Introduction to Modern Cryptography: Principles and Protocols (Chapman & Hall/CRC Cryptography and Network Security Series)

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ICS 201: Cryptography and Communication Security 10/19/2007 Solutions to homework 1 Problem 2.2 If encryption is secure then by Definition 2.1 this condition implies that Pr [ M = m ] = Pr [ M = m ] for all m, m in the message space, which is obviously not true if M is sampled from any distribution over the message space. Problem 2.3 After throwing out the key k = 0 l the OTP encryption is no longer perfectly secure because then the key-space has one fewer element than the message space. A good example is that for any c ∈ { 0 , 1 } l the message m = c is impossible, because O l negationslash∈ K . But any other message is possible, which violates for example the condition in lemma 2.3, which says that encryption is perfectly secure only if for all c, m 0 , m 1 the probability that m 0 encrypts to c (over keys) is the same as the probability that m 1 encrypts to c (over keys). Problem 2.4(b) Since the substitution cipher has key-space K of size 26!, it can provide perfect secrecy only if the message space M has at most 26! elements too. Let M
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern