Abstract
In this work, a novel symmetric cryptosystem for image encryption is presented. The Symmetric Cryptosystem of the Elliptic Curve (SCEC) can resist damage to encrypted figures, up to 40% of the original figure. SCEC uses chaos to generate an $8\times {8}$ S-box with high nonlinearity to avoid the linear attack. A random permutation is used before starting encryption, making the cryptosystem more robust. For testing, damage according to four types of noise was applied to the encrypted images: additive, multiplicative, Gaussian, or occlusion. The median filter was applied to correct the damage in encrypted images, improving its sharpness, and a new measure, the Similarity Parameter (SP), is proposed to evaluate the difference between the original image and the decrypted image with damage. Several parameters and tests were applied to evaluate the performance of SCEC, from the encryption quality to the resistance to the differential attack. Experimental results indicate that SCEC has high-quality cryptographic properties, very much similar to the corresponding values of AES but with the addition of a high protection to noise damage on the encrypted images.
Highlights
B ECAUSE of the advanced development of the communication networks and the high quantity of valuable information that can be contained in an image, the image ciphering for protecting confidential data is a field with a highly dynamic development [1]–[6].Four points have to be considered when designing an encryption system for images, being the first one the resistance to attacks
Attacks can be classified into three categories: those against the elliptic curve, those focused on the cryptosystem, and those directed to the encrypted images
When the elliptic curve is calculated for real implementations of the proposed system, there is a potential problem derived from the fact that there are some values of a where the computation program requires a longer time to find the generator element α
Summary
B ECAUSE of the advanced development of the communication networks and the high quantity of valuable information that can be contained in an image, the image ciphering for protecting confidential data is a field with a highly dynamic development [1]–[6]. When the elliptic curve is calculated for real implementations of the proposed system, there is a potential problem derived from the fact that there are some values of a where the computation program requires a longer time to find the generator element α. This problem is solved by running the algorithm of the Fig. The number of solutions is prime and is calculated according to Eq(10) It follows that the probability of finding the generating element is. Other instruments were applied in this work to verify the randomness
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