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4| Yousif, Hameed & Al-Zuhairi
(a) (b) (c)
(d)
(e)
Fig. 1. Zigzag Scan Permutation (a) Input Sub-image (b) First Zigzag Scan Direction (c) Second Zigzag Scan Direction (d)
Vector Generated by Applying the First Zigzag Scan Direction Started in Position Number 1 in (a) , (e) Vector Generated by
Applying the First Zigzag Scan Direction Started in Position Number 7 in (a)
column, then the resulted vector is depicted in Fig. 1d. On the 1) Key Production Procedure:
other hand, if the zigzag scan in Fig. 1b is implemented on the • Two prime integer numbers p and q are chosen ran-
4 × 4 sub-image in Fig. 1a and the position of starting pixel domly.
is located at the second row-third column, then the resulted
vector is shown in Fig. 1e. A different vector will be produced • Compute n which represents the public modulus by:
if the location of the starting pixel is changed. In this work, n = pq.
the zigzag scan is modified such that the starting pixel location
is variable for each scanned sub-image and it is selected based • Compute Euler’s totient function f (n) by: f (n) = (p -
on chaotic sequences. Consequently, high permutation feature 1)(q - 1).
is achieved to strengthen the security level of TIC.
• A third random integer e is selected such that gcd
B. RSA Mechanism (e, f (n)) = 1 and 1 < e < f (n), where gcd represents
Rivest, Shamir, and Adleman were the first three cryptologists greatest common divisor.
who described RSA public key cryptosystem in 1978. RSA
is utilized for providing authenticity, security and privacy of • Calculate the decryption key (d) by: d = e-1mod(f (n)).
the digital information. It is used in several applications that
demand data security, such as electronic mail security, elec- • (n, e) points to the public key, whereas (n, d) points to
tronic commerce on Internet and banking. This mechanism the secret key.
uses exponentiation modular multiplication. As in standard
asymmetric cryptosystem, the RSA employed two separated 2) Encryption Procedure:
keys; the public and secret keys. The public key is devoted
for data encryption operation and can be sent to anyone inside The plaintext P is divided initially into string of blocks P1, P2,
the system. The secret key is consecrated for decryption pro- .., Pi, such that each block Pi satisfies the condition: 0 < Pi <
cess and should be remain confidential inside the RSA system. n. After that, the encryption process is performed on each
RSA security relies on the complexity of finding the prime fac- plaintext block to obtain the ciphered text C as [3, 14, 38]:
tors of large prime integer numbers which is one of the most
difficult problems in mathematics. The processes of RSA tech- C = Pemod n (1)
nique can be decomposed into three fundamental phases: key
production, encryption and decryption operations [3, 14, 38]. Then, the cipher text C is transmitted to the receiver.
