Well-known LLL algorithm can be viewed as greedy algorithm for solving shortest vector problem. The algorithm can be changed so it will work with Gram matrix (of dot products) of basis vectors b_i. Norm of each lattice vector can be expressed as quadratic form with Gram matrix as its associated matrix. For fixed non-zero x_j, it is easy to find analytically shortest vector v_min,j = (x_1, ..., x_k)*(b_1, ..., b_k)^T. It suffices to minimize quadratic form (x_1, ..., x_k)*G(x_1, ..., x_k). Unfortunately, resulted vector v_min is not (in general) part of the lattice. On the other hand this v_min should be close to some small vector of the lattice. The goal of the thesis is to analyze quadratic forms defined by Gram matrix and propose alternative approach to LLL algorithm that will be based on quadratic forms. Student will: 1. generate many random lattices, find exact SVP using enumeration or sieving, and find corresponding coefficients SV = (X_1, ..., X_k)*(b_1, ..., b_k)^T. 2. analyze distances between v_min, j (for x_j = X_j) and SV. 3. based on statistics or information gained from 3. propose alternative approach or tweak of the LLL algorithm that will use quadratic forms.