[ Home  |  FAQ-Related Q&As  |  General Q&As  |  Answered Questions ]

    Search the Q&A Archives

How do asymetrical cyphers work mathmatically speaking. Can...

<< Back to: Cryptography FAQ (01/10: Overview)

Question by Flunky
Submitted on 11/14/2003
Related FAQ: Cryptography FAQ (01/10: Overview)
Rating: Not yet rated Rate this question: Vote
How do asymetrical cyphers work mathmatically speaking.  Can someone please show me an example of an equation that has a public and private key.  I don't understand how it all works

Answer by Regie
Submitted on 12/16/2003
Rating:  Rate this answer: Vote
Mathematically, the public and private keys are simply two factors of a prime number.  The prime number should be rather large to be practical.

The “secrecy” is due only to the exponential nature of current factoring algorithms and the speed of currently architected computers. This is what keeps the private key “secret”, yet with the knowledge of the private keys, the public key can be computed in seconds.  Take the following examples:

1.  What is the number whose prime factors are 77237 and 3217?

2.  What are the prime factors of the number 77219?

In example 1, the answer can be arrived at quickly by simply multiplying the numbers. In example 2, we can derive a simple brute force algorithm that looks like this:

Start at the number 2, divide it into 77219, if there is a remainder, increment 2 to 3 and continue until the division has no remainder. This takes 36 steps for this example, and if implemented on a slow (human) computer, will take a number of minutes longer than the first example. The number of steps to compute the factor increases exponentially, based on the length of the number.  For a number 100 digits long, this becomes billions of years, even for a fast computer that can complete 10,000,000,000 divisions per second (see http://qubit.org/intros/cyptana.html).

It is this degree of difficulty, from a time perspective, that makes current public key cryptography “secure”.


Your answer will be published for anyone to see and rate.  Your answer will not be displayed immediately.  If you'd like to get expert points and benefit from positive ratings, please create a new account or login into an existing account below.

Your name or nickname:
If you'd like to create a new account or access your existing account, put in your password here:
Your answer:

FAQS.ORG reserves the right to edit your answer as to improve its clarity.  By submitting your answer you authorize FAQS.ORG to publish your answer on the WWW without any restrictions. You agree to hold harmless and indemnify FAQS.ORG against any claims, costs, or damages resulting from publishing your answer.


FAQS.ORG makes no guarantees as to the accuracy of the posts. Each post is the personal opinion of the poster. These posts are not intended to substitute for medical, tax, legal, investment, accounting, or other professional advice. FAQS.ORG does not endorse any opinion or any product or service mentioned mentioned in these posts.


<< Back to: Cryptography FAQ (01/10: Overview)

[ Home  |  FAQ-Related Q&As  |  General Q&As  |  Answered Questions ]

© 2008 FAQS.ORG. All rights reserved.