Information Security Management | Assignment

information security
managEment

Table of Contents
3. Simplified Feige-Fiat-Shamir Accreditation Scheme..............................................................1
4. Tracing of values with parameters n = 15, r = 11....................................................................1
5. Diffie – Hellman protocol for three parties Alice, Bob and Carol..........................................2

3. Simplified Feige-Fiat-Shamir Accreditation Scheme
The accreditation scheme works for the exchange of the secret ‘s’, between Peggy and Victor
making them Prover and Verifier with an RSA modulus n=pq, where p and q are prime
numbers, and are kept hidden. The resultant n and a chosen parameter a, both belongs to the set
of natural numbers.
Now according to the accreditation scheme, following steps are executed –
- Peggy picks a random number r, less than n
- The computation of x takes place, such that x = r2 (mod n)
- Peggy sends x to Victor, the verifier
- Now, Victor send to Peggy a random bit b
- The answer sent by Peggy to Victor becomes
• r if the bit b is 0
• y, another parameter, as y= r * s (mod n) if the bit b is 1
- At the verification end, according to the bit value, Victor verifies
• x = r2 mod n if b is 0 -> Peggy knows √x
• x = y2 * v (mod n) -> Peggy knows √v-1
- The accreditation by Victor is accepted if the verification is successful
4. Tracing of values with parameters n = 15, r = 11
Given n = 15, the possible prime numbers p = 3 and q = 5 makes n = 15
Public and Private Keys
v (public key) equations square roots
1 x2 = 1 mod 15 1, 4, 11, 14
4 x2 = 4 mod 15 2, 7, 8, 13
v v-1 √v-1 (private key)
1 1 1
4 4 2
Now Peggy chooses r = 11 and sends x to Victor as
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x = r2 (mod n)
x= (11)2 (mod 15)
x = 1 (mod 15)
x = 1
Victor sends Peggy, the bit b as either 0 or 1
Based on b, the answer becomes
Bit Value to be sent Answer
0 r 11
1 y = r × s mod n y = 11 * (2 (mod 15))
y = 22
At the verification end,
Bit Value to be verified Value
0 x = r2 mod n 1
1 x = y2 × v mod n y = 222 * (4 (mod 15))
y = 484 * 4 mod 15
y = 1936 mod 15
y = 1
Thus, Victor accepts the accreditation.
5. Diffie – Hellman protocol for three parties Alice, Bob and Carol
The protocol based on three parties Alice, Bob and Carol can be described using the discrete
logarithms as below –
Step 0: Alice, Bob and Carol agree on a large prime number n and an integer g, such that g is a
generator mod n.
Step 1: Alice, Bob and Carol choose their large random integers x, y and z respectively.
Step 2: The sharing (round 1)
- Alice send to Bob: X = gx mod n
- Bob sends to Carol: Y = gy mod n
- Carol sends to Alice: Z = gz mod n
Step 3: The sharing (round 2)
- Alice send to Bob: Y` = = gxy mod n
- Bob sends to Carol: Z` = Zy mod n = gyz mod n
- Carol sends to Alice: X` = Xz mod n = gzx mod n
Step 3: The computation
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- Alice computes: kx = X`x mod n = gyzx mod n
- Bob computes: ky = Y`y mod n = gzxy mod n
- Carol computes: kz = Z`z mod n = gxyz mod n
Step 4: kx = ky = kz is used as the secret key
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