Download presentation

Presentation is loading. Please wait.

Published byKatherine Hall Modified over 4 years ago

1
Diffie-Hellman Diffie-Hellman is a public key distribution scheme First public-key type scheme, proposed in 1976.

2
Diffie-Hellman Public-key distribution scheme Cannot be used to exchange an arbitrary message Exchange only a key, whose value depends on the participants (and their private and public key information) The algorithm is based on exponentiation in a finite field, either over integers modulo a prime, or a polynomial field

3
Diffie-Hellman The algorithm –Alice and Bob agree on two large prime num, p and q. –Alice then chooses another large random number x and calculate A such that A=q ^ x mod p. and send to bob –Bob also chooses a another large num y and calculate B such that B=q ^ y mod p. and send to Alice –Both Alice and Bob can calculate the key as K 1 = B ^ x mod p K2=A ^ y mod p K1 = K2 –The key may then be used in a private-key cipher to secure communications between A and B

4
Diffie-Hellman Let p = 11 and q = 7 Alice chooses another num x = 3 then we have A = q^ x mod p =7 ^ 3 mod 11 = 2 Alice Sends the number A = 2 to Bob Bob chooses another num y = 6 then we have B =q^ y mod p = 7 ^ 6 mod 11 = 4 Bob sends the number B = 4 to Alice Now Alice generate Secret key, K1 =B ^ x mod p = 4 ^ 3 mod 11 =9 Then Bob generate Secret key, K2 =A ^ y mod p = 2 ^ 6 mod 11 = 9

5
Key Exchange: Diffie-Hellman Alice Bob A = g ^ x mod n A K1 = B ^ x mod nK2 = A ^ y mod n B B = g ^ y mod n

6
Mathematical Theory Behind Algorithm First Alice find key K1 = B ^ x mod n but what is B ? B = g ^ y mod n, therefore if we Substitute this value of B in K1 then K1=(g ^ y)^x mod n = g ^ yx mod n Then Bob find key K2 = A ^ y mod n but what is A ? A = g ^ x mod n, therefore if we substitute this value of A in K2 then K2 = (g ^ x)^y mod n = g ^xy mod n Now Basic Maths says that: K^ yx = K^ xy

Similar presentations

OK

Cryptography and Network Security Chapter 10 Fourth Edition by William Stallings Lecture slides by Lawrie Brown.

Cryptography and Network Security Chapter 10 Fourth Edition by William Stallings Lecture slides by Lawrie Brown.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google