Production of a Super-Increasing Sequence based on the Fibonaci Sequence

  • Assia Merzoug University Hadj Lakhdar Batna, 05 Avenue Chahid Boukhlouf Batna 05000, Algeria
  • Adda Ali-Pacha University Science and Technology of Oran Mohamed Boudiaf, BP 1505 El M’Naouer Oran 31000, Algeria
  • Naima Hadj-Said University Science and Technology of Oran Mohamed Boudiaf, BP 1505 El M’Naouer Oran 31000, Algeria
  • Hana Ali-Pacha University Science and Technology of Oran Mohamed Boudiaf, BP 1505 El M’Naouer Oran 31000, Algeria
Keywords: Fibonacci sequence; Merkle-Hellman; super-increasing sequence; Knapsack problem

Abstract

One shows that we can build a long recurring sequence super-increasing and use it in the cryptographic system based on the Knapsack problem, for example the Merkle-Hellman cipher. Thus, we reduce the size of the key with the same system safety. For this, we have modified the generalized Fibonacci sequence to produce of a super-increasing sequence. This modification was based essentially on the use of real coefficients in the main recursive equation. The result of this, it is the transformation of the public key of the Merkle-Hellman crypto system into a secret algorithm and, for an equivalent complexity.

Published
2019-06-30