Random Binary and Non-Binary Sequences Derived from Random Sequence of Points on Cyclic Elliptic Curve Over Finite FieldGF(2m) and Their Properties

Sathyanarayana, S. V.; Kumar, Mahendra; Bhat, Krishnaraj

doi:10.1080/19393550903482759

Cited by 7 publications

(16 citation statements)

References 11 publications

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“…During comparison, if the bits are same, then it is considered as agreement; else disagreement. Depending on the number of agreements

(a)

and disagreements

(d)

in a particular shift, the correlation values

R_{h a} false(τ false)

is computed using the Equation () 30

R_{h a} (τ) = \frac{a - d}{N} 0 < τ \leq N

where N is sequence length. …”

Section: Randomness Testsmentioning

confidence: 99%

“…A key sequence is said to qualify if it can resist all kinds of cryptanalytic, statistical and brute force attacks. Various security aspects in References 30,35,38,39 are considered to evaluate the proposed system. They are: key space, key sensitivity, linear complexity and correlation value.…”

Section: Security Aspectsmentioning

confidence: 99%

“…If the elements in the key are linearly related, in spite of large period, with the knowledge of small segment in key sequence, the entire key sequence could be solved by constructing a set of simultaneous equations and solving them 30 . In the case of arbitrarily chosen IV and due to non‐linearity introduced by S‐box of SDES like structure, the segments of the sequence are non‐linear.…”

Section: Security Aspectsmentioning

confidence: 99%

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Generation of chaotic random binary sequences for cryptographic applications

Sheela¹,

Sathyanarayana²

2021

Concurrency and Computation

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In stream cipher systems, random key sequence generation is the primary task. The concept of chaotic systems can be considered in generating a random key sequence due to its inherent randomness property. Though the chaotic real sequences are random, the randomness will be lost after converting them to binary sequences. In this context, the authors propose a technique which uses a non‐linear feedback system to enhance the randomness of the binary sequences. In this work, three binary chaotic sequences using a logistic map are generated with three different initial conditions and each real value of the chaotic sequence is converted to ‘k’ bit binary value using a thresholding function. Some of the resulting sequences are not random. Hence, in this article a non‐linear structure is used to make the resulting sequence random. Here, a non‐linear function similar to the structure of the Simplified Data Encryption Standard is used to generate a sequence using two non‐random chaotic binary sequences. The resulting sequence is XORed with another non‐random chaotic binary sequence to get a random sequence. Sequences obtained from this nonlinear system are subjected to randomness tests and the results indicate that the sequences pass all the randomness tests. Hence, the sequences qualify as random key sequences, which can be used in a stream cipher based system to encrypt the data samples like audio, image, video, and so forth.

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“…During comparison, if the bits are same, then it is considered as agreement; else disagreement. Depending on the number of agreements

(a)

and disagreements

(d)

in a particular shift, the correlation values

R_{h a} false(τ false)

is computed using the Equation () 30

R_{h a} (τ) = \frac{a - d}{N} 0 < τ \leq N

where N is sequence length. …”

Section: Randomness Testsmentioning

confidence: 99%

Section: Security Aspectsmentioning

confidence: 99%

Section: Security Aspectsmentioning

confidence: 99%

See 1 more Smart Citation

Generation of chaotic random binary sequences for cryptographic applications

Sheela¹,

Sathyanarayana²

2021

Concurrency and Computation

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show abstract

“…From the sequence (xi, yi) several binary and non-binary sequences can be derived and their randomness properties are investigated in [3]. Choosing a linear feedback with connection polynomial primitive over GF (p), can generate periodic sequence with maximum period [13,4]. For any choice of n-stages >1, an appropriate feedback connection can be obtained by using an n th degree primitive polynomial over GF (p).…”

Section: A Cyclic Elliptic Curve Based Pseudorandom Bit Generatormentioning

confidence: 99%

Proposed Method for Multimedia Data Security Using Cyclic Elliptic Curve, Chaotic System, and Authentication Using Neural Network

Baheti¹,

Singh²,

Khan³

2014

2014 Fourth International Conference on Communication Systems and Network Technologies

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As multimedia applications are used increasingly, security becomes an important issue of security of images. The combination of chaotic theory and cryptography forms an important field of information security. In the past decade, chaos based image encryption is given much attention in the research of information security and a lot of image encryption algorithms based on chaotic maps have been proposed. But, most of them delay the system performance, security, and suffer from the small key space problem. This paper introduces an efficient symmetric encryption scheme based on a cyclic elliptic curve and chaotic system that can overcome these disadvantages. The cipher encrypts 256-bit of plain image to 256-bit of cipher image within eight 32-bit registers. The scheme generates pseudorandom bit sequences for round keys based on a piecewise nonlinear chaotic map. Then, the generated sequences are mixed with the key sequences derived from the cyclic elliptic curve points. The proposed algorithm has good encryption effect, large key space, high sensitivity to small change in secret keys and fast compared to other competitive algorithms.

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“…With the increase in available computation power, it is found for a given key size that an EC public-key cryptosystem has higher security compared to RSA cryptosystem [4]. EC operations which used in the generation of pseudo-random sequences with strong cryptographic properties have been studied in the literature, such as [5], [6], [7].…”

Section: Introductionmentioning

confidence: 99%

Pseudo-random Sequence Generation from Elliptic Curves over a Finite Field of Characteristic 2

Reyad

Kotulski

2016

Annals of Computer Science and Information Systems

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Abstract-In this paper, the randomness of binary sequences generated from elliptic curves over a finite field of characteristic 2 is studied. A scheme of construction based on the ChaosDriven Elliptic Curve Pseudo-random Number Generator (C-D ECPRNG) is proposed. The generators based of this scheme are verified by using tests from the NIST Statistical Test Suite to analyze their statistical properties. An elliptic curve used in the numerical example is defined over F 2 8 . The investigations which made for the generated series of two output sequences of the lengths of 2 10 and 2 20 bits shown that 14 generators working according to our general scheme exhibit good randomness properties. Next, the binary sequences generated by these 14 schemes were used for encrypting a 256 × 256 grayscale Lena image as an application example and the security analysis of the ciphered images was carried out.

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Random Binary and Non-Binary Sequences Derived from Random Sequence of Points on Cyclic Elliptic Curve Over Finite FieldGF(2^m) and Their Properties

Cited by 7 publications

References 11 publications

Generation of chaotic random binary sequences for cryptographic applications

Generation of chaotic random binary sequences for cryptographic applications

Proposed Method for Multimedia Data Security Using Cyclic Elliptic Curve, Chaotic System, and Authentication Using Neural Network

Pseudo-random Sequence Generation from Elliptic Curves over a Finite Field of Characteristic 2

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