Key-Based Encryption Algorithms - By: Rance Lucifinil

Key-Based Encryption Algorithms

One very important feature of a good encryption scheme is the ability to specify a 'key' or 'password' of some kind, and have the encryption method alter itself such that each 'key' or 'password' produces a different encrypted output, which requires a unique 'key' or 'password' to decrypt. This can either be a 'symmetrical' key (both encrypt and decrypt use the same key) or 'asymmetrical' (encrypt and decrypt keys are different). The popular 'PGP' public key encryption, and the 'RSA' encryption that it's based on, uses an 'asymmetrical' key. The encryption key, the 'public key', is significantly different from the decryption key, the 'private key', such that attempting to derive the private key from the public key involves many many hours of computing time, making it impractical at best.
There are few operations in mathematics that are truly 'irreversible'. In nearly all cases, if an operation is performed on 'a', resulting in 'b', you can perform an equivalent operation on 'b' to get 'a'. In some cases you may get the absolute value (such as a square root), or the operation may be undefined (such as dividing by zero). However, in the case of 'undefined' operations, it may be possible to base a key on an algorithm such that an operation like division by zero would PREVENT a public key from being translated into a private key. As such, only 'trial and error' would remain, which would require a significant amount of processing time to create the private key from the public key.
In the case of the RSA encryption algorithm, it uses very large prime numbers to generate the public key and the private key. Although it would be possible to factor out the public key to get the private key (a trivial matter once the 2 prime factors are known), the numbers are so large as to make it very impractical to do so. The encryption algorithm itself is ALSO very slow, which makes it impractical to use RSA to encrypt large data sets. What PGP does (and most other RSA-based encryption schemes do) is encrypt a symmetrical key using the public key, then the remainder of the data is encrypted with a faster algorithm using the symmetrical key. The symmetrical itself key is randomly generated, so that the only way to get it would be by using the private key to decrypt the RSA-encrypted symmetrical key.
Example: Suppose you want to encrypt data (let's say this web page) with a key of 12345. Using your public key, you RSA-encrypt the 12345, and put that at the front of the data stream (possibly followed by a marker or preceded by a data length to distinguish it from the rest of the data). THEN, you follow the 'encrypted key' data with the encrypted web page text, encrypted using your favorite method and the key '12345'. Upon receipt, the decrypt program looks for (and finds) the encrypted key, uses the 'private key' to decrypt it, and gets back the '12345'. It then locates the beginning of the encrypted data stream, and applies the key '12345' to decrypt the data. The result: a very well protected data stream that is reliably and efficiently encrypted, transmitted, and decrypted.
It is somewhat difficult to write a front-end to get this code to work (I have done so myself), but for the sake of illustration, the method actually DOES work and by studying the code you can understand the processes involved in RSA encryption. RSA, incidentally, is reportedly patented through the year 2000, and may be extended beyond that, so commercial use of RSA requires royalty payments to the patent holder. But studying the methods and experimenting with it is free, and with source code being published in print (PGP) and outside the U.S., it's a good way to learn how it works, and maybe to help you write a better algorithm yourself.
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