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Test 1 Question Paper - Cryptography | MATH 4176, Exams of Cryptography and System Security

Virginia Polytechnic Institute and State University (Virginia Tech)Cryptography and System Security

Material Type: Exam; Class: Cryptography; Subject: Mathematics; University: Virginia Polytechnic Institute And State University; Term: Fall 2015;

Typology: Exams

2015/2016

Uploaded on 02/23/2016

xevious024
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S15 MATH 4176 – Test 1 27 Feb 2015 NAME:
Answer all questions, and justify all answers completely. No credit will b e given for unsupported answers.
Each numbered question is worth 10 points.
1. Suppose Bob sets up a highly secure instance of RSA with public modulus n= 33.
(a) What is the set of numbers that are permissible to use as encryption exponents given the above n?
(b) If the encryption exponent bis 7, what is the decryption exponent a?
pf3
pf4
pf5

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S15 MATH 4176 – Test 1 27 Feb 2015 NAME:

Answer all questions, and justify all answers completely. No credit will be given for unsupported answers. Each numbered question is worth 10 points.

  1. Suppose Bob sets up a highly secure instance of RSA with public modulus n = 33.

(a) What is the set of numbers that are permissible to use as encryption exponents given the above n?

(b) If the encryption exponent b is 7, what is the decryption exponent a?

  1. Given integer x, show the steps in computing x^45 using the Square-and-Multiply algorithm. Give the power of x that is computed in each step, and state the total number of multiplication operations necessary. (Squaring a number counts as a multiplication operation.)
  1. (a) Define what it means for a to be a primitive element (or, equivalently, primitive root) of Z∗ n.

(b) Does Z∗ 5 have any primitive elements? If so, what are they?

  1. (a) Compute the Jacobi symbol

using the method of reductions as presented in class. (I.e., do it without factoring 51).

(b) In light of your answer to part (a), give a condition that would have to be satisfied in order for the Solovay-Strassen algorithm to output ‘Composite’, given input n = 51 and randomization a = 22