Assessment of the One-Dimensional Generalized New Mersenne Number Transform for Security Systems

With increased reliance on encryption for e-commerce, communications and data storage, new techniques are constantly being developed to meet the demand for secure encryption systems requiring higher levels of security and integrity. A significant aspect of integrity is the diffusion and avalanche effect, which is measured by its sensitivity to a single bit change between the cipher text and the plaintext. This effect should yield a catastrophic result which is measurable and can therefore be readily assessed for its suitability as part of a security system. This paper measures the standard one-dimensional implementations of the generalized new Mersenne number transform suite for its suitability in security applications. The generalized suite is expanded from the existing new Mersenne number transform, by the addition of two new transforms, which have yet to be fully assessed in this aspect. The two new transforms offer the same long power-of-two run lengths and efficient calculations over a field of integers modulo a Mersenne prime. Sharing similar characteristics with the original transform, they also have the cyclic-convolution property, suggesting that they too can wield significant impact in the fields of image-, signal-processing as well as cryptography.