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Periodicity and Correlation Properties of d-FCSR Sequences

2004
*
Designs, Codes and Cryptography
*

A

doi:10.1023/b:desi.0000035467.93014.90
fatcat:r3vhiwfdmfaznpuvffkx3k775q
*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*. ...##
###
Large Period Nearly deBruijn FCSR Sequences
[chapter]

1995
*
Lecture Notes in Computer Science
*

'lhey are balanced,

doi:10.1007/3-540-49264-x_21
fatcat:oqo7ekh7arhxjmtzx6rc534hwi
*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 ...##
###
A New Approach for FCSRs
[chapter]

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*. ...

##
###
A Survey of Feedback with Carry Shift Registers
[chapter]

2005
*
Lecture Notes in Computer Science
*

This leads to the analysis

doi:10.1007/11423461_3
fatcat:f4tprvzq2jg4voukvqm4wu7sxy
*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*. ...##
###
The Robust Stream Cipher for Securing Data in the Smartphones

2019
*
Journal of University of Babylon for Engineering Sciences
*

To implement a new generator key by using these three kinds, we used four LFSRs

doi:10.29196/jubes.v27i1.1981
fatcat:ob6rahgijncopayiuqlgbxpagm
*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. ...##
###
Feedback registers based on ramified extensions of the 2-adic numbers
[chapter]

1995
*
Lecture Notes in Computer Science
*

A new class

doi:10.1007/bfb0053437
fatcat:atgrpfu54ved3by3cy5tjb6pha
*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. ...##
###
F-FCSR: Design of a New Class of Stream Ciphers
[chapter]

2005
*
Lecture Notes in Computer Science
*

Its

doi:10.1007/11502760_6
fatcat:fsv64pi3jzemfg7r5xhhj2uaru
*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. ...##
###
Some Results on FCSR Automata With Applications to the Security of FCSR-Based Pseudorandom Generators

2008
*
IEEE Transactions on Information Theory
*

These results especially concern the structure

doi:10.1109/tit.2007.913244
fatcat:qcrpqdezbfervdzekgetaquppq
*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. ...##
###
Feedback shift registers, 2-adic span, and combiners with memory

1997
*
Journal of Cryptology
*

Feedback shift registers with carry operation (

doi:10.1007/s001459900024
fatcat:5xza7htdpza5rileekvisnktgy
*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 ...##
###
Linearisation Attacks on FCSR-based Stream Ciphers

2012
*
International Journal for Information Security Research
*

The paper demonstrates, these new attacks against F-

doi:10.20533/ijisr.2042.4639.2012.0026
fatcat:24ku6jjshreh7ire3fo7ojlp4u
*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*. ...##
###
Alternating Step Generator Using FCSR and LFSRs: A New Stream Cipher

2019
*
International Journal of Intelligent Engineering and Systems
*

Keystream

doi:10.22266/ijies2019.1031.13
fatcat:um65aok24veftoosdyw4pi7x3u
*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] . ...##
###
A generalized birthday approach for efficiently finding linear relations in $$\ell $$ ℓ -sequences

2013
*
Designs, Codes and Cryptography
*

In this paper we show how to exploit a particular set

doi:10.1007/s10623-013-9845-0
fatcat:5q6qsf3sg5eklfvuz4eig5wsva
*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. ...##
###
Cryptanalysis of the stream cipher BEAN

2011
*
Proceedings of the 4th international conference on Security of information and networks - SIN '11
*

There is a sound motivation behind the use

doi:10.1145/2070425.2070432
dblp:conf/sin/AgrenH11
fatcat:2gsk35s3gbdgllgy6cywcbdwmy
*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*. ...##
###
Arithmetic crosscorrelations of feedback with carry shift register sequences

1997
*
IEEE Transactions on Information Theory
*

Index Terms-Crosscorrelations, binary

doi:10.1109/18.605605
fatcat:fhcezg3m3zf7diu3lxowkupdze
*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*. ...##
###
Periodicity and Distribution Properties of Combined FCSR Sequences
[chapter]

2006
*
Lecture Notes in Computer Science
*

This is a study

doi:10.1007/11863854_29
fatcat:wqjcopodpbaalkmu3ngw3ogjey
*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. ...
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