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Prime Finite Field Arithmetic

Part of the Signals and Communication Technology book series (SCT)

Abstract

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 [64]. Furthermore, the ElGamal signature scheme [80] and the Digital Signature Standard (DSS) of the National Institute for Standards and Technology [90] 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 [35]. 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.

Keywords

Partial Product Modular Multiplication Modular Exponentiation Carry Save Adder Extended Euclidean Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2006

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