1. (10 points) What is the number of possible keys of the following cryptosystems: A. Shift cipher over 26 letter alphabet 26 B. Ane cipher over 26 letter alphabet 26 12 C. Substitution cipher over 26 letter alphabet 26! D. One time pad for sending an n b

1. (10 points) What is the number of possible keys of the following cryptosystems: A. Shift cipher over 26 letter alphabet 26 B. Ane cipher over 26 letter alphabet 26 12 C. Substitution cipher over 26 letter alphabet 26! D. Permutation cipher with block l

CS346 Cryptography, Fall 2010
Homework 1 SOLUTIONS
1. (5 points) You are told that the plaintext proof yields the ciphertext QUPRG, and you know the cipher used is one of Substitution, Vigen`re, or Permutation. Which e type of cipher was used, and what is

CS346 Cryptography, Fall 2009
Homework 5, SOLUTIONS
1. (10 points) Problem 6, Chapter 4.9 (page 147) Solution: The meet-in-the middle attack is a known plaintext attack, so we can assume that Oscar (the attacker) has access to a plaintext-ciphertext pair

CS346 Cryptography, Fall 2009
Homework 4, SOLUTIONS
1. (5 points) Problem 4 (Chapter 8.8) Solution: In this case, the number of possible values of the hash function is 12. Using the formula we have seen in class, the probability that no two have birthdays

CS346 Cryptography, Fall 2009
Homework 3, SOLUTIONS
1. (8 points) Suppose that for using RSA, Bob has chosen a large public modulus n for which the factorization cannot be found in a reasonable amount of time. Suppose Alice sends a message to Bob represen

CS346 Cryptography, Fall 2009
Homework 2, SOLUTIONS
1. (5 points) Give an algorithm that on input integers x and m computes x37 mod m. As a primitive step you may assume an algorithm for modular multiplication: on input y and z it computes (y z ) mod m. Y

CS346 Cryptography, Fall 2009
Homework 1, SOLUTIONS
1. (5 points) Problem 1 (Chapter 2.13) Solution: Antony knows that Caesar used a shift cipher, but he does not know the key. He will not be able to gure out where to meet Caesar. When he tries to decrypt

CS 346 Cryptography
FALL 2010
Background Quiz
SOLUTIONS
1. What is the numeric value of log2 (850 )? log2 (850 ) = 50 log2 8 = 50 log2 23 = 50 3 = 150. 2. Give a big-O estimate for each of the following functions: A. 2n3 + n2 log n = O(n3 ) B. (n2 + 8)(n

CS 346 Cryptography
FALL 2009
Background Quiz - Solutions
1. What is the numeric value of log2 (850 )? 150 2. Give a big-O estimate for each of the following functions: A. 2n3 + n2 log n = O(n3 ) B. (n2 + 8)(n + 1) = O(n3 ) C. n! + 2n = O(n!) 3. An intege

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CS346 Cryptography, Fall 2009
Homework 4, Due November 5
1. (5 points) Problem 4 (Chapter 8.8) 2. (10 points) Problem 10 (Chapter 8.8) 3. (10 points) Using the Die-Lamport signature scheme (see class notes) with encryption e(x, K ) = xK mod n , Alice choo

CS346 Cryptography, Fall 2009
Homework 3, Due October 1
1. (8 points) Suppose that for using RSA, Bob has chosen a large public modulus n for which the factorization cannot be found in a reasonable amount of time. Suppose Alice sends a message to Bob repr

CS346 Cryptography, Fall 2010
Homework 3, Due October 12
1. (10 points) Problem 17 (Chapter 6.8) 2. (10 points) Problem 27 (Chapter 6.8) 3. (10 points) Suppose that Oscar intercepts a message encoded with the RSA encryption, but he does not know the priva

CS346 Cryptography, Fall 2010
Homework 2, Due September 30
1. (10 points) As a reminder, here is a description of the Euclidean algorithm: To compute the greatest common divisor of two positive integers r0 and r1 , where r0 > r1 , the algorithm produces t

CS346 Cryptography, Fall 2009
EXTRA CREDIT LAST CHANCE TO SUBMIT: DECEMBER 1, IN CLASS
1. EXTRA CREDIT from HW1 (10 points) A recreational problem, called the Tower of Hanoi problem, was invented by the French mathematician Lucas in 1883. It is described