Instead one starts with an easily invertible quadratic map F (called central map) and combines it with two invertible

affine maps S and T to get a public key of the form P = S * F * T .

The first one we use to illustrate the meaning of the notions linear and

affine map and to explain the role of the matrix of a linear transformation.

In the last section we use linear maps and

affine maps to characterize E-convex sets.

The Mazur-Ulam theorem [30] says that every surjective isometry between two real Banach spaces is an

affine map.

11 of [22] says that if X is a connected, metric, compact abelian group, y is its normalized Haar measure and V is an

affine map, then V being ergodic is equivalent to having a point with dense orbit, in which case the set of points with dense orbit has measure 1.

The 21 papers propose an algorithm for continuous piecewise

affine maps of compact support, investigate the stability of cycles in gene networks with variable feedbacks, and describe polynomial maps of the affine space.

Affine maps do not affect inflection points, cusps, or loops, so the analysis can be applied to the canonical curve instead of the original one.