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CS Theory Lecture Series: Computing Divisor Class Groups of Function Fields Using Stark Units with Applications to Cryptography

Speaker: Anand Narayanan, USC

Talk Title: Computing Divisor Class Groups of Function Fields Using Stark Units with Applications to Cryptography

Series: USC CS Theory

Abstract: Divisor class groups are structures central to the study of the arithmetic of global fields. We present a brief introduction to these groups and motivate their study in a computational setting by describing their extensive use in cryptography (elliptic and hyperelliptic curve based crypto-systems), error correction (algebraic geometric codes) and in solving certain Diophantine equations (Pell's Equation).

We then describe a new characterization of the structure of divisor class groups through the machinery of Kolyvagin systems from Stark units. This characterization leads to many interesting computational results; two of which we will discuss. The first is an efficient (nearly optimal) algorithm to compute the divisor class number of ray class fields. The second is a reduction relating the discrete logarithm problem in certain families of real elliptic/hyperelliptic curves to the principal ideal problem.

Host: Shang-Hua Teng

Location: SSL 150

Audiences: Everyone Is Invited

Contact: Assistant to CS chair

This event is open to all eligible individuals. USC Viterbi operates all of its activities consistent with the University's Notice of Non-Discrimination. Eligibility is not determined based on race, sex, ethnicity, sexual orientation, or any other prohibited factor.

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