Computer Security Laboratory Course

This repository contains my all lab task code for the Computer Security Laboratory Course. It includes C++ implementations of several classical and public-key cryptographic algorithms used during the lab exercises.

Repository Contents

• ecc_enc_dec.cpp – ECC encryption and decryption
• ecc_homomorphic.cpp – ECC homomorphic property demonstration
• elgamal_enc_dec.cpp – ElGamal encryption and decryption
• elgamal_product.cpp – ElGamal product-based operation
• elgamal_rerandomization.cpp – Ciphertext rerandomization
• elgamal_signature.cpp – ElGamal digital signature
• rsa_enc_dec.cpp – RSA encryption and decryption
• rsa_product.cpp – RSA product-based operation
• rsa_signature.cpp – RSA signature implementation
• vernam_cipher.cpp – Vernam cipher implementation

Theory and Procedure of Each Algorithm

1. RSA Encryption and Decryption

RSA is a public-key cryptosystem based on large prime numbers.

Procedure:

• Choose two large prime numbers p and q.
• Compute n = p × q and phi(n) = (p - 1)(q - 1).
• Select public exponent e with gcd(e, phi(n)) = 1.
• Compute private exponent d such that d × e ≡ 1 (mod phi(n)).
• Encryption: C = M^e mod n.
• Decryption: M = C^d mod n.

This provides confidentiality using a public key for encryption and a private key for decryption.

2. RSA Product Operation

This demonstrates mathematical properties of RSA under multiplication.

Procedure:

• Encrypt two messages separately using the same RSA public key.
• Multiply the ciphertexts together.
• The result corresponds to the product of the original messages after decryption under the right modular relation.

This shows how RSA can behave in a multiplicative setting and is useful for studying algebraic properties.

3. RSA Signature

RSA can also be used for digital signatures.

Procedure:

• Use the private key to sign a message hash.
• Signature = H(M)^d mod n.
• Verification uses the public key: H(M) = Signature^e mod n.

If the verification succeeds, the signature is valid and confirms the sender's identity.

4. ElGamal Encryption and Decryption

ElGamal is based on the discrete logarithm problem.

Procedure:

• Choose a prime p and a generator g.
• Select private key x and compute public key y = g^x mod p.
• Choose random k for each message.
• Compute c1 = g^k mod p.
• Compute c2 = M × y^k mod p.
• Ciphertext = (c1, c2).
• Decryption uses x: M = c2 × (c1^x)^(-1) mod p.

This is a probabilistic encryption scheme because each message can produce different ciphertexts with different random values.

5. ElGamal Product Operation

This focuses on multiplication of ElGamal ciphertexts or values in the group.

Procedure:

• Encrypt messages using ElGamal.
• Combine the encrypted values using modular multiplication.
• Decrypt the combined ciphertext to reveal the corresponding product or transformed value.

It helps understand how group operations affect encrypted data.

6. ElGamal Rerandomization

Rerandomization creates a new valid encryption of the same message without revealing the original plaintext.

Procedure:

• Start with an existing ElGamal ciphertext.
• Choose a new random value.
• Recompute the ciphertext using that random value while preserving the same message.

The result is a different-looking ciphertext but decrypts to the same original message.

7. ElGamal Signature

ElGamal signatures provide authenticity and integrity.

Procedure:

• Choose random secret k with gcd(k, p - 1) = 1.
• Compute r = g^k mod p.
• Compute s = k^(-1) × (H(M) - x × r) mod (p - 1).
• Signature is (r, s).
• Verification checks whether g^H(M) = y^r × r^s mod p.

If the equation holds, the message is accepted as authentic.

8. ECC Encryption and Decryption

ECC (Elliptic Curve Cryptography) uses points on an elliptic curve instead of large primes alone.

Procedure:

• Choose an elliptic curve and a base point G.
• Select private key d and compute public key Q = dG.
• To encrypt a message point P, choose random k.
• Compute C1 = kG and C2 = P + kQ.
• Decrypt using C2 - dC1 = P.

ECC provides strong security with smaller key sizes compared to RSA.

9. ECC Homomorphic Property

ECC also supports homomorphic behavior in additive form on elliptic curve points.

Procedure:

• Take two messages as points on the elliptic curve.
• Choose random scalars and generate encrypted ciphertext pairs.
• Add the ciphertexts together in the curve group.
• Decrypt the combined ciphertext using the private key.
• The result matches the sum of the original messages.

This demonstrates the additive homomorphic property of ECC-based encryption in a practical implementation.

10. Vernam Cipher

The Vernam cipher is a one-time pad cipher.

Procedure:

• Convert plaintext and key to the same length.
• XOR each plaintext bit with the corresponding key bit.
• Encryption and decryption use the same XOR operation.

This is perfectly secure only when the key is truly random, secret, and used only once.

Compiler Requirements

gcc --version

Output:

gcc (Rev5, Built by MSYS2 project) 16.1.0
Copyright (C) 2026 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

This repository uses GCC/MSYS2 compiler support for __int128 and #define ll long long int.

Conclusion

This repository covers the core concepts of modern cryptography and classic cipher design, including public-key systems, digital signatures, homomorphic behavior, elliptic curve methods, and one-time pad encryption. These programs are useful for understanding how cryptographic algorithms work step by step in practice.

---

Pritom Banik
10 Semtember 2026
CSE4116 : Computer Security Laboratory