Cayley Graphs of Semigroups and Applications to Hashing

In 1994, Tillich and Zemor proposed a scheme for a family of hash functions that uses products of matrices in groups of the form $SL_2(F_{2^n})$. In 2009, Grassl et al. developed an attack to obtain collisions for palindromic bit strings by exploring a connection between the Tillich-Zemor functions and maximal length chains in the Euclidean algorithm for polynomials over $F_2$. In this work, we present a new proposal for hash functions based on Cayley graphs of semigroups. In our proposed hash function, the noncommutative semigroup of linear functions under composition is considered as platform for the scheme. We will also discuss its efficiency, pseudorandomness and security features. Furthermore, we generalized the Fit-Florea and Matula\u27s algorithm (2004) that finds the discrete logarithm in the multiplicative group of integers modulo $2^k$ by establishing a connection between semi-primitive roots modulo $2^k$ where $k\geq 3$ and the logarithmic base used in the algorithm

Spartan Daily, September 12, 1989

Volume 93, Issue 7https://scholarworks.sjsu.edu/spartandaily/7867/thumbnail.jp

New Proofs for NMAC and HMAC: Security Without Collision-Resistance

HMAC was proved by Bellare, Canetti and Krawczyk [2] to be a PRF assuming that (1) the underlying compression function is a PRF, and (2) the iterated hash function is weakly collision-resistant. However, recent attacks show that assumption (2) is false for MD5 and SHA-1, removing the proof-based support for HMAC in these cases. This paper proves that HMAC is a PRF under the sole assumption that the compression function is a PRF. This recovers a proof based guarantee since no known attacks compromise the pseudorandomness of the compression function, and it also helps explain the resistance-to-attack that HMAC has shown even when implemented with hash functions whose (weak) collision resistance is compromised. We also show that an even weaker-than-PRF condition on the compression function, namely that it is a privacy-preserving MAC, suffices to establish HMAC is a MAC as long as the hash function meets the very weak requirement of being computationally almost universal, where again the value lies in the fact that known attacks do not invalidate the assumptions made

A Pairwise Key Pre-Distribution Scheme for Wireless Sensor Networks

To achieve security in wireless sensor networks, it is important to be able to encrypt and authenticate messages sent between sensor nodes. Before doing so, keys for performing encryption and authentication must be agreed upon by the communicating parties. Due to resource constraints, however, achieving key agreement in wireless sensor networks is non-trivial. Many key agreement schemes used in general networks, such as Diffie-Hellman and other public-key based schemes, are not suitable for wireless sensor networks due to the limited computational abilities of the sensor nodes. Pre-distribution of secret keys for all pairs of nodes is not viable due to the large amount of memory this requires when the network size is large. In this paper, we provide a framework in which to study the security of key pre-distribution schemes, propose a new key pre-distribution scheme which substantially improves the resilience of the network compared to previous schemes, and give an in-depth analysis of our scheme in terms of network resilience and associated overhead. Our scheme exhibits a nice threshold property: when the number of compromised nodes is less than the threshold, the probability that communications between any additional nodes are compromised is close to zero. This desirable property lowers the initial payoff of smaller-scale network breaches to an adversary, and makes it necessary for the adversary to attack a large fraction of the network before it can achieve any significant gain

Mustang Daily, January 15, 1997

Student newspaper of California Polytechnic State University, San Luis Obispo, CA.https://digitalcommons.calpoly.edu/studentnewspaper/6087/thumbnail.jp

Spartan Daily, May 14, 1993

Volume 100, Issue 68https://scholarworks.sjsu.edu/spartandaily/8426/thumbnail.jp

Spartan Daily, October 24, 2000

Volume 115, Issue 38https://scholarworks.sjsu.edu/spartandaily/9605/thumbnail.jp

Spartan Daily, October 3, 1983

Volume 81, Issue 24https://scholarworks.sjsu.edu/spartandaily/7073/thumbnail.jp

Spartan Daily, September 25, 1972

Volume 60, Issue 4https://scholarworks.sjsu.edu/spartandaily/5639/thumbnail.jp