A Pre - Computation Scheme for Speeding Up Public - Key Cryptosystems

This thesis presents fast and practical methods for generating randomly distributed pairs of the form (x, gX mod p) or (x, xe mod N), using precomputation. These generation schemes are of wide applicability for speeding-up public key systems that depend on exponentiation and offer a smooth memory-speed trade-off. The steps involving exponentiation in these systems can be reduced significantly in many cases. The schemes are most suited for server applications. The thesis also presents security analyses of the schemes using standard assumptions. The methods are novel in the sense that they identify and thoroughly exploit the randomness issues related to the instances generated in these public-key schemes. The constructions use random walks on Cayley (expander) graphs over Abelian groups. Thesis Supervisor: Shafi Goldwasser Title: Professor of Computer Science Acknowledgments I would like to start by expressing my deepest gratitude to Shafi Goldwasser, my thesis advisor, for her continued advice and fruitful discussions. She has been very helpful and supporting throughout my time at MIT, and I look forward to further work with her. The work for this thesis was performed in part at Bellcore under the direction of and in collaboration with Ramarathnam Venkatesan. I would like to thank Marcus Peinado for investigating the hidden subset sum problems related to our generators, and for collaborating on the conference version of our paper. I would also like to thank Ronald Rivest and Arjen Lenstra for their help, advice, and discussions. Finally, I would like to thank my parents for making me possible, and for their constant love and encouragement.