Introduction to Cryptography Practice Questions for Quiz 1 Page 1 ... [PDF]

Sep 20, 2017 - Introduction to Cryptography. Practice Questions for Quiz 1. Problem 1 (9 points) For each term below, gi

22 downloads 32 Views 105KB Size

Recommend Stories


Practice Quiz #1 sol
Pretending to not be afraid is as good as actually not being afraid. David Letterman

1 | Page 1. Introduction
The best time to plant a tree was 20 years ago. The second best time is now. Chinese Proverb

Quiz 1 Sample Questions IE406
And you? When will you begin that long journey into yourself? Rumi

Introduction to Cloud Computing-101 Quiz 1
You often feel tired, not because you've done too much, but because you've done too little of what sparks

Page 1 (1.PDF)
The greatest of richness is the richness of the soul. Prophet Muhammad (Peace be upon him)

Introduction to Quantum Cryptography
Seek knowledge from cradle to the grave. Prophet Muhammad (Peace be upon him)

Introduction to Cryptography
We must be willing to let go of the life we have planned, so as to have the life that is waiting for

PdF Introduction to Modern Cryptography, Second Edition
Ask yourself: What do I need to change about myself? Next

Project Management Professional Practice Quiz 1 - GoCertify [PDF]
Project Management Professional Practice Quiz 1. This practice quiz contains 20 questions, provided by Whizlabs Software. Which of the following is a tool used to secure expert ... A. Drop the alternative approach. B. Work out a mitigation plan. C. P

Cryptography: CEO Questions for CTOs
The greatest of richness is the richness of the soul. Prophet Muhammad (Peace be upon him)

Idea Transcript


Introduction to Cryptography

Practice Questions for Quiz 1

Problem 1 (9 points) For each term below, give (i) a brief definition and (ii) a small example. (a) chosen plaintext attack (b) greatest common divisor (c) Euler’s ϕ function Problem 2 (6 points) ∗ . Evaluate the following to obtain a element of Z11 (a) (7 × 6) mod 11 (b) (7−1 × 6) mod 11 (c) (1043210 ) mod 11 Problem 3 (5 points) Notice that the bottom row of the ×11 table is the reverse of the top. Use a bit of algebra to prove: For each n ≥ 2, the bottom row of the ×n table is the reverse of the top row (i.e., that the bottom row’s i-th entry is n − i).

Math Facts Fermat’s Little Lemma (FLL). If p is prime & gcd( a, p) = 1, then a p−1 ≡ 1 (mod p). Euler’s Theorem. If n > 1 & gcd( a, n) = 1, then a ϕ(n) ≡ 1 (mod n). ∗ The multiplication table for Z11

×11 1 2 3 4 5 6 7 8 9 10

Page 1

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 1 3 5 7 9

3 3 6 9 1 4 7 10 2 5 8

4 4 8 1 5 9 2 6 10 3 7

5 5 10 4 9 3 8 2 7 1 6

6 6 1 7 2 8 3 9 4 10 5

7 7 3 10 6 2 9 5 1 8 4

8 8 5 2 10 7 4 1 9 6 3

9 9 7 5 3 1 10 8 6 4 2

10 10 9 8 7 6 5 4 3 2 1

September 20, 2017

Introduction to Cryptography

Practice Questions for Quiz 1

Answers for Problem 1 (a) Def: The attacker chooses what plaintext is to be encrypted. Ex: Suppose the cipher used a a cyclic shift. If the attacker chooses ”a” as the plaintext, he can read of the shift from the ciphertext. (b) Def: gcd( a, b) = the largest natural number dividing both a and b. Ex: gcd(20, 35) = 5. (c) Def: ϕ(n) = Card({ k ∈ Zn | gcd(k, n) = 1 }). Ex: ϕ(5) = 4. Answers for Problem 2 (a) By the ×11 table, 7 ×13 6 = 9. (b) By the ×11 table, 7 ×11 8 = 1.

So: 7−1 ×11 6 = 8 ×13 6 = 4.

∗ . (c) By FLL, k10 (mod 11) ≡ 1 for all k ∈ Z11

So:

1043210 ≡ 104321·10 ≡ (1010 )4321 ≡ (1)4321 ≡ 1 (mod 11). Answer for Problem 3 The number in the i-column of the bottom row is (n − 1) · i (mod n). So:

( n − 1) · i = n · i − i ∼ = −i (mod n) ∼ = n − i (mod n).

Page 2

September 20, 2017

Smile Life

When life gives you a hundred reasons to cry, show life that you have a thousand reasons to smile

Get in touch

© Copyright 2015 - 2024 PDFFOX.COM - All rights reserved.