1. DHKE Example
ABDULAZIZ A. HAMEDA

2. DHKE: Set-up Choose a large prime p. Choose a primitive root g of p.
Publish p and g Alice and Bob must agree on the values of p and g; (where g for example is 2 or 5).

3. DHKE: Steps Alice Bob gA mod p gB mod p y y = AESkAB(x)
Choose random private key kprA=A ∈{1,2,…,p-1}
Choose random private key kprB=B ∈ {1,2,…,p-1}
Compute corresponding public key kpubA= gA mod p
gA mod p
Compute correspondig public key kpubB= gB mod p
gB mod p
Compute common secret kAB = (gB mod p)A = gAB mod p
Compute common secret kAB = (gA mod p)B = gBA mod p
We can now use the joint key kAB for encryption, e.g., with AES y
y = AESkAB(x)
x = AES-1kAB(y)

4. Domain parameters p=29, g=2
DHKE: Example
Alice
Domain parameters p=29, g=2
Bob
Choose random private key kprA= A = 5
Choose random private key kprB=B = 12
Compute corresponding public key kpubA= 25 mod 29 = 3 3
Compute corresponding public key kpubB= 212 mod 29 = 7 7
Compute common secret kAB = 75 mod 29 = 16
Compute common secret kAB = 312 mod 29 = 16
Proof of correctness:
Alice computes: (gb)a mod p.
Bob computes: (ga)b mod p.