Joint k-Error 2-Adic Complexity for Binary Periodic Multi-Sequences

Abstract

Cryptographically strong sequences should have a large 2-adic complexity to thwart the known feedback with carry shift register synthesis algorithms. At the same time the change of a few terms should not cause a significant decrease of the 2-adic complexity,that is,the k -error 2-adic complexity should also be large. Recent developments in stream ciphers point towards an interest in word-based stream ciphers,which require the study of the complexity of multi-sequences. This paper introduces joint k -error 2-adic complexity measures for multi-sequences. Several results on the existence and lower bounds on the number of multi-sequences with maximal joint 2-adic complexity and large joint k -error 2-adic complexity are proved. The existence of many such sequences thwarts attacks against the keystreams by exhaustive search.