Internet Security - Dang Thanh Binh's Page

170 INTERNET SECURITY
Thus, the whole ciphertext blocks ci, 1 � i � 10, are computed as:
3223 3155 1012 1712 1595
2653 0802 2360 0832 1369
To decrypt the first ciphertext c1 = 3223, use the decryption key, d = 1019, and compute:
(mod n)
m1 ≡ c d 1
≡ 3223 1019 (mod 3337) ≡ 914
(mod n)
m2 ≡ c d 2
≡ 3155 1019 (mod 3337) ≡ 615
.
The recreated message of this example is computed as:
0914 0615 1813 0120 0915
1400 1905 0321 1809 2025
5.2.2 RSA Signature Scheme
The RSA public-key cryptosystem can be used for both encryption and signatures. Each
user has three integers e, d and n, n = pq with p and q large primes. For the key pair
(e, d), ed ≡ 1 (mod φ(n)) must be satisfied. If sender A wants to send signed message c
corresponding to message m to receiver B, A signs it using A’s private key, computing
c ≡ mdA (mod nA). First A computes
ϕ(nA) ≡ lcm (pA − 1,qA − 1)
where lcm stands for the least common multiple. The sender A selects his own key pair
(eA,dA) such that
eA •dA ≡ 1 (mod ϕ(nA))
The modulus nA and the public key eA are published., Figure 5.3 illustrates the RSA
signature scheme.
Example 5.7 Choose p = 11 and q = 17. Thenn = pq = 187.
Compute ϕ(n) = 1 cm (p − 1,q− 1)
= 1 cm (10, 16) = 80
Select eA = 27. TheneAdA ≡ 1 (mod ϕ(nA))
27dA ≡ 1 (mod 80)
dA = 3
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