, and, finally, Dobbertin and Dillon (1999) proved it for even n. In this paper, we investigate a two-faced property of the WG transformation sequences for application in stream ciphers and pseudorandom number generators. One is to present the randomness or unpredictability of the WG transformation sequences. The other is to exhibit the security properties of the WG transformations regarded as Boolean functions. In particular, we prove that the WG transformation sequences, in addition to the known two-level autocorrelation and three-level cross correlation with m-sequences, have the ideal 2-tuple distribution, and large linear span increasing exponentially with n. Moreover, it can be implemented efficiently. This is the first type of pseudorandom sequences with good correlation, statistic properties, large linear span, and efficient implementation. When WG transformations are regarded as Boolean functions, they have high nonlinearity. We derive a criterion for the Boolean representation of WG transformations to be r-resilient and show that they are at least 1-resilient under some basis of the finite field GF (2n). An algorithm to find such bases is given. The degree and linear span of WG transformations are presented as well