Tài liệu Thuật toán Algorithms (Phần 32) pdf

303 Exercises 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Decrypt the following message, which was encrypted with a Vigenere cipher using the pattern CAB (repeated as necessary) for the key (on a 27-letter alphabet, with blank preceding A): DOBHBUAASXFZWJQQ What table should be used to decrypt messages that have been encrypted using the table substitution method? Suppose that a Vigenere cipher with a two-character key is used to encrypt a relatively long message. Write a program to infer the key, based on the assumption that the frequency of occurrence of each character in odd positions should be roughly equal to the frequency of occurrence of each character in the even positions. Write matching encryption and decryption procedures which use the “exclusive or” operation between a binary version of the message with a binary stream from one of the linear congruential random number generators of Chapter 3. Write a program to “break” the method given in the previous exercise, assuming that the first 10 characters of the message are known to be blanks. Could one encrypt plaintext by “and”ing it (bit by bit) with the key? Explain why or why not. True or false: Public-key cryptography makes it convenient to send the same message to several different users. Discuss your answer. What is P(S(M)) for the RSA method for public-key cryptography? RSA encoding might involve computing Mn, where M might be a k digit number, represented in an array of k integers, say. About how many operations would be required for this computation? Implement encryption/decryption procedures for the RSA method (as- sume that s, p and N are all given and represented in arrays of integers of size 25). 304 SOURCES for String Processing The best references for further information on many of the algorithms in this section are the original sources. Knuth, Morris, and Pratt’s 1977 paper and Boyer and Moore’s 1977 paper form the basis for much of the material from Chapter 19. The 1968 paper by Thompson is the basis for the regular- expression pattern matcher of Chapters 20-21. Huffman’s 1952 paper, though it predates many of the algorithmic considerations here, still makes interesting reading. Rivest, Shamir, and Adleman describe fully the implementation and applications of their public-key cryptosystem in their 1978 paper. The book by Standish is a good general reference for many of the topics covered in these chapters, especially Chapters 19, 22, and 23. Parsing and compiling are viewed by many to be the heart of computer science, and there are a large number of standard references available, for example the book by Aho and Ullman. An extensive amount of background information on cryptography may be found in the book by Kahn. A. V. Aho and J. D. Ullman, Principles of Compiler Design, Addison-Wesley, Reading, MA, 1977. R. S. Boyer and J. S. Moore, “A fast string searching algorithm,” Communica- tions of the ACM, 20, 10 (October, 1977). D. A. Huffman, “A method for the construction of minimum-redundancy codes,” Proceedings of the IRE, 40 (1952). D. Kahn, The Codebreakers, Macmillan, New York, 1967. D. E. Knuth, J. H. Morris, and V. R. Pratt, “Fast pattern matching in strings,” SIAM Journal on Computing, 6, 2 (June, 1977). R. L. Rivest, A. Shamir and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Communications of the ACM, 21, 2 (February, 1978). T. A. Standish, Data Structure Techniques, Addison-Wesley, Reading, MA, 1980. K. Thompson, “Regular expression search algorithm,” Communications of the ACM, 11, 6 (June, 1968). GEOMETRIC ALGORITHMS . applications and give rise to an interesting set of problems and algorithms. Geometric algorithms are important in design and analysis systems for physical. mathematicians has useful application in the development of algorithms for modern computers. The field of geometric algorithms is interesting to study because there