Image encryption based on elliptic curve cryptosystem and reducing its complexity is still being actively researched. Generating matrix for encryption algorithm secret key together with Hilbert matrix will be involved in this study. For a first case we will need not to compute the inverse matrix for the decryption processing cause the matrix that be generated in encryption step was self invertible matrix. While for the second case, computing the inverse matrix will be required. Peak signal to noise ratio (PSNR), and unified average changing intensity (UACI) will be used to assess which case is more efficiency to encryption the grayscale image.
Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself k times. It is used in elliptic curve cryptography (ECC) as a means of producing a trapdoor function. In this paper, algorithms to compute the elliptic curve scalar multiplication using a special form for integers will introduce, and then two types of signed digit representation will use. The signed digit form of the scalar is calculated by many types of algorithms such as binary , non adjacent form and direct recoding. The results indicate that the proposed methods perform better to compute the scalar multiplication on elliptic curves and it is more efficient than the existing methods.
Asymmetric image encryption schemes have shown high resistance against modern cryptanalysis. Massey Omura scheme is one of the popular asymmetric key cryptosystems based on the hard mathematical problem which is discrete logarithm problem. This system is more secure and efficient since there is no exchange of keys during the protocols of encryption and decryption. Thus, this work tried to use this fact to propose a secure asymmetric image encryption scheme. In this scheme the sender and receiver agree on public parameters, then the scheme begin deal with image using Massey Omura scheme to encrypt it by the sender and then decrypted it by the receiver. The proposed scheme tested using peak signal to noise ratio, and unified average changing intensity to prove that it is fast and has high security.
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