Cryptography using generalized Fibonacci matrices with Affine-Hill cipher

Prasad, Kalika; Mahato, Hrishikesh

doi:10.1080/09720529.2020.1838744

Cited by 20 publications

(24 citation statements)

References 10 publications

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“…holds but in other cases, it does not hold, some of such observations has been found in [8,13,16,22,23].…”

Section: Introductionmentioning

confidence: 89%

A novel public key cryptography based on generalized Lucas matrices

Prasad¹,

Mahato²,

Kumari³

2022

Preprint

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In this article, we have proposed a generalized Lucas matrix (recursive matrix of higher order) having relation with generalized Fibonacci sequences and established many special properties in addition to that usual matrix algebra. Further, we have proposed a modified public key cryptography using these matrices as keys in Affine cipher and key agreement for encryption-decryption with the combination of terms of generalized Lucas sequences under residue operations. In this scheme, instead of exchanging the whole key matrix, only a pair of numbers(parameters) need to be exchanged, which reduces the time complexity as well as space complexity of the key transmission and has a large key-space.

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“…holds but in other cases, it does not hold, some of such observations has been found in [8,13,16,22,23].…”

Section: Introductionmentioning

confidence: 89%

A novel public key cryptography based on generalized Lucas matrices

Prasad¹,

Mahato²,

Kumari³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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“…Then the cipher text converted to decimal. The result of decimal is re-encrypted using the Hill Cipher method generate Cipher text [3].To process the description or return to the original message with the process carried out it is the opposite of the encryption process, if in the first encryption process with the Caesar Cipher method then on the first description process is the Hill Cipher method [4].…”

Section: Methodsmentioning

confidence: 99%

Combination of Hill Cipher Algorithm and Caesar Cipher Algorithm for Exam Data Security

Agung¹,

Heryana²,

Solehudin³

2020

bit-cs

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The progress of communication technology has had a positive impact on human life, including in the field of education. The education office is currently implementing computer-based exams starting from the State Higher Education Entrance Joint Selection (SBMPTN) exam to the School Final Examination. But with the implementation of computer-based exams this is of course the less secure the level, therefore the authors make this research with the aim of securing the exam data that will be tested with Hill cipher cryptography and Caesar cipher. Cryptography is a technique of hiding data that is done to secure data, in this case cryptography aims to secure data on exam questions.

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“…2.2 Generalized Fibonacci Matrix [11] Definition 2.2. The generalized Fibonacci sequence of order n is defined by the recurrence relation,…”

Section: Preliminariesmentioning

confidence: 99%

“…Kalika et.al. [11] proposed a public key cryptography based on generalized Fibonacci matrices where they also discussed properties of Fibonacci matrices. Nowadays dependency of the people across the world on the internet has been increased.…”

Section: Introductionmentioning

confidence: 99%

On the role of the Fibonacci matrix as key in modified ECC

Kumari¹,

Tanti²

2021

Preprint

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In this paper, we have proposed a modified cryptographic scheme based on the application of recursive matrices as key in ECC and ElGamal. For encryption, we consider mapping analogous to affine Hill cipher in which a plaintext matrix has been constructed by points corresponding to letters on elliptic curves. In the formation of key-space, the generalized Fibonacci matrices have been taken into account, which is the sequence of matrices. The beauty of considering Fibonacci matrices is their construction where we need only two parameters(integers) in place of n 2 elements. The use of a recursive matrix makes a large keyspace for our proposed scheme and increases its efficiency. Thus, it reduces time as well space complexity, and its security & strength is based on EC-DLP which is a hard problem in number theory.

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Cryptography using generalized Fibonacci matrices with Affine-Hill cipher

Cited by 20 publications

References 10 publications

A novel public key cryptography based on generalized Lucas matrices

A novel public key cryptography based on generalized Lucas matrices

Combination of Hill Cipher Algorithm and Caesar Cipher Algorithm for Exam Data Security

On the role of the Fibonacci matrix as key in modified ECC

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