The Diffie-Hellman key exchange algorithm allows two users to securely exchange a secret key over an insecure channel. It uses discrete logarithms over finite fields. Each user generates a public/private key pair, and the exchange of the public keys allows both to independently calculate a shared secret key. The security of the algorithm relies on the difficulty of solving the discrete logarithm problem.

1. Diffie-Hellman Key
Exchange
Subject : Information and Network Security
CE-B
Maulik togadiya 130240107090

2. What is Diffie-Hellman?
 A Public Key Algorithm
 Only for Key Exchange
 Does NOT Encrypt or Decrypt
 Based on Discrete Logarithms
 Widely used in Security Protocols and Commercial Products
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3. Discrete Logarithms
 What is a logarithm?
 log10100 = 2 because 102
= 100
 In general if logmb = a then ma
= b
 Where m is called the base of the logarithm
 A discrete logarithm can be defined for integers
only
 In fact we can define discrete logarithms mod p
also where p is any prime number
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4. Diffie-Hellman Algorithm
 The purpose of the algorithm is to enable two users to
securely exchange a key that can then be used for
subsequent encryption of messages.
 The algorithm itself is limited to the exchange of secret
values.
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5. The Algorithm
 There are two publicly known numbers: a prime number q
and an integer that is a primitive root of q.
 Suppose the users A and B wish to exchange a key. User A
selects a random integer XA< q and computes YA= α X
A mod
q.
 Similarly, user B independently selects a random integer XA
< q and computes YB= α X
B mod q.
 Each side keeps the X value private and makes the Y value
available publicly to the other side. User A computes the
key as K = (YB)X
A mod q and user B computes the key as
K = (YA)X
B mod q
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6. What are primitive roots?
 Let p be a prime. Then b is a primitive root for p if
the powers of b,
1, b, b^2, b^3, ...
include all of the residue classes mod p (except 0).
 If p=7, then 3 is a primitive root for p because the
powers of 3 are 1, 3, 2, 6, 4, 5---that is, every
number mod 7 occurs except 0. But 2 isn't a
primitive root because the powers of 2 are 1, 2, 4,
1, 2, 4, 1, 2, 4...missing several values.
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7. These two calculations produce identical results:
 K = (YB)X
A mod q
= (α X
B mod q)X
A mod q
= (α X
B )X
Amod q by the rules of modular arithmetic
= (α X
B
X
A mod q
= (α X
A )X
B mod q
= (α X
A mod q)X
B mod q
= (YA)X
B mod q
 Both User A and User B can use this number as their key.
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8. Diffie-Hellman Algorithm
 Five Parts
1. Global Public Elements
2. User A Key Generation
3. User B Key Generation
4. Generation of Secret Key by User A
5. Generation of Secret Key by User B
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9. Diffie-Hellman Key Exchange
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10. Why Diffie-Hellman is Secure?
 Opponent has q, α, YA and YB
 To get XA or XB the opponent is forced to take a
discrete logarithm
 The security of the Diffie-Hellman Key Exchange
lies in the fact that, while it is relatively easy to
calculate exponentials modulo a prime, it is very
difficult to calculate discrete logarithms. For large
primes, the latter task is considered infeasible.
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