An Algorithm for Constructing a Fastest Galois NLFSR Generating a Given Sequence

Chabloz, Jean-Michel; Mansouri, Shohreh Sharif; Dubrova, Elena

doi:10.1007/978-3-642-15874-2_3

Cited by 15 publications

(8 citation statements)

References 16 publications

(22 reference statements)

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“…The construction of a non‐linear type shift registers of n ‐stage with the degree n or less, in which each stage operates at a v rate, is necessary for the generation of maximum sequence of length. The construction of binary machine stages for generating the periodic maximum length sequence with no chain connection between the minimum stages of binary machines is still limited.…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…Further, the galois configuration is more flexible, and the necessary next state values are still limited . In the construction of NLFSR, it requires (2∗⌈ l o g 2 n ⌉) numbers of stages for the shift register to construct the feedback Boolean functions. Thus, the Boolean functions are used to generate the recursive pseudorandom sequence of order

O (\frac{n^{2}}{⌈ lo g_{2} n ⌉})

.…”

Section: Pseudorandom Key Stream Analysismentioning

confidence: 99%

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Non‐singular sequence folding‐based pseudorandom key generation algorithm for cryptographic processor

Pandian

Ray

2015

Security Comm Networks

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In this paper, a new algorithm to construct the non-linear-based Boolean function using non-singular sequence folding technique is proposed to generate pseudorandom binary key sequence for cryptographic processor. Unlike the conventional methodology to generate recursive pseudorandom nibble of 15 (60-bit) from minimum seed of four bits, the proposed algorithm has the novelty to generate non-recursive pseudorandom nibble of 63 (252-bit) from the same minimum seed of four bits. In this proposed algorithm, a given binary sequence is converted to de Bruijn sequence and folded to minimum state with the strategy of binary encoding, which supports to determine the non-linear Boolean function. Further, the next state functions with minimum logic complexity is formulated using the algebraic normal form to generate nonrecursive pseudorandom binary sequence. The key stream analysis is performed, and randomness tests for the generated pseudorandom binary sequence (key stream) is validated using National Institute of Standards and Technology test suite. The proposed algorithm in this paper has improved in terms of sequence size and number of stages compared with existing algorithms. secured system, in which the basic techniques are pooled together. Blaze [8] postulates that the asymmetric cryptography is more secure than the symmetric in key distribution and exchange, and the key size should be larger than the symmetric cryptographic key. Thus, the pseudorandom key size, which is static or dynamic, plays the vital and most critical part in cryptographic processor apart from the cryptographic algorithm.This paper conferred the construction of a non-linearbased Boolean function using non-singular sequence folding technique to generate non-recursive pseudorandom binary key sequence for cryptographic processor. In order to determine the non-linear Boolean functions, a given binary sequence is converted to de Bruijn sequence and folded to minimum state with the strategy of binary encoding using proposed algorithm 1. Further, the constructed de Bruijn sequence fold is used to construct the non-linear Boolean functions with the minimum number of stages using proposed algorithm 2. Further, the next state functions with minimum logic complexity is constructed using the algebraic normal form (ANF) to generate non-recursive pseudorandom binary sequence (key stream) using proposed algorithm 3. Thus, the generated non-recursive pseudorandom binary key sequence satisfies the randomness properties and unpredictable, so that the adversary could not disrupt the key. The proposed algorithm for generating the non-recursive pseudorandom key sequence can be used for any application that requires randomizing the data for security. Such cryptographic applications include wireless communications, data transmission, and many others [9][10][11][12]. The rest of the paper is structured with the preliminary concept, algorithmic development, analysis, and testing. Section 2 highlights the concepts of de Bruijn sequence and the necessity of feedback Boole...

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Section: Proposed Algorithmmentioning

confidence: 99%

O (\frac{n^{2}}{⌈ lo g_{2} n ⌉})

.…”

Section: Pseudorandom Key Stream Analysismentioning

confidence: 99%

Non‐singular sequence folding‐based pseudorandom key generation algorithm for cryptographic processor

Pandian

Ray

2015

Security Comm Networks

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“…It was shown in [12] that a nonlinear recurrence of order n always exists for uniform n-bit NLFSRs. An algorithm for constructing a best uniform Galois NLFSR which is equivalent to a given Fibonacci NLFSR was presented in [20].…”

Section: Previous Workmentioning

confidence: 99%

An Equivalence-Preserving Transformation of Shift Registers

Dubrova

2014

Sequences and Their Applications - SETA 2014

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Abstract. The Fibonacci-to-Galois transformation is useful for reducing the propagation delay of feedback shift register-based stream ciphers and hash functions. In this paper, we extend it to handle Galois-to-Galois case as well as feedforward connections. This makes possible transforming Trivium stream cipher and increasing its keystream data rate by 27% without any penalty in area. The presented transformation might open new possibilities for cryptanalysis of Trivium, since it induces a class of stream ciphers which generate the same set of keystreams as Trivium, but have a different structure.

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“…The transformation from a given Fibonacci NLFSR to the equivalent uniform Galois NLFSRs can potentially reduce the depth of the circuits implementing feedback functions, thus decreasing the propagation time and increasing the throughput. A method of finding the fastest equivalent uniform Galois configuration for a given Fibonacci NLFSR has been mentioned in [15].…”

Section: Introductionmentioning

confidence: 99%

The Transformation from the Galois NLFSR to the Fibonacci Configuration

Lin

2013

2013 Fourth International Conference on Emerging Intelligent Data and Web Technologies

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Two configurations of nonlinear feedback shift registers (NLFSRs) are considered. Conventional NLFSRs use the Fibonacci configuration in which the feedback is applied to the last bit only. The Galois configuration, in which the feedback can be applied to every bit, is attractive for stream ciphers to which high throughput is very important. In this paper, we show how to transform a Galois NLFSR into an equivalent NLFSR in the Fibonacci configuration. The mapping between the initial states of the Galois NLFSR and its equivalent Fibonacci configuration is also derived. Moreover, some properties of Galois NLFSRs are found with the transformation.

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An Algorithm for Constructing a Fastest Galois NLFSR Generating a Given Sequence

Cited by 15 publications

References 16 publications

Non‐singular sequence folding‐based pseudorandom key generation algorithm for cryptographic processor

Non‐singular sequence folding‐based pseudorandom key generation algorithm for cryptographic processor

An Equivalence-Preserving Transformation of Shift Registers

The Transformation from the Galois NLFSR to the Fibonacci Configuration

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