An Equivalence-Preserving Transformation of Shift Registers

Dubrova, Elena

doi:10.1007/978-3-319-12325-7_16

Cited by 10 publications

(4 citation statements)

References 17 publications

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“…Then the transformation algorithm [3] is used to convert F into the Galois NLFSR G. Therefore, the period of the output sequence of G is 2 256 − 1, which provides very good statistical properties for the cipher. Later, the author extend the transformation algorithm to handle Galois-to-Galois case in [6]. This algorithm is the generalized version of the Fibonacci-to-Galois transformation algorithm [3].…”

Section: Transformation Algorithmsmentioning

confidence: 99%

“…Besides, the common problem in all the discussed algorithms is that the output function of an NLFSR is assumed to only tap from the 0th bit, which is infeasible in stream ciphers where the output takes multiple bits from the NLFSR. Furthermore, it is pointed out by the author in [6] that the sequence of states of the two NLFSRs before and after transformation differ in several bit positions. How to efficiently and correctly transform more generalized NLFSRs with output function taken arbitrary taps from the NLFSR remain unsolved.…”

Section: Transformation Algorithmsmentioning

confidence: 99%

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Generalized NLFSR Transformation Algorithms and Cryptanalysis of the Class of Espresso-like Stream Ciphers

Yao,

Parampalli

2019

Preprint

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Lightweight stream ciphers are highly demanded in IoT applications. In order to optimize the hardware performance, a new class of stream cipher has been proposed. The basic idea is to employ a single Galois NLFSR with maximum period to construct the cipher. As a representative design of this kind of stream ciphers, Espresso is based on a 256-bit Galois NLFSR initialized by a 128-bit key. The 2 256 − 1 maximum period is assured because the Galois NLFSR is transformed from a maximum length LFSR. However, we propose a Galois-to-Fibonacci transformation algorithm and successfully transform the Galois NLFSR into a Fibonacci LFSR with a nonlinear output function. The transformed cipher is broken by the standard algebraic attack and the Rønjom-Helleseth attack with complexity O(2 68.44 ) and O(2 66.86 ) respectively. The transformation algorithm is derived from a new Fibonacci-to-Galois transformation algorithm we propose in this paper. Compare to existing algorithms, proposed algorithms are more efficient and cover more general use cases. Moreover, the transformation result shows that the Galois NLFSR used in any Espresso-like stream ciphers can be easily transformed back into the original Fibonacci LFSR. Therefore, this kind of design should be avoided in the future.

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Section: Transformation Algorithmsmentioning

confidence: 99%

Section: Transformation Algorithmsmentioning

confidence: 99%

Generalized NLFSR Transformation Algorithms and Cryptanalysis of the Class of Espresso-like Stream Ciphers

Yao,

Parampalli

2019

Preprint

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“…The current state in LFSRs is a linear function of the previous state [5]. Unlike NLFSRs, LFSRs have a unique transformation between Galois and Fibonacci configurations [6] [7] [8].…”

Section: Fig 1: An N-bit Fsr General Structure [14]mentioning

confidence: 99%

A New Type of NLFSR Functions with Maximum Periods

Al-Hejri

Al-Kharobi

2018

TNC

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Nonlinear feedback shift registers (NLFSRs) have received much attention in designing various cryptographic algorithms such as stream ciphers and light weight block ciphers in the provision of high-level security in communication systems. The main purpose of NLFSRs is to generate pseudorandom sequences of bits. NLFSRs are known to be more secure than their linear counterparts. However, there is no mathematical foundation on how to construct an NLFSR with optimal period. In this paper, we propose a new type of NLFSR function of degree 2 with optimal periods. Using our construction method, we propose 639 new functions of this type with optimal periods. N e t w o r k s a n d C o m m u n i c a t i o n s ; V o l u m e 7 , N o . 2 , A p r i l 2 0 1 9 C o p y r i g h t © S o c i e t y f o r S c i e n c e a n d E d u c a t i o n , U n i t e d K i n g d o m 21 Section 3 reviews the existing studies related to NLFSR functions with optimal periods. Section 4 describes the proposed construction method. Section 5 presents the new NLFSR feedback functions. Finally, Section 6 concludes the present study and offers recommendations for future work. T r a n s a c t i o n s o n

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“…In [13], although the uniform conditions are not satisfied, it requires that the update functions only take input from lower stages than the stages they update. Later on, in [14], Dubrova proposed a novel transformation, which can be applied to arbitrary Galois FSRs rather than just the uniform FSRs, but some constraints on the update functions were still necessary to realize this transformation. Very recently, in order to further relax the constraints, Lu et al firstly utilized the Boolean networkbased method to investigate the transformation between these two types of FSRs in [15], where an FSR is regarded as a Boolean networks (BNs).…”

Section: Introductionmentioning

confidence: 99%

An improved transformation between Fibonacci FSRs and Galois FSRs

Li¹,

Zhu²,

Lu³

2019

Preprint

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Feedback shift registers (FSRs), which have two configurations: Fibonacci and Galois, are a primitive building block in stream ciphers. In this paper, an improved transformation is proposed between Fibonacci FSRs and Galois FSRs. In the previous results, the number of stages is identical when constructing the equivalent FSRs. In this paper, there is no requirement to keep the number of stages equal for two equivalent FSRs here. More precisely, it is verified that an equivalent Galois FSR with fewer stages cannot be found for a Fibonacci FSR, but the converse is not true. Furthermore, a given Fibonacci FSR with n stages is proved to have a total of 2 n−1 ! 2 − 1 equivalent Galois FSRs. In order to reduce the propagation time and memory, an effective algorithm is developed to find equivalent Galois FSR and is proved to own minimal operators and stages. Finally, the feasibility of our proposed strategies, to mutually transform Fibonacci FSRs and Galois FSRs, is demonstrated by numerical examples.

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An Equivalence-Preserving Transformation of Shift Registers

Cited by 10 publications

References 17 publications

Generalized NLFSR Transformation Algorithms and Cryptanalysis of the Class of Espresso-like Stream Ciphers

Generalized NLFSR Transformation Algorithms and Cryptanalysis of the Class of Espresso-like Stream Ciphers

A New Type of NLFSR Functions with Maximum Periods

An improved transformation between Fibonacci FSRs and Galois FSRs

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