LAB 8 Manual ElGamal Algorithm

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LAB 8 CPIT 425 Prepared by: Mohammed Ghazi Al-Obeidallah

Information Security CPIT 425

LAB 8 Manual ElGamal Algorithm

Prepared By:

Mohammed Ghazi Al‐Obeidallah

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LAB 8 Objectives:

1. Using Elgamal algorithm to Encrypt and Decrypt plain text.

2. Learn how to achieve Elgamal algorithm parameters using some calculations, predefined procedures, and user defined in procedures.

3. Trying to adjust Elgamal algorithm by using different tactics

LAB 8 main Outcomes:

1. Students will able to use Elgamal algorithm to encrypt and decrypt plaintext and they should also implement their work using a suitable programming language (Java, C#, or any .net language).

2. Students will be able calculate different Elgamal algorithm parameters such as :

a. Calculating α ( primitive root) b. Calculating YA

c. Calculating C1 and C2

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Example 1

Elgamal algorithm Pseudo code:

- Select Q where Q is a prime number

- Select α where α is a primitive root of Q and α < Q.

- Select Random Xa such that Xa < Q -1 - Calculate Ya , such that Ya = α^Xa mod Q - Public key = { Q, α, Ya}

- Private key = { Xa}

- Plain Text M < Q

- Select random k0 such that k0 < Q

- Calculate K1 such that K1 = Ya ^k mod Q - Calculate C1 = α^k0 mod Q

- Calculate C2 = K1 * M mod Q - Cipher = (C1, C2)

- Decryption : Cipher = C1,C2

- Calculate K1 such that K1 = C1 ^Xa mod Q - PlainText M = (C2K1^-1) mod Q

Quiz:

Use Elgamal algorithm to encrypt and decrypt the following plain text :

LAB Elgamal

Students should build their own programs to implement and test the above pseudo code.

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Example:

- Select Q = 19 - Select α =10.

- Select Random Xa = 5

- Calculate Ya , such that Ya = 10⁵ mod 19 = 3 - Public key = { 19, 10, 4}

- Private key = { 5}

- Plain Text M = 17 < Q - Select random k0 = 6

- Calculate K1 such that K1 = 3⁶ mod 19 - Calculate C1 = 10⁶ mod 19 = 11

- Calculate C2 = 7 * 17 mod 19 = 7 - Cipher = (11, 7)

- Decryption : Cipher = C1,C2

- Calculate K1 such that K1 = C1 ^Xa mod Q - PlainText M = (C2K1^-1) mod Q