Domain 8
Cryptography

Although cryptography is an ancient art, it had not been universally implemented in most computer systems until now. Outside of government classified systems the primary users of encryption have been financial institutions with their electronic fund transfer operations.

The advent of the Internet as a cheap vehicle for transferring information electronically to all parts of the world and its inherent lack of security has inspired the use of encryption as a protection for sensitive information. As a direct result, new and rather esoteric encryption technology has been developed and installed to meet the challenges now being recognized.

One result of the growing economic use of the Internet is the recognition by users and vendors alike that there is a need to provide a mechanism to protect the confidentiality of Internet users and the content of their transactions. One mechanism that can provide such confidentiality, when selected and used intelligently, is encryption.

Domain 8’s focus is on “Cryptography.” Chapter 8-1-1, “Cryptography and Escrowed Encryption,” gives an overview of the basic concepts of cryptography, including single-key cryptography, public-key cryptography, key negotiation, message authentication, and digital signatures. Much of this is a whole new arena for information security practitioners but demands special attention because of the dire consequences of not employing this important tool when circumstances dictate.

Section 8-1
Cryptography Applications and Uses

Chapter 8-1-1
Cryptography and Escrowed Encryption

Dorothy E. Denning

This chapter provides an overview of the basic concepts of cryptography, including single-key cryptography, public-key cryptography, key negotiation, authentication, and digital signatures. Particular attention is given to the new escrowed encryption chip (originally called Clipper) that is designed to provide secure communications through strong encryption while preserving law enforcement’s ability to lawfully intercept communications through a key escrow arrangement.

CRYPTOSYSTEMS

Cryptography is the art and science of transforming (i.e., encrypting) information under secret keys for the purpose of secrecy or authenticity. A cryptographic system, or cryptosystem, consists of encrypt and decrypt transformations together with a set of keys that parameterize the transformations. The encrypt function scrambles data into what appears as gibberish; the decrypt function restores the original data. The original data is referred to as plaintext or cleartext, and the scrambled data is ciphertext. Because the keys are not hard-wired into the functions, the same functions can be used with different keys. The decrypt key must be kept secret to prevent an eavesdropper from decrypting intercepted ciphertext; the transformations themselves may be public (see Exhibit 1).

Exhibit 1.  A Cryptosystem

The strength of a cryptosystem refers to its ability to withstand attack by someone who intercepts ciphertext. A system is breakable if it is possible to systematically determine the secret key or plaintext of an intercepted ciphertext message. The process of attempting to break a cryptosystem is called cryptanalysis.

A system’s strength depends on the number of its possible keys and its underlying mathematics. If the key length, which is typically expressed as a number of bits, is too short, a system may be broken by an exhaustive search, that is, by systematically trying all possible keys until one is found that produces known or meaningful plaintext. For example, if the key length is 32 bits, there are about 4 billion possibilities. Assuming that 1 million keys can be checked per second, all 4 billion could be checked in about an hour. Even if the key length is long enough that an attack by exhaustive search is infeasible, a cryptosystem may be vulnerable to a shortcut solution that exploits the system’s underlying mathematics or some trapdoor. Examples of shortcut methods are factoring and differential cryptanalysis.

With one exception, all cryptosystems are at least theoretically breakable by exhaustive search, given sufficient resources. The exception is the one-time pad, which uses a random key as long as the message and never uses the same key more than once. In digital systems, the key and message are both streams of bits (each text character is 8 bits), and each key bit is XORed (exclusive-or’ed) with the corresponding message bit to produce a ciphertext bit. The XOR operation yields 0 if both bits are the same (i.e., 00 or 11) and 1 if they are different (i.e., 01 or 10) as illustrated by the following encryption of a message beginning with the letter H:

Decryption is identical except that the key bits are XORed with the ciphertext bits. The second XOR with key stream restores the original message stream because the XOR operation implements addition modulo 2, that is, for each message bit m and key bit k:

(m (+) k) (+) k = ((m + k) (+) k)mod2 = (m + 2k)mod2 = m

where:

(+) denotes XOR. (In modular arithmetic, all numbers are in the range from 0 through p – 1 where p is the modulus. When a combination yields a result in excess of p – 1, the result is divided by p and replaced by the remainder.) Logical AND and OR do not have this property and therefore cannot be used for encryption.

The one-time pad is unbreakable because it is impossible to deduce any information about the key or plaintext from an intercepted ciphertext. The one-time pad and systems that stimulate it are called stream ciphers.

Although theoretically breakable, many systems are computationally strong or practically unbreakable in the sense that the resources required to break them are unavailable or prohibitively expensive. In practice, a system need only be strong enough to provide security commensurate with the risk and consequences of breakage. Increasing security usually increases costs and decreases performance; it does not make sense to pay more for encryption than the expected loss resulting from breakage.