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COMP 170 L2 Page 1 Review for Midterm 2 Part II: Number Theory and Cryptography L06: RSA Part III: Logic L07, L08, L09 Part IV: Induction and Recurrence L10, L11, L12 Big-O, Asymptotic behaviors excluded from midterm 2
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COMP 170 L2 L06: Public-Key Cryptography
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COMP 170 L2 RSA Algorithm lKey generation lEncrypt/decrypt message
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COMP 170 L2 Theorems Page 4
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COMP 170 L2 Decipherability/Security
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COMP 170 L2 Repeated Squaring Page 6
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COMP 170 L2 The Chinese Remainder Theorem
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COMP 170 L2 Part III: Logic l Introduce the basics of logic (L07, L08) l Discuss the logic principles behind proofs (L09) Page 8
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COMP 170 L2 What make up logic statements? Page 9
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COMP 170 L2 Truth Table for Logic Statements l Shows whether a compound statement is true for false in all cases l Allow us to determine whether two statements are equivalent Page 10
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COMP 170 L2 Quantifiers Page 11
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COMP 170 L2 Quantifiers Page 12
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COMP 170 L2 Proving Quantified Statements True or False Page 13
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COMP 170 L2 Inference Rules l Rules for logic connectives Page 14
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COMP 170 L2 Inference Rules Page 15 l Modus Ponens l Rules for proving implication
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COMP 170 L2 Page 16
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COMP 170 L2 L10: Induction Page 17 l Base Case (n=b): Show that p(b) is True l Induction (n>b): Show p(n-1) => p(n) n Induction Hypothesis p(n-1) is True n Inductive Step: p(n) is True l Inductive conclusion: n p(n) is True for all n>=b
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COMP 170 L2 l Equivalent to Proof by smallest counter example n Can you rewrite proof in one form into proof in another form? Page 18 L10: Induction
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COMP 170 L2 L11/12: Recursion and Recurrence Page 19 l Towers of Hanoi: First order linear recurrence l D&C, Binary Search l Can you figure out recurrence for running time of simple recursive algorithms?
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COMP 170 L2 Closed-Form Solution: Iterating Recurrences l Pay attention to the red terms Page 20
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COMP 170 L2 Closed-Form Solution: Iterating Recurrences l Pay attention to the red terms
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COMP 170 L2 Asymptotic Behaviors Page 22
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COMP 170 L2 Asymptotic Behaviors Page 23
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