This presentation contains the contents pertaining to the undergraduate course on Cryptography and Network Security (UITC203) at Sri Ramakrishna Institute of Technology. This covers the ElGamal Cryptosystem.

1. ElGamal Cryptosystem
Adri Jovin J J, M.Tech., Ph.D.
UITC203 CRYPTOGRAPHY AND NETWORK SECURITY

2. ElGamal Cryptosystem
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Global Public Elements
𝑞 prime number
𝛼 𝛼 < 𝑞and 𝛼 is a primitive root of 𝑞
Key Generation by Alice
Select private 𝑋 𝐴 𝑋 𝐴 < 𝑞 − 1
Calculate 𝑌𝐴 𝑌𝐴 = 𝛼 𝑋 𝐴 𝑚𝑜𝑑 𝑞
Public key 𝑞, 𝛼, 𝑌𝐴
Private key 𝑋 𝐴

3. Elgamal Cryptosystem (Contd…)
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Encryption by Bob with Alice’s Public Key
Plain text 𝑀 < 𝑞
Select random integer 𝑘 𝑘 < 𝑞
Calculate 𝐾 𝐾 = (𝑌𝐴) 𝑘
𝑚𝑜𝑑 𝑞
Calculate 𝐶1 𝐶1 = 𝛼 𝑘 𝑚𝑜𝑑 𝑞
Calculate 𝐶2 𝐶2 = 𝐾𝑀𝑚𝑜𝑑 𝑞
Ciphertext (𝐶1, 𝐶2)
Decryption by Alice with Alice’s Private Key
Ciphertext 𝐶1, 𝐶2
Calculate 𝐾 𝐾 = (𝐶1) 𝑋 𝐴 𝑚𝑜𝑑 𝑞
Plain text 𝑀 = 𝐶2 𝐾−1 𝑚𝑜𝑑 𝑞

4. Problem
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5. References
Schneier, B. (2007). Applied cryptography: protocols, algorithms, and source code in C. John Wiley & Sons.
Stallings, W. (2014). Cryptography and network security, 6/E. Pearson Education India.
Katz, J., & Lindell, Y. (2014). Introduction to modern cryptography. CRC press.
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