Boris fancies himself a connectionist. Check out the relationship between
Pipes and Bricks. I can't stop laughing.
Auguste Kerckhoffs was a 19th century linguist and cryptographer. In 1883, he published two expositions (in French) entitled "Military Cryptography". In these essays, he states six principles (desiderata) as follows:
- The system must be practically, if not mathematically, indecipherable
- It must not be required to be secret, and it must be able to fall into the hands of the enemy without inconvenience
- Its key must be communicable and retainable without the help of written notes, and changeable or modifiable at the will of the correspondents
- It must be applicable to telegraphic correspondence
- It must be portable, and its usage and function must not require the concourse of several people
- Finally, it is necessary, given the circumstances that command its application, that the system be easy to use, requiring neither mental strain nor the knowledge of a long series of rules to observe.
From these principles, we derive Kerckhoffs' Law or Kerckhoffs' Principle (most notably from principle #2). In simple terms, it states:
The security of a cryptosystem must depend solely on the key. The cryptosystem must not depend on the secrecy of the algorithm, i.e. the algorithm may be public knowledge.
Claude Shannon is credited with restating this as "the enemy knows the system".
The ideals of Kerckhoffs' principle are held in high esteem by the cryptography community. In particular, there are only a few known one-way hard problems that are useful for public key-private key cryptography. They all can be shown that they are one-way hard (in the face of the lack of a solution to P?=NP or other hypotheses), are easy to represent mathematically and can be implemented in computer code in reasonable implementations (performance, size and other considerations). The known problems are:
- Discrete Logarithm - Formalized by Diffie, Hellman and Merkle.
- Integer Factorization - Formalized by RSA
- Elliptic Curve - Formalized by Koblitz, Vanstone, Menezes and others.
- Ring based (modular algebra) - Formalized by Silverstein, Pipher and Hoffstein
- Shortest Vector Problem (SVP) or Closest Vector Problem (CVP) in Lattices - Formalized by Atjai, Dwork, Goldwasser, Goldreich and others
The description and treatment of these problems is beyond scope here. These problems are all well known and are considered of varying degrees of difficulty (hardness of algorithm, required key size in usage, etc.). Suitable keys held in secret using these algorithms are likely to protect information even in the face of all of the PUBLIC formal knowledge and understanding of these problems.
Check out ivan's post on the Residential Centroid problem. I'm looking forward to coplanar day.
By the way, bigH just figured out that the outline of the Earth on the plane is the shape of a circle. Ummmmmmmmmmm, yeah, way to go big guy.