Abstract:

Autocorrelation properties of coordinate sequence generated by single cycle Tfunction (the kth coordinate sequence) are investigated to check whether Tfunctions can be the substitution of linear feedback shift register in the design of stream ciphers. Based on single cycle Tfunctions properties and autocorrelation functions periodicity, the bounds of autocorrelation functions are calculated, where the shift is equal to the period of the kth coordinate sequence multiplied by 2 to the minus power. According to the bounds, it is concluded that the smaller the shift is, the larger the value of autocorrelation functions is. As a result, Tfunctions are not suitable for generating pseudorandom sequences.

Key words: cryptography, pseudorandom sequences, Tfunctions, autocorrelation, nonlinear