Pipeline architectures for radix-2 new Mersenne number transform
IEEE Transactions on Circuits and Systems Part I: Regular Papers - Special section on 2008 custom integrated circuits conference (CICC 2008)
Design of an RNS reverse converter for a new five-moduli special set
Proceedings of the great lakes symposium on VLSI
On the design of modulo 2n+1 dot product and generalized multiply-add units
Computers and Electrical Engineering
Image encryption based on the finite field cosine transform
Image Communication
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We investigate image and video convolutions based on Fermat number transform (FNT) modulo q=2M+1 where M is an integer power of two. These transforms are found to be ideal for image convolutions, except that the choices for the word length, restricted by the transform modulus, are rather limited. We discuss two methods to overcome this limitation. First, we allow M to be an arbitrary integer. This gives much wider variety in possible moduli, at the cost of decreased transform length of 16 or 32 points for M1=216+1 and q2=28+1, which allow transforms up to 256 points with a dynamic range of about 24 bits. We design an efficient reconstruction circuit based on mixed radix conversion for converting the result from diminished-1 RNS into normal binary code. The circuit is implemented in VHDL and found to be very small in area. We also discuss the necessary steps in performing convolutions with the GFNT and evaluate the integrated circuit implementation cost for various elementary operations.