Abstract

A REINFORCED DIFFIE-HELLMAN KEY

S. M. Tudunkaya

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Abstract This paper displayed the implementation of DH key with the aid of the finite multiplicative group R_p^* of rhotrices defined over the finite field F_pfor a prime p. The main contribution of this paper is that for each DH protocol implemented by the use of a traditional group Z_p^* of order p-1, this work developed a corresponding DH protocol where the group R_p^*of order p(p-1) was used. Similarly, to each finite field F_p of order p, a groupR_p^*of order p(p-1) was also proposed. This relationship indicated a significant increase in the number of subgroups also. This means a DH key that was implemented with R_p^*is at least p- times or (p-1)- times stronger than the one implemented with Z_p^* or F_prespectively and hence the method presented here has a higher resistance to attacks. Another importance is that since numbers are too exposed by every where's, every time's and every person's usage, the use of groups that are unique in their representations and operations will also improve the security of the DH key. Key words: Group; Finite group; Cyclic group; Cryptography; Diffie-Hellman key.

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