Proof of Rueppel's linear complexity conjecture
IEEE Transactions on Information Theory
Shift Register Sequences
The probabilistic theory of linear complexity
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
On the randomness of Legendre and Jacobi sequences
CRYPTO '88 Proceedings on Advances in cryptology
The linear complexity profile and the jump complexity of keystream sequences
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
On the limit of maximal density of sequences with a PerfectLinear Complexity Profile
Designs, Codes and Cryptography
A New Class of Stream Ciphers Combining LFSR and FCSR Architectures
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Design and Properties of a New Pseudorandom Generator Based on a Filtered FCSR Automaton
IEEE Transactions on Computers
A tamper-proof and lightweight authentication scheme
Pervasive and Mobile Computing
Expected values for the rational complexity of finite binary sequences
Designs, Codes and Cryptography
Linear complexity of periodically repeated random sequences
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Sequences with almost perfect linear complexity profile
EUROCRYPT'87 Proceedings of the 6th annual international conference on Theory and application of cryptographic techniques
F-FCSR: design of a new class of stream ciphers
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
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The problem of characterizing the randomness of finite sequences arises in cryptographic applications. The idea of randomness clearly reflects the difficulty of predicting the next digit of a sequence from all the previous ones. The approach taken in this paper is to measure the (linear) unpredictability of a sequence (finite or periodic) by the length of the shortest linear feedback shift register (LFSR) that is able to generate the given sequence. This length is often referred to in the literature as the linear complexity of the sequence. It is shown that the expected linear complexity of a sequence of n independent and uniformly distributed binary random variables is very close to n/2 and, that the variance of the linear complexity is virtually independent of the sequence length, i.e. is virtually a constant! For the practically interesting case of periodically repeating a finite truly random sequence of length 2m or 2m-1, it is shown that the linear complexity is close to the period length.