In the interest of good mathematical terminology, here is a short primer on the most basic algebraic structures. The definitions are not complete but rather evocative and are designed to prevent confusion. Field -- has addition, subtraction, multiplication, and division. Examples are the real numbers (R), the complex numbers (C), and the rational numbers (Q). An important class of fields for crypto are integers modulo a prime (Z/pZ or F_p). An important class of fields for error coding are polynomials with binary coeffients modulo an irreducible polynomial (F_2[x]/p(x)F_2[x]). Ring -- has addition, subtraction, multiplication, but no division. Every field is a ring but not vice-versa. Examples are the integers (Z), the integers modulo a composite number (Z/nZ) and polynomials with various rings, including R[x], Z[x]. Group -- has either addition/subtraction or multiplication/division, but not necessarily both. Every ring is a group under addition, but not vice-versa. If the group is commutative, we write the operation as addition typically; if not, we use multiplication. Examples of commutative groups are solutions of an elliptic curves and rotations in the plane. Examples of non-commutative groups are permutations, rotations in three dimensions, and Euclidean transformations of the plane. Eric