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Copyrighted Material CHAPTER1 APERITIFS “Yet it may be roundly asserted that human ingenuity cannot concoct a cipher that human ingenuity cannot resolve” — The Gold Bug (Edgar Allan Poe) “It Ain’t Necessarily So” — Song from Porgy and Bess (George and Ira Gershwin)1 “Skipper” the sailor said to his captain as he saluted, “A special message just came in for you from the admiral. I have it right here.” “Read it to me,” the captain ordered. The sailor began reading nervously, “You are without a doubt the most idiotic, lame-brained officer ever to command a ship in the United States Navy.” “Have that communication decoded at once!,” The skipper responded — Pastor Tim’s Clean Laugh List 1.1 THE LEXICON OF CRYPTOGRAPHY The word “cryptography” is derived from the Greek words kryptos, meaning hidden, and gra- phien, meaning to write. Historians believe Egyptian hieroglyphics, which began about 1900 B.C.E., to be an early instance of encipherment. The key that unlocked the hieroglyphic secrets was the Rosetta Stone, discovered in 1799 in lower Egypt and now located in the British Museum in London. Franc¸ois Champollion, using the Rosetta Stone, deciphered the hieroglyphics in 1822. The books by David Kahn [1967, 1983] and Simon Singh [1999] provide extensive accounts of cryptography and its influence on history. Every scientific discipline develops its own lexicon, and cryptography is no exception. We begin with a brief summary of the principal terms used in cryptography. An alphabet A¼{a0, a1, ..., amÀ1} is a finite set of letters; examples include 1. m ¼ 2r: (0,1)-sequences of fixed length r Zr,2 ¼ {x ¼ (x0, x1, ..., xrÀ1): xi ¼ 0, 1, 0 i , r}; 2. m ¼ 27:COPYRIGHTED the ASCII character alphabet; MATERIAL 3. m ¼ 26: the alphabet consisting of upper-case Latin letters: {A, B, ..., Z} Text is formed by concatenating letters of A;ann-gram (a0, a1; ... ; anÀ1) is the concatenation of n letters. We do not require that the text be understandable nor that it be grammatically correct relative to a natural language; thus Good_Morning and vUIÃ_9Uiing8 are both examples of ASCII text. Computer Security and Cryptography. By Alan G. Konheim Copyright # 2007 John Wiley & Sons, Inc. 1 2 CHAPTER 1 APERITIFS Figure 1.1 The encipherment transformation. Encipherment or encryption is a transformation process (Fig. 1.1), T enciphering the plaintext x ¼ (x0, x1, ..., xnÀ1) to the ciphertext y ¼ ( y0, y1, ..., ymÀ1Þ, where T: Good_Morning ! Kssh_Qsvrmrk is an example of encipherment introduced nearly 2000 years ago by Julius Caesar during the Gallic Wars in order to communicate with his friend and lawyer Marcus Tullius Cicero. It is not necessary that 1. The plaintext and ciphertext alphabets be identical; nor that 2. Encipherment leaves the number of letters unchanged. The only requirement on T is the obvious one; it must be possible to reverse the process of encipherment. Decipherment,ordecryption, is also a transformation, T21 (Fig. 1.2), which recovers the plaintext x from the ciphertext y. T21: Kssh_Qsvrmrk ! Good_Morning. Additional properties are sometimes imposed on T, for example, that encipherment does not change the number of letters. The three principal applications of cryptography are secrecy, authentication, and access control. Secrecy intends to deny information contained in text by disguising its form, for example, 1. In order to prevent an eavesdropper from learning the content of the communication when two users communicate over an open or insecure network; and 2. To hide information stored in a file system. When two parties communicate over an open or insecure network, each needs to be certain of the identity of the other. Webster’s dictionary defines authentication as “a process by which each party to a communication verifies the identity of the other.” The term IFF, for identification, friend or foe, was an authentication protocol introduced during World War II to protect U.S. airspace from intrusion by enemy aircraft. The identity of a plane entering U.S. airspace was authenticated using a challenge– response pair; the correct response is determined by a cryptographic function of the challenge. Access to files and other facilities in an information processing system is still another area in which cryptographic ideas have found application. In Chapter 18, we Figure 1.2 The decipherment transformation. 1.1 THE LEXICON OF CRYPTOGRAPHY 3 describe the authentication process when a customer engages in an ATM (automated teller machine) transaction. Authentication requires the customer to have 1. Possession of a valid ATM card; and 2. Knowledge of the corresponding personal identification number (PIN). A new class of security problems in the twentieth century arose from communication over public networks. The ubiquitous nature of computer networks has given rise to e-commerce, and in the process has enlarged the area in which cryptography is needed. Transactions over the Web have changed the scale and environment in which the problems of secrecy and authentication exist. As discussed in Chapter 18, the principal security issues are: 1. Privacy. Users may insist that their data transmitted on the Web be hidden from any parties who monitor communications and the contents of their records in a file system be hidden. 2. Authentication: User Identity. As users communicating data over a network are not in physical proximity – for example, do not see or talk to one another – both need to be confident of the identity of the other. 3. Authentication: Message Integrity. When users communicate over a network, each wants to be certain that not other party has maliciously modified the transmitted data. Although it is not possible to prevent transaction data from being altered a scheme must be implemented that will be likely to detect changes. A transaction between two users involves one or more exchanges of data. Each transmission of transaction data is suffixed by a message authentication code (MAC) or digital signature (SIG); the MAC/SIG authenticates both the (sender, receiver) pair and the content of the communication (Fig. 1.3). The MAC is a sequence of 0’s and 1’s functionally dependent on the transaction data and the identities of the corresponding parties. 1. If privacy is required, the concatenated Transaction Data and MAC must be enciphered. 2. The authenticity of participants in a transaction must be established. 3. To insure the integrity of the exchange of information, the MAC must depend on the transaction data in such a way that (a) MAC-1, a secret element is involved in the construction of the MAC; (b) MAC-2, no user can expect to construct a valid MAC for the transaction data without knowledge of the secret element; (c) MAC-3, any change in the transaction data will likely change the MAC. Web-based electronic transactions (Chapter 18) require a framework in which the purchaser and seller can be confident of the integrity of their transactions. We shall show that each of these different applications of cryptography involves the same principles. Figure 1.3 The message authentication MAC appended to transaction data. 4 CHAPTER 1 APERITIFS Figure 1.4 The software encipherment/decipherment processes. 1.2 CRYPTOGRAPHIC SYSTEMS When a pair of users encipher the data they exchange over a network, the cryptographic transformation they use must be specific to the users. A cryptographic system is a family T¼fTk: k [ K} of cryptographic transformations. A key k is an identifier specifying a transformation Tk in the family T . The key space K is the totality of all key values. In some way the sender and receiver agree on a particular k and encipher their data with the enciphering transformation Tk. Encipherment originally involved pen-and-pencil calculations. Mechanical devices were introduced to speed up encipherment in the eighteenth century, and they in turn were replaced by electromechanical devices a century later. Encipherment today is often implemented in software (Fig. 1.4); Tk is an algorithm whose input consists of plaintext x and key k and with ciphertext y as output. 1.3 CRYPTANALYSIS Will encipherment provide secrecy? Cryptography is a contest between two adversaries: . The designer of the system (algorithm, key space, protocol implementation), and . The opponent, who attempts to circumvent the effect of encipherment. x y ¼ T x Can an opponent recover all or part of the plaintext from the ciphertext k0( )and knowledge of the cryptographic system T but without the key k0. Cryptanalysis encompasses all of the techniques to recover the plaintext and/or key from the ciphertext. The ground rules of this contest were set forth in the nineteenth century by Kerckhoffs1 in his book “La Cryptographie militare.” Kerckhoffs formulated six attributes that a cryptographic system should enjoy in order for the designer to triumph in the struggle. K1. The System Should be, if not Theoretically Unbreakable, Unbreakable in Practice. The term unbreakable is colloquially used to mean that no technique exists to deter- mine the key k or plaintext x from the ciphertext y ¼ Tk(x). It is possible to design an unbreakable system, but it is impractical to use except in situations in which 1Jean-Guiullaume-Hubert-Victor-Francois-Alexandre-Auguste-Kerckhoffs von Niuewenof, born in 1835 in Nuth (Netherlands), was a professor of German in Paris. The Kerckhoffs must have had spectacular towels! 1.3 CRYPTANALYSIS 5 only a modest amount of traffic is exchanged and an alternative secure path for exchanging the key is available. More relevant is the amount of computational effort – measured by time and memory – needed to produce k and/or x. Claude Shannon’s paper [Shannon, 1949] developed a theory of secrecy systems and defined the work function, a quantitative measure (computational time/memory) of the strength of encipherment. The larger the work function, the more secrecy that results from encipherment.
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