In this paper, we present a new encryption scheme using generalization k-Fibonacci-like sequence, we code the points of an elliptic curve with the terms of a sequence of k-Fibonacci-like using of Fibonacci sequence and we call it as k-Fibonacci like sequence {Vk,n} defined by the recurrence relation:
Vk,n+1=kVk,n+Vk,n−1;n≥1,Vk,0=2m(k+1),Vk,1=pk+k(k+1)m(1)
and we present some relation among k-Fibonacci like sequence, k-Fibonacci sequence and k-Lucas sequence. After that, we give application of elliptic curves in cryptography using k-Fibonacci like sequence.
