Prime Finite Field Arithmetic
The modular exponentiation operation is a common operation for scrambling; it is used in several cryptosystems. For example, the Diffie-Hellman key exchange scheme requires modular exponentiation . Furthermore, the ElGamal signature scheme  and the Digital Signature Standard (DSS) of the National Institute for Standards and Technology  also require the computation of modular exponentiation. However, we note that the exponentiation process in a cryptosystem based on the discrete logarithm problem is slightly different: The base (M) and the modulus (n) are known in advance. This allows some precomputation since powers of the base can be precomputed and saved . In the exponentiation process for the RSA algorithm, we know the exponent (e) and the modulus (n) in advance but not the base (M); thus, such optimizations are not likely to be applicable.
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