DHKE Example ABDULAZIZ A. HAMEDA.

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Presentation transcript:

DHKE Example ABDULAZIZ A. HAMEDA

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).

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)

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.