## CryptoDB

### Jason E. Gower

#### Publications

Year
Venue
Title
2006
PKC
2006
EPRINT
We present the Zhuang-Zi algorithm, a new method for solving multivariate polynomial equations over a finite field. We describe the algorithm and present examples, some of which cannot be solved with the fastest known algorithms.
2006
EPRINT
We use the Bateman-Horn conjecture to study the order of the set of $\mathbb{F}_q$-rational points of primitive subgroups that arise in torus-based cryptography. We provide computational evidence to support the heuristics and make some suggestions regarding parameter selection for torus-based cryptography.
2005
EPRINT
We demonstrate how to prevent differential attacks on multivariate public key cryptosystems using the Plus (+) method of external perturbation. In particular, we prescribe adding as few as 10 Plus polynomials to the Perturbed Matsumoto-Imai (PMI) cryptosystem when $g=1$ and $r=6$, where $\theta$ is the Matsumoto-Imai exponent, $n$ is the message length, $g=\gcd{(\theta,n)}$, and $r$ is the internal perturbation dimension; or as few as $g+10$ when $g \neq 1$. The external perturbation does not significantly decrease the efficiency of the system, and in fact has the additional benefit of resolving the problem of finding the true plaintext among several preimages of a given ciphertext. We call this new scheme the Perturbed Matsumoto-Imai-Plus (PMI+) cryptosystem.
2003
ASIACRYPT

#### Coauthors

Jintai Ding (3)
Dieter Schmidt (1)