On binary sequences from recursions “modulo \(2^e\)” made non-linear by the bit-by-bit “xor” function. (English) Zbl 0766.94001
Advances in Cryptology, Proc. Workshop, EUROCRYPT ’91, Brighton/UK 1991, Lect. Notes Comput. Sci. 547, 200-204 (1991).
Summary: [For the entire collection see Zbl 0756.00008.]
We consider binary sequences obtained by choosing the most significant bit of each element in a sequence obtained from a feedback shift register of length \(n\) operating over the ring \(\mathbb Z/2^e\), that is with arithmetic carried out modulo \(2\^e\). The feedback has been made nonlinear by using the bit-by-bit exclusive-or function as well as the linear operation of addition. This should increase the cryptologic strength without greatly increasing the computing overheads. The periods and linear equivalences are discussed. Provided certain conditions are met it is easy to check that the period achieves its maximal value.
We consider binary sequences obtained by choosing the most significant bit of each element in a sequence obtained from a feedback shift register of length \(n\) operating over the ring \(\mathbb Z/2^e\), that is with arithmetic carried out modulo \(2\^e\). The feedback has been made nonlinear by using the bit-by-bit exclusive-or function as well as the linear operation of addition. This should increase the cryptologic strength without greatly increasing the computing overheads. The periods and linear equivalences are discussed. Provided certain conditions are met it is easy to check that the period achieves its maximal value.
MSC:
| 94A55 | Shift register sequences and sequences over finite alphabets in information and communication theory |
