We describe a new hardware architecture to perform the modular
exponentiation operation, i.e., the computation of $c=m^e \bmod{n}$
where $c, m, e, n$ are large integers. The modular exponentiation
operation is the most common operation in public-key cryptography.
The new method, named as the spectral modular exponentiation,
uses the discrete Fourier transform over a finite
ring, and relies on new techniques to perform
multiplication and reduction operations. The method yields
an efficient and highly parallel architecture for hardware
realizations of public-key cryptosystems which use the
modular exponentiation as the core computation, such
as the RSA and Diffie-Hellman algorithms.
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