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Periodicity and Correlation Properties of d-FCSR Sequences

Mark Goresky, Andrew Klapper
2004 Designs, Codes and Cryptography  
A d-feedback-with-carry shift register (d-FCSR) is a finite state machine, similar to a linear feedback shift register, in which a small amount of memory and a delay (by d-clock cycles) is used in the  ...  We also analyze the "arithmetic cross-correlation" between pairs of these sequences and show that it often vanishes identically.  ...  shown that various desirable statistical properties hold for FCSR sequences (see below), in most cases paralleling properties of LFSR sequences.  ... 
doi:10.1023/b:desi.0000035467.93014.90 fatcat:r3vhiwfdmfaznpuvffkx3k775q

Large Period Nearly deBruijn FCSR Sequences [chapter]

Andrew Klapper, Mark Goresky
1995 Lecture Notes in Computer Science  
'lhey are balanced, and nearly have the deBruijn property for distributions of subsequences. Index Terms -Binary sequences, feedback with carry shift registers, deBruijn property, 2-adic numbers.  ...  However, it appears to be significantly more difficult to find maximal period FCSR sequences.  ...  Then the shifted u d h m e t i c cross-correlation Q a b ( r ) of a and b is the difference between the number of zeros and the number of ones in a completeperiod of the periodic part of the sequence formed  ... 
doi:10.1007/3-540-49264-x_21 fatcat:oqo7ekh7arhxjmtzx6rc534hwi

A New Approach for FCSRs [chapter]

Franc̨ois Arnault, Thierry Berger, Cédric Lauradoux, Marine Minier, Benjamin Pousse
2009 Lecture Notes in Computer Science  
FCSRs have good statistical properties and they provide a built-in non-linearity. However, two attacks have shown that the current representations of FCSRs can introduce weaknesses in the cipher.  ...  Our approach preserves the statistical properties and circumvents the weaknesses of the Fibonacci and Galois representations.  ...  FCSRs share many of the good properties of LFSRs: sequences with known period and good statistical properties.  ... 
doi:10.1007/978-3-642-05445-7_27 fatcat:jeuyrckbc5fs5c3xop5h7c6gcq

A Survey of Feedback with Carry Shift Registers [chapter]

Andrew Klapper
2005 Lecture Notes in Computer Science  
This leads to the analysis of periodicity of FCSR sequences, their exponential representation, and a description of maximal period FCSR sequences.  ...  We also discuss an arithmetic analog of cross-correlations, the FCSR register synthesis problem, and how FCSRs can be efficiently implemented in parallel architecture.  ...  We also discuss an arithmetic analog of cross-correlations and see that maximal period FCSR sequences have remarkable arithmetic correlation properties.  ... 
doi:10.1007/11423461_3 fatcat:f4tprvzq2jg4voukvqm4wu7sxy

The Robust Stream Cipher for Securing Data in the Smartphones

Abdullah S. Abid, Mohammed J. Zaiter, Tayseer S. Atia
2019 Journal of University of Babylon for Engineering Sciences  
To implement a new generator key by using these three kinds, we used four LFSRs and one of NLFSRs or FCSRs to produce five variables Boolean function.  ...  One of these techniques is a stream cipher which considered the strongest and fastest method used in encryption and decryption process.  ...  The algebraic degree is not exceeding of d ≤ n-m-1 [8] , [19] . 4-Correlation Immunity. The correlation immunity of ƒ must be high.  ... 
doi:10.29196/jubes.v27i1.1981 fatcat:ob6rahgijncopayiuqlgbxpagm

Feedback registers based on ramified extensions of the 2-adic numbers [chapter]

Mark Goresky, Andrew Klapper
1995 Lecture Notes in Computer Science  
A new class of feedback register, based on ramified extensions of the 2-adic numbers, is described. An algebraic framework for the analysis of these re~ters and the sequences they output is given.  ...  TilLs framework parallels that of linear feedback shift resistere. As one consequence of this, a method for cracking summation ciphers is given.  ...  The period and other properties of the binary sequence are de~rminad from number theoretic properties of q. 5. An ~-sequence is s FCSR sequence with ma.'cimum possible period T = }(R/(g))'i.  ... 
doi:10.1007/bfb0053437 fatcat:atgrpfu54ved3by3cy5tjb6pha

F-FCSR: Design of a New Class of Stream Ciphers [chapter]

François Arnault, Thierry P. Berger
2005 Lecture Notes in Computer Science  
Its properties are well mastered: proved period, non-degenerated states, good statistical properties, high non-linearity.  ...  The third and the fourth are similar, but use a dynamic filter depending on the key (F-FCSR-DF1 and F-FCSR-DF8).  ...  Acknowledgments: Both authors would like to thank Anne Canteaut and Marine Minier for helpful comments and suggestions.  ... 
doi:10.1007/11502760_6 fatcat:fsv64pi3jzemfg7r5xhhj2uaru

Some Results on FCSR Automata With Applications to the Security of FCSR-Based Pseudorandom Generators

FranÇois Arnault, Thierry P. Berger, Marine Minier
2008 IEEE Transactions on Information Theory  
These results especially concern the structure of the transition graph of an FCSR automaton and the number of iterations of the FCSR transition function required to reach the main part of the graph.  ...  This article describes new theoretical results concerning the general behavior of a Feedback with Carry Shift Register (FCSR) automaton.  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous referees for their helpful comments, remarks, and suggestions.  ... 
doi:10.1109/tit.2007.913244 fatcat:qcrpqdezbfervdzekgetaquppq

Feedback shift registers, 2-adic span, and combiners with memory

Andrew Klapper, Mark Goresky
1997 Journal of Cryptology  
Feedback shift registers with carry operation (FCSRs) are described, implemented, and analyzed with respect to memory requirements, initial loading, period, and distributional properties of their output  ...  sequence, constructs the smallest FCSR which will generate the sequence.  ...  We have profited from useful conversations with Mark McConnell, and we would like to thank two anonymous referees for their careful reading and many thoughtful comments on an earlier version of this paper  ... 
doi:10.1007/s001459900024 fatcat:5xza7htdpza5rileekvisnktgy

Linearisation Attacks on FCSR-based Stream Ciphers

Arshad Ali
2012 International Journal for Information Security Research  
The paper demonstrates, these new attacks against F-FCSR-H and an eSTREAM candidate F-FCSR-H v2 stream ciphers by presenting state recovery algorithms based on CLAs, FLAs and ILAs.  ...  This paper presents a new class of cryptanalytic attacks, which are applicable against those binary additive synchronous stream ciphers, whose analysis theory is based on the properties of 2-adic numbers  ...  If q is prime such that 2 is a primitive element in the ring of units * / ( ) q , then the sequence generated by the FCSR has maximum period and is known as l-sequence.  ... 
doi:10.20533/ijisr.2042.4639.2012.0026 fatcat:24ku6jjshreh7ire3fo7ojlp4u

Alternating Step Generator Using FCSR and LFSRs: A New Stream Cipher

Nagendar Yerukala, C.R. Rao Advanced Institute of Mathematics, Statistics and Computer Science, Venu Nalla, Padmavathi Guddeti, V Prasad, C.R. Rao Advanced Institute of Mathematics, Statistics and Computer Science, C.R. Rao Advanced Institute of Mathematics, Statistics and Computer Science, JNTUH College of Engineering
2019 International Journal of Intelligent Engineering and Systems  
Keystream of ASGF passes almost all NIST tests for randomness and the results are tabulated. For fixed extreme patterns of key and IV, ASGF is giving random sequence.  ...  This paper presents a new design of stream cipher for generating pseudorandom keystream with two LFSR's, one FCSR and a non-linear combiner function, which is a bit oriented based on alternating step generator  ...  The hamming weight W(d) of the binary expansion of "d" is not too small. Typically, W(d) is about n/2 or slightly greater. Stream ciphers designs using FCSR were discussed in [10, 12, 13] .  ... 
doi:10.22266/ijies2019.1031.13 fatcat:um65aok24veftoosdyw4pi7x3u

A generalized birthday approach for efficiently finding linear relations in $$\ell $$ ℓ -sequences

Hui Wang, Paul Stankovski, Thomas Johansson
2013 Designs, Codes and Cryptography  
In this paper we show how to exploit a particular set of linear relations in ring FCSR sequences.  ...  Recently, a generalized and unifying FCSR structure and theory was presented. The new ring FCSRs model repairs some weaknesses of the older architectures.  ...  The arguably most important property is that it completely determines the length of the period of the binary sequence that the FCSR outputs.  ... 
doi:10.1007/s10623-013-9845-0 fatcat:5q6qsf3sg5eklfvuz4eig5wsva

Cryptanalysis of the stream cipher BEAN

Martin Ågren, Martin Hell
2011 Proceedings of the 4th international conference on Security of information and networks - SIN '11  
There is a sound motivation behind the use of FCSRs in BEAN as they provide several cryptographically interesting properties. In this paper, we show that the output function is not optimal.  ...  BEAN is a recent stream cipher proposal that uses Feedback with Carry Shift Registers (FCSRs) and an output function.  ...  Thus, BEAN has two shift register components, both providing nonlinearity, large period and random-looking sequences.  ... 
doi:10.1145/2070425.2070432 dblp:conf/sin/AgrenH11 fatcat:2gsk35s3gbdgllgy6cywcbdwmy

Arithmetic crosscorrelations of feedback with carry shift register sequences

M. Goresky, A. Klapper
1997 IEEE Transactions on Information Theory  
Index Terms-Crosscorrelations, binary sequences, feedback with carry shift register (FCSR) sequences, 2-adic numbers.  ...  An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum's arithmetic autocorrelations.  ...  INTRODUCTION In the study of pseudorandom binary sequences, we are often interested in the correlation properties of the sequences.  ... 
doi:10.1109/18.605605 fatcat:fhcezg3m3zf7diu3lxowkupdze

Periodicity and Distribution Properties of Combined FCSR Sequences [chapter]

Mark Goresky, Andrew Klapper
2006 Lecture Notes in Computer Science  
This is a study of some of the elementary statistical properties of the bitwise exclusive or of two maximum period feedback with carry shift register sequences.  ...  We obtain conditions under which the resulting sequences has the maximum possible period, and we obtain bounds on the variation in the distribution of blocks of a fixed length.  ...  Recall that a binary -sequence is a maximal length FCSR sequence [4] of 0's and 1's.  ... 
doi:10.1007/11863854_29 fatcat:wqjcopodpbaalkmu3ngw3ogjey
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