Kalika Prasad

Kalika Prasad, Hrishikesh Mahato, Munesh Kumari

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.

Kalika Prasad, Munesh Kumari

In this review article, we discussed the Mathematics and mechanics behind the Enigma machine with an analysis of security strength. The German army used the Enigma machine during the second world war to encrypt communications. Due to its complexity, the encryption done by the Enigma Machine was assumed to be almost unbreakable. However, the Polish believed that people with good background and deep knowledge of science and mathematics would have a better chance to break the encryption done by Enigma. They appointed twenty mathematicians from Poznan University to work on this problem at the Polish Cipher Bureau. Three of those, Marian Rejewski, Jerzy Rozycki and Henryk Zygalski were able to exploit certain flaws in the encryption, and by using permutation group theory finally managed to decipher the Enigma messages. The mathematics discovered by them is presented here.

Kalika Prasad, Hrishikesh Mahato

In this article, we have proposed a public key cryptography using Affine-Hill cipher with a generalized Fibonacci matrix(called multinacci matrix). Also proposed a key establishment(exchange of key matrix $K=Q_λ^{k}$ of order $λ\timesλ$ for encryption-decryption) scheme with the help of multinacci sequences under prime modulo. In this scheme, instead of exchanging key matrix, we need to exchange the only pair of numbers $(λ, k)$, which reduces the time complexity as well as space complexity and comes with a large key-space.