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Some Background and Fundamentals:

Cryptography is derived from the Greek word kruptos meaning hidden. The use of cryptography dates back to the early Egyptian civilization. Nearly 2000 years later the "Caesar Cipher" was used to protect military communications of the Roman Empire . If you're interested in a brief history of cryptography you can go off-site to review this excellent timeline for cryptographic development compiled by Carl M. Ellison from the book The Codebreakers by David Kahn and other sources.

Data encryption is conceptually straightforward: a message or item of data which we desire to keep private is transformed from its original or cleartext form to an encrypted or ciphertext form. Ciphertext data is secure from disclosure because the original data is disguised; this allows us to protect data even when we cannot control who has access to it.. This disguise is created by transforming the cleartext in accordance with a set of rules and mathematical operations called an algorithm (e.g. DES).

Many of the cryptographic algorithms in use today employ a "key". The key is simply a number (preferably a large one) used by the algorithm to transform plaintext to ciphertext, and vice versa. If the algorithm works as we'd like, every possible key value uniquely transforms the data; i.e. there is only one key in the set of all possible keys which will correctly recover the plaintext. While it is certainly possible to develop cryptographic algorithms which do not use a key, these are generally regarded as weaker than and inferior to those that do. These algorithms rely on the principle of "security through obscurity"; that is, the operations or algorithm used to transform the data is kept secret by the designer. To appreciate this important point consider that the Data Encryption Standard (DES) algorithm was published and released into the public domain in 1976, and has withstood 20 years of scrutiny without being "cracked". Contrast this record with the password protection offered in many of the popular desktop applications today...the cracker software page documents the failings of this approach to cryptography. A logical question to ask is, "What makes ciphertext secure?"; i.e. given that the details of the encryption algorithm are known (and typically they are for truly secure algorithms), what is to prevent an electronic eavesdropper from simply implementing the algorithm himself, and using it to decrypt the ciphertext? To answer this question requires that we examine the role of the key in cryptography. A cryptographic key is a numerical value provided as input to the algorithm which causes it to perform its transformations in a unique way. In other words given the same cleartext as input to an encryption algorithm, different key values will produce different ciphertext as output. We could compare the decryption process to navigating through a maze, and the key as a map of the maze; it’s easy to get through the maze with the map, but difficult without it. Knowledge of the key value used for encryption is required to (easily) decrypt the data. Without knowledge of the key value (assuming the algorithm has no defects or weaknesses) the eavesdropper is forced to resort to a brute force, trial and error approach to recover cleartext from ciphertext; he may have to try decrypting the ciphertext with all possible key values to be sure of recovering the original cleartext. Thus the cryptographic strength of an encryption algorithm is at least partly dependent on the size, or the number of possible values of the key. We will discuss the topic of key length in greater detail in the next section. The other determinant of cryptographic strength is the algorithm itself. A flawed algorithm is one which allows the encryption transformation to be reversed without knowledge of the key. Good cryptographic algorithms are strongly one-way transformations; they are one-way in the sense that it is easy (straightforward, at least) to transform cleartext to ciphertext, but difficult to reverse the process (without the key value). Achieving this one-way property is the Grail of cryptographic algorithm design. Unfortunately it is not currently possible to prove whether or not the Grail has been obtained; we have only the test of time as evidence. So, key size (or key length) and algorithmic "one-wayness" are the two factors which determine cryptographic strength or security. Let’s examine how each of these factors influence security: A brute force attack will always be successful given enough time and/or computational resources. Longer keys simply force your opponent to expend greater time, or devote more resources to his attack. However, unless all data is protected with a single key value the opponent must mount a brute force attack for each item of data; in other words the opponent must work just as hard to recover the second data item as he did the first. Algorithmic flaws pose a much more serious threat to security. Once an algorithmic flaw has been found, all data items are compromised; the key value is no longer necessary to reverse the encryption process, and no further work is required for the opponent to recover the cleartext from any data item protected by the flawed algorithm.

A Cryptographic Taxonomy:

While conceptually straightforward, cryptography sees widespread use today in a variety of specialized applications which employ various protocols and ancillary functions to meet their unique security requirements. Construction of a simple taxonomy of cryptographic algorithms will support a basic understanding of all cryptosystems, and which algorithms are appropriate for a specific problem.

• Secret Key (a.k.a. Symmetric Key) Cryptography: Same Key for Encryption and Decryption.

  Secret key or symmetric key cryptography utilizes a single key for both encryption and decryption. Recovery of plaintext data from the ciphertext is accomplished only with the same key value used to transform the plaintext to ciphertext.

  A fairly common misconception is that symmetric key cryptography has been rendered "obsolete" by the recent (1976) introduction of public key cryptography. In fact, due to some limitations (see next bullet) of public key cryptography, today's cryptosystems still depend exclusively on symmetric key cryptography for "bulk" data encryption (i.e. for any dataset larger than a few hundred bytes, encryption with a public key algorithm becomes impractical due to the amount of time required). Symmetric key algorithms may be further classified as either "block" ciphers, or "stream" ciphers; block ciphers operate on the data in blocks, whereas stream ciphers operate on the data one bit at a time. Secret key algorithms include: DES, IDEA, RC2 (block ciphers), and RC4 (a stream cipher).

  
  

• Public Key (aka Asymmetric Key) Cryptography: One key for encryption, another key for decryption.

  The public key label covers a large number of cryptographic algorithms having different capabilities. It is interesting to note that most of these algorithms are incapable of data encryption! Their principal applications are for digital signatures, secure exchange of secret keys, and authentication.

  The RSA algorithm (named for its inventors Rivest, Shamir and Adleman) is the best known, and probably synonomous with public key cryptography for many. We'll discuss it here as the representative of the entire class, and then briefly compare it to some other well-known public key algorithms. The RSA algorithm utilizes key pairs, each pair consisting of a public and private key component. RSA is one of the few public key algorithms capable of encryption; data encrypted with the public key can only be decrypted with the corresponding private key, and vice versa. This allows anyone with a copy of your public key component to use it to send you a secure, encrypted message; assuming your secret key is known only to you, then this message may be decrypted only by you. The private key component may also be used to form a "digital signature". A message is "signed" by encrypting it with the private key; the signature is verified by decrypting it with the public key. There is an important caveat to using RSA for data encryption: it is too slow to be of any practical use for encrypting any significant amounts of data. It is generally recognized that this sluggish performance (owing to the mathematics used by the algorithm) limits its utility to digital signatures, and the secure exchange of secret keys. These applications require encryption of very small quantities of data, on the order of a few hundred bits or less. This is why secret key algorithms remain essential components of cryptosystems which must provide data privacy. Many of today's cryptosystems are hybrid systems, employing both public and symmetric key algorithms. Other public key algorithms include DSS (Digital Signature Standard), and Diffie-Hellman. Compared to RSA, DSS provides only digital signatures (no encryption, no secure key exchange capability). Diffie-Hellman's utility is limited solely to secure key exchange; it will neither encrypt data, nor provide digital signatures.

  
  

• Hash Functions: Keys optional.

  Hash functions (a.k.a. one-way hash functions, data authentication codes, etc.) describe a large class of cryptographic algorithms with a common purpose: to produce a fixed-length "fingerprint" of the given input data. Unlike encryption algorithms hash functions return a fixed-length output value regardless of the size of the input; the length of the output being dependent on the particular function or algorithm being used.

  The principal application for hash functions is data authentication; for example a hash function could be employed to determine if an electronic document (word processor file, e-mail message, etc.) had been altered in any way. Security or "strength" of a hash function results from the "one-way" nature of the algorithm...it is easy to compute a hash value for a given input, but it is extremely difficult to derive an input which will produce a specified hash value. All other things being equal, algorithms which produce longer hash values exacerbate this difficulty. Hash functions may be further classified as keyed and non-keyed: non-keyed hash functions may be calculated by anyone, whereas keyed hash functions require the correct key value be supplied to reproduce a hash value. Common non-keyed hash functions inlude MD5, and the SHS; keyed hash functions include the DAC and RIPE-MAC.

The FAQs:

• Cryptography FAQ (01/10: Overview)
• Cryptography FAQ (02/10: Net Etiquette)
• Cryptography FAQ (03/10: Basic Cryptology)
• Cryptography FAQ (04/10: Mathematical Cryptology)
• Cryptography FAQ (05/10: Product Ciphers)
• Cryptography FAQ (06/10: Public Key Cryptography)
• Cryptography FAQ (07/10: Digital Signatures)
• Cryptography FAQ (08/10: Technical Miscellany)
• Cryptography FAQ (09/10: Other Miscellany)
• Cryptography FAQ (10/10: References)

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