**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# RSA Encryption: Main Concepts

Description

This lecture covers the main concepts behind RSA encryption, including groups defined by generators and relations, homomorphisms of groups, isomorphism, and automorphism. Examples of homomorphisms between cyclic groups are also discussed, illustrating the application of RSA in practice.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

Instructor

Related concepts (40)

MATH-310: Algebra

This is an introduction to modern algebra: groups, rings and fields.

Homomorphism

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: ὁμός () meaning "same" and μορφή () meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German ähnlich meaning "similar" to ὁμός meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925).

Automorphism

In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object. In the context of abstract algebra, a mathematical object is an algebraic structure such as a group, ring, or vector space.

Group homomorphism

In mathematics, given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h : G → H such that for all u and v in G it holds that where the group operation on the left side of the equation is that of G and on the right side that of H. From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, and it also maps inverses to inverses in the sense that Hence one can say that h "is compatible with the group structure".

Automorphism group

In mathematics, the automorphism group of an object X is the group consisting of automorphisms of X under composition of morphisms. For example, if X is a finite-dimensional vector space, then the automorphism group of X is the group of invertible linear transformations from X to itself (the general linear group of X). If instead X is a group, then its automorphism group is the group consisting of all group automorphisms of X. Especially in geometric contexts, an automorphism group is also called a symmetry group.

Group (mathematics)

In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way).

Related lectures (81)

Fundamental GroupsMATH-410: Riemann surfaces

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Classification of ExtensionsMATH-506: Topology IV.b - cohomology rings

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Group Theory - Part 2PHYS-314: Quantum physics II

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Kirillov Paradigm for Heisenberg Group

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

Group Homomorphisms: Kernels, Images, and Normal SubgroupsMATH-310: Algebra

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.