Cryptography and Network Security

The RSA algorithm was proposed in 1978 and is named after its inventors: Rivest, Shamir, and Adleman. RSA: A Cornerstone of Cryptography In 1976, the first asymmetric key encryption algorithm, Diffie-Hellman, was proposed. However, this algorithm left open the problem of realizing a one-way function — a function that is hard to invert. The three cryptographers — Ron Rivest, Adi Shamir, and Leonard Adleman — solved the aforementioned problem. RSA algorithm This algorithm is divided into three phases, namely, key generation, encryption, and decryption.  A. Key Generation:           1. Select two large prime numbers (say p, and q).          2. Calculate n = pq.          3. Calculate Euler totient function   Φ (n) = (p-1)(q-1)          4. Choose value of e (where 1 < e <  Φ (n), and gcd( Φ (n),e)=1).          5. Calculate d such that ed = 1 m...

Elliptic Curve Cryptography (ECC) Elliptic curve (EC) was first introduced by Neal Kobiltz and Victor Miller in 1985. Elliptic curve is a non-singular curve that is operated on a finite field Zq (where q is the order of elliptic curve). EC consists of set of points that satisfies the following equation as follows.                                                                   Y 2 = X 3 + aX + b Where {X,Y,a,b} ∈ Zq, and 4a 3 + 27b 2 ≠ 0. Next, we discuss the encryption and decryption mechanism between two parties (Say α and γ ). Remark 1: Elements selected from party α is represented by capital letters whereas elements selected from party γ is represented by small letters. i) Key Generation: 1. Secret key: Each party α and γ selects secret keys S ∈ Zq and s ∈ Zq. 2. Public key: P ...