Properties of an IV depend on the cryptographic scheme used.

A group is a very general algebraic object and most cryptographic schemes use groups in some way.

Demonstrating the resistance of any cryptographic scheme to attack is a complex matter, requiring extensive testing and reviews, preferably in a public forum.

For that reason, one of the definitions of "breaking" a cryptographic scheme is to find a method faster than a brute force attack.

The concept of a cryptographic scheme is to define higher level algorithms or uses of the primitives so they achieve certain security goals.

The Vigenère cipher is a well-known example of a cryptographic scheme that uses a tableau.

Many lattice problems have been conjectured or proven to be average-case hard, making them an attractive class of problems to base cryptographic schemes on.

Moreover, worst-case hardness of some lattice problems have been used to create secure cryptographic schemes.

This algorithm and its further refinements were used to break several cryptographic schemes, establishing its status as a very important tool in cryptanalysis.

The length, in bits, of the key used in a cryptographic scheme.