Project Stevens2006-01:

Real-life applications of digital signature schemes
Mentor: Johannes Buchmann, TU Darmstadt

Digital signatures are a mechanism by which someone, called a signer, can electronically "sign" a message so that receivers can verify that the message came from the signer and was not changed in transit. Most digital signatures rely on a cryptographic hash function for part of their operations. This project will explore one or more ways to makes digital signatures more efficient and to use these improvements in real world applications. Two examples are described below.

Problem 1: The Merkle signature scheme, introduced by Ralph Merkle in 1990, is efficient and provably secure. However, its architecture is different from most signature schemes, in that it only allows a limited number of signatures. The goal here is to explore the use of the Merkle scheme in real applications such as SSL, https, etc.

Problem 2: The Courtois-Finiasz-Sendries signature scheme, which is based on coding theory, computes the signature of a document m as the decoding of the hash of h(m xor i) where h is a hash function that hashes to vectors and i is a counter that makes h(m xor i) decodable. Unfortunately, one needs to inspect 100 million counters before a decodable vector is found. This signature algorithm is therefore not very efficient. The goal here is to modify the scheme to make it more efficient.

Project Stevens2006-02:

Applications of computational algebraic number theory in cryptography
Mentors: Alexander May, TU Darmstadt and Susanne Wetzel, Stevens Institute of Technology

Cryptography has strong ties to computational algebraic number theory. Examples in public key cryptography include the RSA and ElGamal cryptosystems which are based on the difficulty of factoring and solving the discrete logarithm problem, respectively. Lattice theory has not only proven to be an effective tool for cryptanalysis but is also expected to give rise to cryptographic primitives that sustain their strength even in the context of quantum computing. Algebraic structures have also taken a prominent place in secret key cryptography with the Advanced Encryption Standard.

The exact problem will be chosen from the general topic of computational algebraic number theory in cryptography. Depending on the interests and expertise of the student, this project can be more focused on foundational mathematical results, or on implementation and experimentation. A background in mathematics, computer science, and programming is desired.