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We then multiply these two primes to produce the product, N. The difficulty arises when, being given N, we try and find the original P1 and P2.

The Rivest-Shamir-Adleman public key infrastructure encryption protocol is one of many based on this problem. To simplify matters to a great degree, the N product is the public key and the P1 and P2 numbers are, together, the private key.

This problem is one of the most fundamental of all mathematical concepts. It has been studied intensely for the past 20 years and the consensus seems to be that there is some unproven or undiscovered law of mathematics that forbids any shortcuts.

That said, the mere fact that it is being studied intensely leads many others to worry that, somehow, a breakthrough may be discovered. This is a new cryptographic protocol based upon a reasonably well-known mathematical problem.

The properties of elliptic curves have been well known for centuries, but it is only recently that their application to the field of cryptography has been undertaken.

First, imagine a huge piece of paper on which is printed a series of vertical and horizontal lines. Each line represents an integer with the vertical lines forming x class components and horizontal lines forming the y class components.

The intersection of a horizontal and vertical line gives a set of coordinates x,y. In the highly simplified example below, we have an elliptic curve that is defined by the equation:.

For the above, given a definable operator, we can determine any third point on the curve given any two other points. This definable operator forms a "group" of finite length.

To add two points on an elliptic curve, we first need to understand that any straight line that passes through this curve intersects it at precisely three points.

Now, say we define two of these points as u and v: We can then draw a vertical line through w to find the final intersecting point at x. This rule works, when we define another imaginary point, the Origin, or O, which exists at theoretically extreme points on the curve.

As strange as this problem may seem, it does permit for an effective encryption system, but it does have its detractors.

On the positive side, the problem appears to be quite intractable, requiring a shorter key length thus allowing for quicker processing time for equivalent security levels as compared to the Integer Factorization Problem and the Discrete Logarithm Problem.

On the negative side, critics contend that this problem, since it has only recently begun to be implemented in cryptography, has not had the intense scrutiny of many years that is required to give it a sufficient level of trust as being secure.

This leads us to more general problem of cryptology than of the intractability of the various mathematical concepts, which is that the more time, effort, and resources that can be devoted to studying a problem, then the greater the possibility that a solution, or at least a weakness, will be found.

Please check the box if you want to proceed. Microsoft's secretive, potential new feature InPrivate Desktop could give security teams access to disposable sandboxes.

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This page was last edited on 2 September , at Or something like that. Test your vocabulary with our question quiz!

Examples of cryptology in a Sentence Recent Examples on the Web Others areas include automobiles, cryptology , healthcare, lockpicking and wireless networks.

The Honor Flight gave me the chance," 30 Apr. First Known Use of cryptology , in the meaning defined above. Learn More about cryptology.

Resources for cryptology Time Traveler! Explore the year a word first appeared. From the Editors at Merriam-Webster. Dictionary Entries near cryptology cryptohalite Cryptolaemus cryptolite cryptology cryptomedusoid cryptomelane cryptomere.

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