The Discrete Logarithm Problem

Abstract

The discrete logarithm problem is the basis for the security of a number of cryptographic systems, including the celebrated Diffee-Hellman protocol and the El Gamal system. In this talk, we will describe the problem and some applications, and discuss why it is believed to be difficult.

Local periods and binary partial words: An algorithm

Abstract

The study of the combinatorial properties of strings of symbols from a finite alphabet (also referred to as words) is profoundly connected to numerous fields such as biology, computer science, mathematics, and physics. Research in combinatorics on words goes back roughly a century. There is a renewed interest in combinatorics on words as a result of emerging new application areas such as molecular biology. Partial words were recently introduced in this context. The motivation behind the notion of a partial word is the comparison of genes (or proteins). Alignment of two genes (or two proteins) can be viewed as a construction of partial words that are said to be compatible.

While a word can be described by a total function, a partial word can be described by a partial function. More precisely, a partial word of length n over a finite alphabet A is a partial function from {1,...,n} into A. Elements of {1,...,n} without an image are called holes. A word is just a partial word without holes. The notion of a period of a word is central in combinatorics on words. In the case of partial words, there are two notions: one is that of period, the other is that of local period.

This paper extends to partial words with one hole the well known result of Guibas and Odlyzko which states that for every word u, there exists a word v of same length as u over the alphabet {0,1} such that the set of all periods of u coincides with the set of all periods of v. Our result states that for every partial word u with one hole, there exists a partial word v of same length as u with at most one hole over the alphabet {0,1} such that the set of all periods of u coincides with the set of all periods of v and the set of all local periods of u coincides with the set of all local periods of v.

To prove our result, we use the technique of Halava, Harju and Ilie, which they used to characterize constructively the set of periods of a given word. As a consequence of our constructive proof, we obtain a linear time algorithm which, given a partial word with one hole, computes a partial word with at most one hole over the alphabet {0,1} with the same length and the same sets of periods and local periods. A World Wide Web server interface at http://www.uncg.edu/mat/AlgBin/ has been established for automated use of the program.

Probabilistic Belief Networks for Modeling Genomic Health

Abstract

Project GenIE (http://www.uncg.edu/~nlgreen/GenIE-web-page.html) is using artificial intelligence knowledge representation and natural language generation techniques to create patient-tailored genomic health information. In this talk we describe our approach to modeling the patient's genomic health using probabilistic belief networks.

Characterization of the finger loop domain of Ffh by random sequence libraries and sequence analysis

Abstract

Although the role of the function of the signal recognition particle (SRP) from Escherichia coli in targeting of proteins to the cytoplasmic membrane is known, details of many of its structural features require further study. The finger loop region of the Ffh protein is essential for SRP function and likely forms part of the binding site for hydrophobic membrane targeting sequences. To investigate the sequence and structural features of this domain important for its function, we have developed a genetic system to screen a random aptamer library for sequences that restored function to a finger loop deletion mutant. About 1% of random sequences can replace the wild type finger loop. Analysis of the random sequences, as well as targeted mutagenesis, shows the importance of hydrophobicity in finger loop function. All functional sequences also lack extensive secondary structural consistent with the role of the finger loop in binding a variety of ligands. Continued isolation and analysis of random sequences should provide new insights into how the finger loop functions in membrane protein targeting.