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Arithmetic Crosscorrelations of FCSR Sequences
 IEEE Trans. Info. Theory
, 1999
"... An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum's arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic crosscorrelations. These sequences are decimations of the 2adic expansions of rat ..."
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An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum's arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic crosscorrelations. These sequences are decimations of the 2adic expansions of rational numbers p/q such that 2 is a primitive root modulo q.
Algebraic feedback shift registers
 Theoretical Comp. Sci
, 1999
"... A general framework for the design of feedback registers based on algebra over complete rings is described. These registers generalize linear feedback shift registers and feedback with carry shift registers. Basic properties of the output sequences are studied: relations to the algebra of the underl ..."
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Cited by 8 (6 self)
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A general framework for the design of feedback registers based on algebra over complete rings is described. These registers generalize linear feedback shift registers and feedback with carry shift registers. Basic properties of the output sequences are studied: relations to the algebra of the underlying ring; synthesis of the register from the sequence (which has implications for cryptanalysis); and basic statistical properties. These considerations lead to security measures for stream ciphers, analogous to the notion of linear complexity that arises from linear feedback shift registers. We also show that when the underlying ring is a polynomial ring over a finite field, the new registers can be simulated by linear feedback shift registers with small nonlinear filters. Key words: cryptography; feedback shift register; complete ring; stream cipher; pseudorandom number generator. 1
Breaking the FFCSRH stream cipher in real time
 ASIACRYPT 2008, To Appear
, 2008
"... Abstract. The FFCSR stream cipher family has been presented a few years ago. Apart from some flaws in the initial propositions, corrected in a later stage, there are no known weaknesses of the core of these algorithms. The hardware oriented version, called FCSRH, is one of the ciphers selected for ..."
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Abstract. The FFCSR stream cipher family has been presented a few years ago. Apart from some flaws in the initial propositions, corrected in a later stage, there are no known weaknesses of the core of these algorithms. The hardware oriented version, called FCSRH, is one of the ciphers selected for the eSTREAM portfolio. In this paper we present a new and severe cryptanalytic attack on the FFCSR stream cipher family. We give the details of the attack when applied on FFCSRH. The attack requires a few Mbytes of received sequence and the complexity is low enough to allow the attack to be performed on a single PC within seconds. 1
Two algebraic attacks against the ffcsrs using the iv mode
 In Progress in Cryptology  INDOCRYPT 2005
, 2013
"... Abstract. This article presents some new results concerning two algebraic attacks against the FFCSR constructions proposed in [2]. We focus on the parameters of the stream ciphers proposed that permit to mount algebraic attacks when using the IV mode. The complexity obtained for the first attack de ..."
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Abstract. This article presents some new results concerning two algebraic attacks against the FFCSR constructions proposed in [2]. We focus on the parameters of the stream ciphers proposed that permit to mount algebraic attacks when using the IV mode. The complexity obtained for the first attack described here is 245 binary instructions using 215 known IV values for the construction FFCSRSF1. All the proposed attacks are full key recovery attacks. We do not contest that the FCSRs are a good and new idea, we just say that the chosen parameters do not ensure the security level claimed.
A new approach for FCSRs
"... Abstract. The Feedback with Carry Shift Registers (FCSRs) have been proposed as an alternative to Linear Feedback Shift Registers (LFSRs) for the design of stream ciphers. FCSRs have good statistical properties and they provide a builtin nonlinearity. However, two attacks have shown that the curre ..."
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Abstract. The Feedback with Carry Shift Registers (FCSRs) have been proposed as an alternative to Linear Feedback Shift Registers (LFSRs) for the design of stream ciphers. FCSRs have good statistical properties and they provide a builtin nonlinearity. However, two attacks have shown that the current representations of FCSRs can introduce weaknesses in the cipher. We propose a new “ring ” representation of FCSRs based upon matrix definition which generalizes the Galois and Fibonacci representations. Our approach preserves the statistical properties and circumvents the weaknesses of the Fibonacci and Galois representations. Moreover, the ring representation leads to automata with a quicker diffusion characteristic and better implementation results. As an application, we describe a new version of FFCSR stream ciphers. Keywords: Stream cipher, FCSRs, ℓsequence, ring FCSRs. 1
Efficient MultiplyWithCarry Random Number Generators With Optimal Distribution Properties
 ACM Transactions on Modeling and Computer Simulation
, 2003
"... Introduction 1.1. A pseudorox"q number gener ator (RNG) for high speed simulation and Monte CarS integrSqKx should have sever" pr" er"US : (1) it should haveenor""x perz d, (2) it should e hibitunifor distrqS""xI of dtuples(for all d), (3) it should exhibi ..."
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Cited by 5 (0 self)
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Introduction 1.1. A pseudorox"q number gener ator (RNG) for high speed simulation and Monte CarS integrSqKx should have sever" pr" er"US : (1) it should haveenor""x perz d, (2) it should e hibitunifor distrqS""xI of dtuples(for all d), (3) it should exhibit a good lattice str""Ezx in high dimensions, and (4) it should be e#ciently computable(prablexzF with a base b which is a power of 2). Typically the RNG is a member of a family ofsimilar generrxI withdi#erq tparU"xIEU and one hopes that parKq"qxI and seeds may be easily chosen so as toguarF tee pr" er"E" (1), (2), (3) and (4). Ther is no known family of RNG with all four pr" er"KS (see,for example, [M1]). 1.2. In [MZ], Mar aglia and Zaman showed that their addwithcarc (AWC) gener ator satisfy condition (1). By giving up on (4) and using an appr"FxIE" base b, they achieve good distrxSKEKx pr" er"Kq of dtuplesfor values d wh
XFCSR – A New Software Oriented Stream Cipher Based Upon FCSRs
 INDOCRYPT 2007
, 2007
"... Feedback with Carry Shift Registers (FCSRs) are a promising alternative to LFSRs in the design of stream ciphers. The previous constructions based on FCSRs were dedicated to hardware applications [3]. In this paper, we will describe XFCSR a family of software oriented stream ciphers using FCSRs. T ..."
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Feedback with Carry Shift Registers (FCSRs) are a promising alternative to LFSRs in the design of stream ciphers. The previous constructions based on FCSRs were dedicated to hardware applications [3]. In this paper, we will describe XFCSR a family of software oriented stream ciphers using FCSRs. The core of the system is composed of two 256bits FCSRs. We propose two versions: XFCSR128 and XFCSR256 which output respectively 128 and 256 bits at each iteration. We study the resistance of our design against several cryptanalyses. These stream ciphers achieve a high throughput and are suitable for software applications (6.3 cycles/byte).