{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CS283 Lecture 3 - Part 1 - Public Key Cryptography - 20090922

# CS283 Lecture 3 - Part 1 - Public Key Cryptography - 20090922

This preview shows pages 1–11. Sign up to view the full content.

GWU CS 172/283 Autumn 2009 Public Key Cryptography GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922

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

View Full Document
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922 2 Lecture Topics - Polynomial Time - Diffie-Hellman Key Exchange - Discrete Log Problem - Public Key Cryptography - Rivest Shamir Adelman (RSA) Algorithm - Identity Based Encryption - Cryptographic Hash
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922 3 Mathematics Break – Polynomial Time (from Wikipedia) polynomial time refers to the running time of an algorithm , that is, the number of computation steps a computer or an abstract machine requires to evaluate the algorithm. An algorithm is said to be polynomial time if its running time is upper bounded by a polynomial in the size of the input for the algorithm. A Formal definition More formally, let T(n) be the running time of the algorithm on inputs of size at most n . Then the algorithm is polynomial time if there exists a polynomial p(n) such that, for all input sizes n , the running time T(n) is no larger than p(n)

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

View Full Document
Diffie-Hellman Key Exchange GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922 4
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922 5 Diffie-Hellman Key Exchange Published in 1976 A Protocol for exchanging a secret key over a public channel. Select global parameters p , n and α . p is prime and α is of order n in Z p * . These parameters are public and known to all.

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

View Full Document
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922 6 Diffie-Hellman Key Exchange contd. Alice privately selects random b (secret) and sends to Bob α b mod p. Bob privately selects random c (secret) and sends to Alice α c mod p. Alice and Bob privately compute α bc mod p which is their shared secret . An observer Oscar can compute α bc if he knows either c or b or can solve the discrete log problem. This is a key agreement protocol .
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922 7 The cryptographic Strength of Diffie-Hellman is based on the difficulty of solving the Discrete Logarithm problem Given a multiplicative group G, an element γ G such that o( γ ) = n, and an element α < γ > Find the unique integer x, 0 x n-1 such that α = γ x x denoted as log γ α Not known to be solvable in polynomial time , however exponentiation is.

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

View Full Document
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922 8 Man in the Middle attack on Diffie- Hellman Diffie-Hellman key exchange is susceptible to a man-in-the- middle attack. Mallory captures b and c in transmission and replaces with own b’ and c’. Essentially runs two Diffie-Hellman’s. One with Alice and one with Bob.
Public-Key Cryptography GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922 9

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

View Full Document
GWU CS 172/283 - Autumn 2009 Holmblad - Lecture 03 – Part 1- Rev 20090922 10 Whitfield Diffie and Martin Hellman proposed Public Key Cryptography Computationally easy to encrypt/decrypt given access to the relevant key Computationally infeasible to derive the private key from the public key
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern