2 Questions 2.1 Q1 For this question, every encryption scheme satisfies complete correctness. Security is for a single message. 2.1.1 A Let h1, h2 be negligible functions (that are never equal to zero). Prove or disprove: 1. is negligible as well. 2. h h2 is negligible as well.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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2
Questions
2.1 Q1
For this question, every encryption scheme satisfies complete correctness.
Security is for a single message.
2.1.1
A
Let h1, h2 be negligible functions (that are never equal to zero). Prove or
disprove:
1. 1 is negligible as well.
2. h1 · h2 is negligible as well.
2.1.2 В
We will define a variation of OTP with a key length k = k||k2 where |k1| =
|k2| and M = C = {0,1}10, K = 0, 120. The encryption function :
Enc(k = k1||k2, m) = m k1 e k2
Complete the decryption algorithm. Prove that the scheme satisfies per-
fect correctness and perfect secrecy.
2.1.3
We will define a variation of OTP with M = {0, 1}10, C = {0, 1}1', K =
0,110 Where the encryption algorithm is defined as:
{ (me k, 1)
(т,0)
if k ¢ {0lº, 1º}
Enc(k, m)
otherwise
2
Complete the decryption algorithm. Specify for which e the scheme sat-
isfies e statistical security. Prove it is the correct e.
Transcribed Image Text:2 Questions 2.1 Q1 For this question, every encryption scheme satisfies complete correctness. Security is for a single message. 2.1.1 A Let h1, h2 be negligible functions (that are never equal to zero). Prove or disprove: 1. 1 is negligible as well. 2. h1 · h2 is negligible as well. 2.1.2 В We will define a variation of OTP with a key length k = k||k2 where |k1| = |k2| and M = C = {0,1}10, K = 0, 120. The encryption function : Enc(k = k1||k2, m) = m k1 e k2 Complete the decryption algorithm. Prove that the scheme satisfies per- fect correctness and perfect secrecy. 2.1.3 We will define a variation of OTP with M = {0, 1}10, C = {0, 1}1', K = 0,110 Where the encryption algorithm is defined as: { (me k, 1) (т,0) if k ¢ {0lº, 1º} Enc(k, m) otherwise 2 Complete the decryption algorithm. Specify for which e the scheme sat- isfies e statistical security. Prove it is the correct e.
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