Small cancellation groups form an interesting class with many desirable properties. It is a well-known fact that small cancellation groups are generic; however, all previously known results of their genericity are asymptotic and provide no information about "small" group presentations. In this note, we give closed-form formulas for both lower and upper bounds on the density of small cancellation presentations, and compare our results with experimental data.
The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. In this paper, we will argue that initial minors are a viable way to solve this problem. This paper will present necessary algorithms for this attack. We have written a code to verify the conjecture of initial minors using Schur complements. We were able to solve the problem for groups of order up to 250.