Exam (elaborations) TEST BANK FOR An Introduction to Mathematical Cryptography 2nd Edition By Jeffrey Hoffstein, Jill Pipher, Joseph H. Silvermana (Solution Manual)-Converted

1.1. Build a cipher wheel as illustrated in Figure 1.1, but with an inner wheel that rotates, and use it to complete the following tasks. (For your convenience, there is a cipher wheel that you can print and cut out at . edu/~jhs/MathCrypto/CipherW.) (a) Encrypt the following plaintext using a rotation of 11 clockwise. A page of history is worth a volume of logic." (b) Decrypt the following message, which was encrypted with a rotation of 7 clockwise. AOLYLHYLUVZLJYLAZILAALYAOHUAOLZLJYLALZAOHALCLYFIVKFNBLZZLZ (c) Decrypt the following message, which was encrypted by rotating 1 clock- wise for the ¯rst letter, then 2 clockwise for the second letter, etc. XJHRFTNZHMZGAHIUETXZJNBWNUTRHEPOMDNBJMAUGORFAOIZOCC Solution to Exercise 1.1. (a) apageofhistoryisworthavolumeoflogic LALRPZQSTDEZCJTDHZCESLGZWFXPZQWZRTN This quote is in a court decision of Oliver Wendell Holmes, Jr. (1921). (b) therearenosecretsbetterthanthesecretsthateverybodyguesses AOLYLHYLUVZLJYLAZILAALYAOHUAOLZLJYLAZAOHALCLYFIVKFNBLZZLZ There are no secrets better than the secrets that everybody guesses. This quote is due to George Bernard Shaw, Mrs. Warren's Profession (1893) 1 2 Exercises for Chapter 1 (c) whenangrycounttenbeforeyouspeakifveryangryanhundred XJHRFTNZHMZGAHIUETXZJNBWNUTRHEPOMDNBJMAUGORFAOIZOCC When angry, count ten before you speak; if very angry, an hundred. This quote is due to Thomas Je®erson, A Decalogue of Canons. . . (1825). 1.2. Decrypt each of the following Caesar encryptions by trying the various possible shifts until you obtain readable text. (a) LWKLQNWKDWLVKDOOQHYHUVHHDELOOERDUGORYHOBDVDWUHH (b) UXENRBWXCUXENFQRLQJUCNABFQNWRCJUCNAJCRXWORWMB (c) BGUTBMBGZTFHNLXMKTIPBMAVAXXLXTEPTRLEXTOXKHHFYHKMAXFHNLX Solution to Exercise 1.2. (a) ithinkthatishallneverseeabillboardlovelyasatree LWKLQNWKDWLVKDOOQHYHUVHHDELOOERDUGORYHOBDVDWUHH I think that I shall never see, a billboard lovely as a tree. This quote is due to Ogden Nash, Many Long Years Ago (1945), Song of the Open Road. (b) loveisnotlovewhichalterswhenitalterationfinds UXENRBWXCUXENFQRLQJUCNABFQNWRCJUCNAJCRXWORWMB Love is not love which alters when it alteration ¯nds. This quote is due to William Shakespeare, Sonnet 116. (c) inbaitingamousetrapwithcheesealwaysleaveroomforthemouse BGUTBMBGZTFHNLXMKTIPBMAVAXXLXTEPTRLEXTOXKHHFYHKMAXFHNLX In baiting a mousetrap with cheese, always leave room for the mouse. This quote is due to H.H. Munro (Saki), The Square Egg (1924). 1.3. For this exercise, use the simple substitution table given in Table 1.11. (a) Encrypt the plaintext message The gold is hidden in the garden. (b) Make a decryption table, that is, make a table in which the ciphertext alphabet is in order from A to Z and the plaintext alphabet is mixed up. (c) Use your decryption table from (b) to decrypt the following message. IBXLX JVXIZ SLLDE VAQLL DEVAU QLB Solution to Exercise 1.3. (a) Exercises for Chapter 1 3 a b c d e f g h i j k l m n o p q r s t u v w x y z S C J A X U F B Q K T P R W E Z H V L I G Y D N M O Table 1.1: Simple substitution encryption table for exercise 1.3 t h e g o l d i s h i d d e n i n t h e g a r d e n I B X F E P A Q L B Q A A X W Q W I B X F S V A X W Breaking it into ¯ve letter blocks gives the ciphertext IBXFE PAQLB QAAXW QWIBX FSVAX W (b) d h b w o g u q t c j s y x z l i m a k f r n e v p A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (c) t h e s e c r e t p a s s w o r d i s s w o r d f i s h I B X L X J V X I Z S L L D E V A Q L L D E V A U Q L B Putting in word breaks gives the plaintext The secret password is swordfish. 1.4. Each of the following messages has been encrypted using a simple sub- stitution cipher. Decrypt them. For your convenience, we have given you a frequency table and a list of the most common bigrams that appear in the ciphertext. (If you do not want to recopy the ciphertexts by hand, they can be downloaded or printed from the web site listed in the preface.) (a) A Piratical Treasure" JNRZR BNIGI BJRGZ IZLQR OTDNJ GRIHT USDKR ZZWLG OIBTM NRGJN IJTZJ LZISJ NRSBL QVRSI ORIQT QDEKJ JNRQW GLOFN IJTZX QLFQL WBIMJ ITQXT HHTBL KUHQL JZKMM LZRNT OBIMI EURLW BLQZJ GKBJT QDIQS LWJNR OLGRI EZJGK ZRBGS MJLDG IMNZT OIHRK MOSOT QHIJL QBRJN IJJNT ZFIZL WIZTO MURZM RBTRZ ZKBNN LFRVR GIZFL KUHIM MRIGJ LJNRB GKHRT QJRUU RBJLW JNRZI TULGI EZLUK JRUST QZLUK EURFT JNLKJ JNRXR S The ciphertext contains 316 letters. Here is a frequency table: R J I L Z T N Q B G K