Cryptographic error correction

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 67-71).It has been said that "cryptography is about concealing information, and coding theory is about revealing it." Despite these apparently conflicting goals, the two fields have common origins and many interesting relationships. In this thesis, we establish new connections between cryptography and coding theory in two ways: first, by applying cryptographic tools to solve classical problems from the theory of error correction; and second, by studying special kinds of codes that are motivated by cryptographic applications. In the first part of this thesis, we consider a model of error correction in which the source of errors is adversarial, but limited to feasible computation. In this model, we construct appealingly simple, general, and efficient cryptographic coding schemes which can recover from much larger error rates than schemes for classical models of adversarial noise. In the second part, we study collusion-secure fingerprinting codes, which are of fundamental importance in cryptographic applications like data watermarking and traitor tracing. We demonstrate tight lower bounds on the lengths of such codes by devising and analyzing a general collusive attack that works for any code.by Christopher Jason Peikert.Ph.D

Cryptographic Error Correction

It has been said that “cryptography is about concealing information, and coding theory is about revealing it. ” Despite these apparently conflicting goals, the two fields have common origins and many interesting relationships. In this thesis, we establish new connections between cryptography and coding theory in two ways: first, by applying cryptographic tools to solve classical problems from the theory of error correction; and second, by studying special kinds of codes that are motivated by cryptographic applications. In the first part of this thesis, we consider a model of error correction in which the source of errors is adversarial, but limited to feasible computation. In this model, we construct appealingly simple, general, and efficient cryptographic coding schemes which can recover from much larger error rates than schemes for classical models of adversarial noise. In the second part, we study collusion-secure fingerprinting codes, which are of fundamental importance in cryptographic applications like data watermarking and traito

Adaptive Security in the Threshold Setting: From Cryptosystems to Signatures

Threshold cryptosystems and signatures schemes provide ways to distribute trust throughout a group and increase the availability of cryptographic systems. A standard approach in designing these protocols is to base them upon existing single-party systems having the desired properties. Two recent signature schemes [13, 18] have been developed which are provably secure using only some standard number-theoretic hardness assumptions. Both schemes rely upon inversion of a prime number modulo a secret value. We provide a multiparty modular inversion protocol that is secure against an adaptive adversary, thereby enabling threshold signature schemes with stronger security properties than any previous result. As a tool, we also develop an adaptively-secure, erasure-free threshold version of the Paillier cryptosystem. Because of its homomorphic properties, this cryptosystem is of independent interest and is useful in the context of secure elections, lotteries, and general multiparty computation