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All classic systems are s y m m e t r i c ciphers, meaning that the same key is used to encrypt as to decrypt In so-called public k e y cryptography the encryption and decryption keys are different, which means that the encryption key can be be made public, but the decryption key must remain private We cover public key cryptosystems in s 6 and 7, while all of the remaining chapters--including the remaining sections of this chapter~---deal with symmetric ciphers Note that decryption is distinct from cryptanalysis, since cryptanalysis implies an attack of some sort has been used to read the messages, while decryption implies that the plaintext has been retrieved using the key by the expectcd process Of course, if Trudy recovers the key via cryptanalysis, then she can simply decrypt a particular ciphertext The typical encryption and decryption process is illustrated in Figure 1.

7-3.1 Method of Moments 229 7-3.2 Method of Maximum Likelihood 230 7-3.3 Bayesian Estimation of Parameters (CD Only) 237

5-3.1 Joint Probability Distributions 157 5-3.2 Marginal Probability Distributions 159 5-3.3 Conditional Probability Distributions 162 5-3.4 Independence 164

7-4 7-5

1, where Pi is the ith unit of plaintext (which may be a bit, a letter, a word, or a larger block, depending on the particular cipher), Ci is the corresponding unit of ciphertext, and the squiggly line represenh the transmission of the ciphertext over an insecure channel There are several generic types of attacks on ciphers In a ciphertext only attack, the attacker attempts to recover the key or plaintext from the ciphertext In particular, in a ciphertext-only attack, the cryptanalyst does.

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Multiple Continuous Random Variables 167 5-5 Covariance and Correlation 171 5-6 Bivariate Normal Distribution 177 5-7 Linear Combinations of Random Variables 180 5-8 Functions of Random Variables (CD Only) 185 5-9 Moment Generating Functions (CD Only) 185 5-10 Chebyshev s Inequality (CD Only) 185

8-1 8-2 Introduction 248 Con dence Interval on the Mean of a Normal Distribution, Variance Known 249

I 1 1917, Gilbert Vernam and Joseph Mauborgne invented a cipher system 1 which would eventually become known as the one-time pad. When correctly used, this system is invulnerable to a ciphertext only attack. This is the only real-world cipher that is provably secure. Suppose Alice wants to send a message to Bob and she wants to encrypt her message using a one-time pad. Alice first converts her plaintext message P into binary. She then generates a random binary key K of the same length as P . Encryption is accomplished by adding K to P , bit by bit, modulo 2, to obtain the ciphertext C. That is, C = P @ K , where @ is XOR. To recover the plaintext P from the ciphertext C, Bob, knowing the key K , computes C @ K = ( P @ K ) @ K = P . For example, suppose P = 01001100 and K = 11010110. Then

8-2.1 Development of the Con dence Interval and Its Basic Properties 249 8-2.2 Choice of Sample Size 252 8-2.3 One-sided Con dence Bounds 253 8-2.4 General method to Derive a Con dence Interval 253 8-2.5 A Large-Sample Con dence Interval for 254 8-2.6 Bootstrap Con dence Intervals (CD Only) 256

6-1 6-2 6-3 6-4

Data Summary and Display 190 Random Sampling 195 Stem-and-Leaf Diagrams 197 Frequency Distributions and Histograms 203 6-5 Box Plots 207 6-6 Time Sequence Plots 209 6-7 Probability Plots 212 6-8 More About Probability Plotting (CD Only) 216

The one-time pad is immune to a ciphertext only attack, since the ciphertext yields no information about the plaintext, other than its length. To see why this is true, consider the eight-letter alphabet in Table 1.8, with the given binary encodings.

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8-3.1 The t Distribution 258 8-3.2 Development of the t Distribution (CD Only) 259 8-3.3 The t Con dence Interval on 259

8-5 8-6 8-7

A 001

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