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Register synthesis for algebraic feedback shift registers based on nonprimes
 DESIGNS, CODES, AND CRYPTOGRAPHY
"... In this paper, we describe a solution to the register synthesis problem for a class of sequence generators known as Algebraic Feedback Shift Registers (or AFSRs). These registers are based on the algebra of adic numbers, where is an element in a ring R, and produce sequences of elements in R=(). W ..."
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In this paper, we describe a solution to the register synthesis problem for a class of sequence generators known as Algebraic Feedback Shift Registers (or AFSRs). These registers are based on the algebra of adic numbers, where is an element in a ring R, and produce sequences of elements in R=(). We give several cases where the register synthesis problem can be solved by an ecient algorithm. Consequently, any keystreams over R=() used in stream ciphers must be unable to be generated by a small register in these classes. This paper extends the analyses of feedback with carry shift registers and algebraic feedback shift registers by Goresky, Klapper, and Xu [4, 5, 11].
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
Expected πAdic Security Measures of Sequences
"... Various measures of security of stream ciphers have been studied that are based on the problem of finding a minimum size generator for the keystream in some special class of generators. These include linear and padic spans, as well as πadic span, which is based on a choice of an element π in a fin ..."
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Various measures of security of stream ciphers have been studied that are based on the problem of finding a minimum size generator for the keystream in some special class of generators. These include linear and padic spans, as well as πadic span, which is based on a choice of an element π in a finite extension of the integers. The corresponding sequence generators are known as linear feedback shift registers, feedback with carry shift registers, and the more general algebraic feedback shift registers, respectively. In this paper the average behavior of such security measures when π d = p> 0 or π 2 = −p < 0 is studied. In these cases, if Z[π] is the ring of integers in its fraction field and is a UFD, it is shown that the average πadic span is n − O(log(n)) for sequences with period n.
The Asymptotic Behavior of NAdic Complexity
"... We study the asymptotic behavior of stream cipher security measures associated with classes of sequence generators such as linear feedback shift registers and feedback with carry shift registers. For nonperiodic sequences we consider normalized measures and study the set of accumulation points for a ..."
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We study the asymptotic behavior of stream cipher security measures associated with classes of sequence generators such as linear feedback shift registers and feedback with carry shift registers. For nonperiodic sequences we consider normalized measures and study the set of accumulation points for a fixed sequence. We see that the the set of accumulation points is always a closed subinterval of [0, 1]. For binary or ternary FCSRs we see that this interval is of the form [B, 1 − B], a result that is an analog of an earlier result by Dai, Jiang, Imamura, and Gong for
Algebraic Feedback Shift Registers Based on Function Fields
"... We study algebraic feedback shift registers (AFSRs) based on quotients of polynomial rings in several variables over a finite field. These registers are natural generalizations of linear feedback shift registers. We describe conditions under which such AFSRs produce sequences with various ideal ran ..."
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We study algebraic feedback shift registers (AFSRs) based on quotients of polynomial rings in several variables over a finite field. These registers are natural generalizations of linear feedback shift registers. We describe conditions under which such AFSRs produce sequences with various ideal randomness properties. We also show that there is an efficient algorithm which, given a prefix of a sequence, synthesizes a minimal such AFSR that outputs the sequence.
Supervisor at CSC was Johan Håstad
"... As a response to the lack of efficient and secure stream ciphers, ECRYPT (a 4year Network of Excellence funded by the European Union) manages and coordinates a multiyear effort called eSTREAM to identify new stream ciphers suitable for widespread adoption. Polar Bear, one of the eSTREAM candidates, ..."
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As a response to the lack of efficient and secure stream ciphers, ECRYPT (a 4year Network of Excellence funded by the European Union) manages and coordinates a multiyear effort called eSTREAM to identify new stream ciphers suitable for widespread adoption. Polar Bear, one of the eSTREAM candidates, is a new synchronous stream cipher proposed by Johan H˚astad, and Mats Näslund. In this thesis, the first known attack is presented. It is a guessanddetermine attack with a computational complexity of O(2 78.8) that recovers the initial state. We propose that this weakness is fixed by adding a keydependent premixing of the dynamic permutation in conjunction with the key schedule. Further suggested tweaks strengthen the security and improves performance on long sequences. The updated Polar Bear specification that will be sent to eSTREAM before June 30, 2006, is based on tweaks suggested in this thesis. We have also optimized the source code of Polar Bear, which enables it to run almost twice as fast. We have not found any other weaknesses in Polar Bear, and it seems resistant to all known generic attacks.
A New Class of Pseudonoise Sequences
, 2003
"... We apply the framework of piadic algebra and algebraic feedback shift registers to polynomial rings over finite fields. We give a construction of new pseudorandom sequences over a nonprime finite field that satisfy Golomb's randomness criteria. ..."
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We apply the framework of piadic algebra and algebraic feedback shift registers to polynomial rings over finite fields. We give a construction of new pseudorandom sequences over a nonprime finite field that satisfy Golomb's randomness criteria.
Register Synthesis for Algebraic Feedback Shift Registers Based on NonPrimes
"... Abstract In this paper, we describe a solution to the register synthesis problem for a class of sequence generators known as Algebraic Feedback Shift Registers (or AFSRs). These registers are based on the algebra of ssadic numbers, where ss is an element in a ring R, and produce sequences of elemen ..."
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Abstract In this paper, we describe a solution to the register synthesis problem for a class of sequence generators known as Algebraic Feedback Shift Registers (or AFSRs). These registers are based on the algebra of ssadic numbers, where ss is an element in a ring R, and produce sequences of elements in R=(ss). We give several cases where the register synthesis problem can be solved by an efficient algorithm. Consequently, any keystreams over R=(ss) used in stream ciphers must be unable to be generated by a small register in these classes. This paper extends the analyses of feedback with carry shift registers and algebraic feedback shift registers by Goresky, Klapper, and Xu [4, 5, 11].