Coding Theory and Cryptology
The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. The topics range from mathematical areas such as computational number theory, exponential sums and algebraic function fields through coding-theory subjects such as extremal problems, quantum error-correcting codes and algebraic-geometry codes to cryptologic subjects such as stream ciphers, public-key infrastructures, key management, authentication schemes and distributed system security.
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access control algebraic function field applications authentication schemes authorization binary bits Boolean function certificate clone codeword coding theory coefficients consider construct correlation attack cryptography Cryptology cryptosystem decoding defined Definition denote Diffie-Hellman discrete logarithm distance distribution divisor domain elements elliptic curve encoding rule encryption entitlement example excluded users exists exponent exponential sums factor field sieve finite field given group key Hamming Hamming bound I. E. Shparlinski IEEE Trans integer irreducible polynomial keystream Lecture Notes Lemma Lenstra LFSR LFSRC LILI-II linear code LNCS lower bound mapping matrix method modulo Montgomery multiplicative nonlinear object parameters parity-check plaintext points policy management polynomial prime number principal privilege attributes probability problem Proof public key quadratic quadratic sieve quantum code quantum error random number result runtime secret key Section server Springer-Verlag stream ciphers subset Theorem valid vector Z/mZ Z/nZ