You are Alice. You have agreed with your friend Bob that you will use the Diffie
ID: 3916040 • Letter: Y
Question
You are Alice. You have agreed with your friend Bob that you will use the Diffie-Hellman public-key algorithm to exchange secret keys. You and Bob have agreed to use the public base g = 9 and public modulus p = 817. You have secretly picked the value SA = 23 You begin the session by sending Bob your calculated value of TA. Bob responds by sending you the value TB = 272. What is the value of TA What is the value of your shared secret key? Can you guess Bob’s secret value SB and what it would be? Show each and every step of your calculations, if you use Excel or any other method of mod calculation, include the spreadsheet or the steps in that method (for mod calculation, the following identity may be useful Mod ( X^n, p) = mod [mod(X,p)*mod(X^n-1, p), p] mod(X*Y,p) = mod[mod(X,p)*mod(Y,p),p]
Explanation / Answer
Public base : g = 9
Public modulus : p = 817
Secret key of Alice = a = 23
Secret key of Bob = b = ?
TA = g^a mod p = 9^23 mod 817 = 339
TB = g^b mod p = 9^b mod 817 = 272 (Given)
TB^a mod p = TA^b mod p = shared secret key
272^23 mod 817 = 339^b mod 817
24 = 339^b mod 817 ---- eq 1
plot graph for eq1 and solve for integer solutions
b = 63n + 31 where n belongs to W
b = 31,94,157, 220, 283, 346.....
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