Windmill generators: A generalization and an observation of how many there are
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Algebraic feedback shift registers
Theoretical Computer Science - Special issue: cryptography
Fast Software Encryption, Cambridge Security Workshop
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Design and Properties of a New Pseudorandom Generator Based on a Filtered FCSR Automaton
IEEE Transactions on Computers
On the xorshift random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On binary signed digit representations of integers
Designs, Codes and Cryptography
Breaking the F-FCSR-H Stream Cipher in Real Time
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
An Efficient State Recovery Attack on X-FCSR-256
Fast Software Encryption
Selected Areas in Cryptography
Software Oriented Stream Ciphers Based upon FCSRs in Diversified Mode
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
X-FCSR: a new software oriented stream cipher based upon FCSRs
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Galois LFSR, embedded devices and side channel weaknesses
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
F-FCSR: design of a new class of stream ciphers
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
Periodicity and distribution properties of combined FCSR sequences
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Arithmetic crosscorrelations of feedback with carry shift register sequences
IEEE Transactions on Information Theory
Fibonacci and Galois representations of feedback-with-carry shift registers
IEEE Transactions on Information Theory
Feedback with carry shift registers synthesis with the Euclidean algorithm
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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LFSRs are primitives widely used in information theory, coding theory and cryptography. However since 2002, they have faced algebraic attacks. To avoid this kind of attacks, FCSRs have been proposed as an alternative in [2---4]. In this paper, we first give a general representation of 2-adic automata using a traditional matrix representation. We then explore the special case of binary and ternary automata. We also study the complexity in terms of memory to implement such automata. Finally, we expose some proposed FCSR constructions for hardware and software oriented stream ciphers.