9. | Learn Encryption Techniques with BASIC and C++

Learn Encryption Techniques with BASIC and C++
(Publisher: Wordware Publishing, Inc.)
Author(s): Gil Held
ISBN: 1556225989
Publication Date: 10/01/98

Table of Contents

Table 1.5 contains the key space obtained by the use of digits, letters, and alphanumeric characters for keys varying in length from 1 to 20 positions. The field width column indicates the number of characters in a key. You should note that the discussion of key space will be limited to the use of all uppercase or all lowercase letters when alphabetic or alphanumeric keys are used unless otherwise noted. Although the use of both uppercase and lowercase letters significantly increases the key space, it also increases the potential for confusion. That is, it becomes quite easy to remember a word or phrase but to forget which letters are uppercase and which letters are lowercase. For that reason we will normally restrict the use of keys in this book to letters of a single case. That is, if our key is limited to eight positions and we wish to use the word “computer,” we would enter the key as “COMPUTER” or “computer,” but not as “Computer,” unless we develop a program which is case insensitive and converts all characters to one case.

**Table 1.5** Key space based on characters used and field width.

Field Width	Digit Combinations	Letter Combinations	Alphanumeric Combinations

1	1.00000E+01	2.60000E+01	3.60000E+01
2	1.00000E+02	6.76000E+02	1.29600E+03
3	1.00000E+03	1.75760E+04	4.66560E+04
4	1.00000E+04	4.56976E+05	1.67962E+06
5	1.00000E+05	1.18814E+07	6.04662E+02
6	1.00000E+06	3.08916E+08	2.17678E+09
7	1.00000E+07	8.03181E+09	7.83642E+10
8	1.00000E+08	2.08827E+11	2.82111E+12
9	1.00000E+09	5.42950E+12	1.01560E+14
10	1.00000E+10	1.41167E+14	3.65616E+15
11	1.00000E+11	3.67034E+15	1.31622E+17
12	1.00000E+12	6.54290E+16	4.73838E+18
13	1.00000E+13	2.48115E+18	1.70582E+20
14	1.00000E+14	6.45100E+19	6.14094E+21
15	1.00000E+15	1.67726E+21	2.21074E+23
16	1.00000E+16	4.36087E+22	7.95866E+24
17	1.00000E+17	1.13383E+24	2.86512E+26
18	1.00000E+18	2.94795E+25	1.03144E+28
19	1.00000E+19	7.66467E+26	3.71319E+29
20	1.00000E+20	1.99281E+28	1.33675E+31

In examining the entries in Table 1.5, you should note that E+6 represents one million, while E+9 represents one billion. Thus, a six-character alphanumeric field produces 2.17 billion combinations even when we restrict our alphabet to all uppercase or all lowercase letters! Readers should also note that a nine-character field would be required to obtain just one billion key combinations if the key was restricted to digits. Thus, we can maintain a large key space with a lesser number of key characters or increase our key space by using alphanumeric characters instead of restricting our key to digits or letters.

Types of Encryption Systems

There are two types of encryption systems—private and public key based. The previously described method of encipherment and decipherment based upon the use of the same key for encryption and decryption is referred to as a private key based encryption system. That is, the key must remain private and cannot be disclosed to the person or persons who are intended recipients of an encrypted message. Otherwise the key is said to be compromised, meaning that any message encrypted using the key is potentially compromised. Another term commonly used to reference a private key based encryption system is a “symmetric” key system. Here, the term symmetric is used to reference the fact that the same key is used at both ends of the process.

One of the major problems associated with the use of a private key based encryption system is key generation and key distribution. For example, if you only need to send an encrypted message between two persons using a private key system, a single key used by each person becomes sufficient. If three people need to send encrypted messages to each other you could use one common key; however, if that key is compromised, then any messages transmitted between any of the three persons could become compromised. Thus, many organizations using a public key based encryption system commonly elect to use different keys for encryption between different persons. This means that the use of a public key based encryption system linking three persons or corporate offices would require three keys, while a system linking four persons or offices would require four keys.

This also means that for n users or organizational locations the number of unique keys required becomes 2ⁿ-2. While this may not be a problem for a small number of users or organizational locations, as those numbers increase they can reach a point where the administration process to include key generation and distribution becomes unmanageable. This is particularly true when you consider the use of modern electronic mail systems where employees may have to communicate with hundreds or thousands of persons. In this type of situation a private key based encryption system obviously becomes unsuitable. Similarly, it would be virtually impossible to use a private key based encryption system to secure electronic commerce from browsers to World Wide Web servers. Fortunately, the efforts of mathematicians resulted in the development of another type of encryption which significantly alleviates the previously described key generation and distribution problems associated with private key based encryption systems. This type of encryption is referred to as a public key based encryption system.

Public key based encryption dates to the late 1970s when mathematicians discovered certain mathematical relationships that resulted in a key used to encrypt a message being unable to perform decryption while another key in a matched pair of keys could be used for decryption. The mathematical relationship requires the use of two keys, one which remains private while the second can be provided to anybody, and can even be posted on a person’s home page on the Web. That key is referred to as a public key.

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