Cryptography - Mathematics

Cryptography can be roughly defined as a set of techniques designed to ensure secure communications. A quick look at this security reveals that it can take two quite distinct forms, depending on the threats we're trying to protect against.

• If an entity A sends a message to an entity B, and wants to make it impossible for anyone other than B to intercept the message, the service it is seeking is confidentiality: the aim is to make a passive attack (e.g. phone tapping, mail opening) ineffective. The answer to this need lies in the use of an encryption algorithm.

• Let's take the same configuration again. A sends a message to B, but we're no longer concerned about confidentiality; we want B to be sure of the origin of the information he receives, of its authenticity. We want to prevent an active attack, for example, by adding information while it is in transit on the communication line. There is a whole family of needs of this type. You want to be sure of the integrity of the data transmitted, or you want to be sure of the identity of the sender (the authenticity of the bank card and its owner withdrawing money from an ATM, for example). This is a problem of authentication or identification. If you want to go even further and require "proof" of the sender's identity, you may need a signature.

• It was mainly the first type of need that prevailed for entire centuries (confidentiality). In those days, cryptography was used exclusively by the military and diplomats. Today, banking exchanges have reached an impressive volume; the use of e-mail and e-commerce is growing and, in general, information technology is revolutionizing the means of communication. Although the traditional users of cryptography are also seeing their needs grow, they are losing their monopoly (which is not always without difficulties, as cryptographic means are covered by arms legislation in many countries), and other fields are making use of cryptography. The needs of the second type mentioned (authentication, signature) are perhaps the most crucial for these "civilian" applications.

The "Cryptography" article is the subject of two booklets:

AF 172 Mathematics

AF 173 Algorithms

The subjects are not independent of each other.

Readers will need to refer to the other booklet often enough.