Graduate Thesis Or Dissertation

High-speed implementation of the RSA cryptosystem

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  • A public key cryptosystem allows two or more parties to securely communicate over an insecure channel without establishing a physically secure channel for key exchange. The RSA cryptosystem is the most popular public key cryptosystem ever invented. It is based on the difficulty of factoring large composite numbers. Once the RSA system is setup, i.e., the modulus, the private and public exponents are determined, and the public components have been published, the senders as well as the receivers perform a single operation for signing, encryption, decryption, and verification. This operation is the computation of modular exponentiation. In this thesis, we focus on fast implementations of the modular exponentiation operation. Several methods for modular exponentiation are presented, including the binary method and the m-ary method. We give a general algorithm of implementing the m-ary method, and some examples of the quaternary method and the octal method. The standard multiplication and squaring algorithms are also discussed as methods to implement the modular multiplication and squaring operations. Two methods for performing the modular multiplication operation are given: the multiply and reduce method and the Montgomery method. The Montgomery product algorithm is used in the implementation of the modular exponentiation operation. The algorithms presented in this thesis are implemented in C and 16-bit in-line 80486 assembly code. We have performed extensive testing of the code, and obtained timing results which are given in the last chapter of the thesis.
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