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1. Optimal Asymmetric Encryption Padding (OAEP) in RSA Postgraduate Presentation Prepared by: Ms. A. Gomathy Department of Computer Science and Engineering

2. Introduction to RSA • RSA is an asymmetric cryptographic algorithm. • It uses a pair of keys: Public key (encryption) and Private key (decryption). • Plain RSA is deterministic – the same plaintext produces the same ciphertext. • This makes it vulnerable to chosen-plaintext attacks. • Padding schemes like OAEP improve RSA’s security.

3. Need for Padding in RSA • Without padding, RSA is not semantically secure. • Predictable ciphertexts can leak information. • Padding introduces randomness into encryption. • Ensures two encryptions of the same message produce different ciphertexts. • Prevents dictionary and replay attacks.

4. What is OAEP? • OAEP stands for Optimal Asymmetric Encryption Padding. • Introduced by Bellare and Rogaway in 1994. • It combines a message with random data using hash-based masks. • Designed to make RSA encryption probabilistic and secure under chosen plaintext attacks. • Standardized in PKCS#1 v2.0.

5. OAEP Components • Message (M): The plaintext to encrypt. • Random seed (r): Randomly generated bit string. • Hash function (G, H): Used to create masks. • Mask Generation Function (MGF1): Expands input to desired length. • XOR operations: Combine masks with data to hide information.

6. OAEP Encoding Process 1. Start with message M and random seed r. 2. Generate a mask for M using G(r). 3. XOR M with G(r) to produce masked message. 4. Generate a mask for r using H(masked message). 5. XOR r with H(masked message) to produce masked seed. 6. Concatenate masked seed || masked message for encryption.

7. OAEP Decoding Process 1. Split the ciphertext block into masked seed and masked message. 2. Recover r by XORing masked seed with H(masked message). 3. Recover message by XORing masked message with G(r). 4. Verify correctness and remove padding. 5. Output original message M.

8. Mathematical Representation Let M be the message and r the random seed. Encoding: X = M ⊕ G(r) Y = r ⊕ H(X) Encoded = X || Y Decoding: r = Y ⊕ H(X) M = X ⊕ G(r)

9. Mask Generation Function (MGF1) • MGF1 is a deterministic algorithm based on a hash function. • Expands a fixed-length seed into an arbitrary-length mask. • Example: MGF1(SHA-256, seed, maskLen) • Ensures uniform randomness distribution across data blocks.

10. Example of OAEP with RSA Given: • Message M = 'HELLO' • Random seed r = 0xA1B2C3 Process: 1. Compute G(r) and H(M⊕G(r)). 2. Apply XOR to create masked message and masked seed. 3. Encrypt concatenated block using RSA public key. 4. Decrypt and reverse the process to recover 'HELLO'.

11. Security Benefits of OAEP • Provides semantic security (IND-CPA). • Protects against partial decryption attacks. • Prevents chosen-plaintext and replay attacks. • Randomized process ensures unique ciphertexts. • Enhances RSA’s theoretical and practical security.

12. Comparison: OAEP vs PKCS#1 v1.5 Feature | PKCS#1 v1.5 | OAEP ---------|---------------|------ Randomness | Partial | Full Security Level | Moderate | High Chosen Plaintext Attack | Vulnerable | Resistant Standardization | Older | PKCS#1 v2.0+ Mathematical Proof | Limited | Proven under RSA assumptions

13. OAEP in Practice • Widely used in modern cryptographic libraries. • Supported in RSA implementations like OpenSSL, Java, .NET, and Python. • Used for encrypting small data or symmetric keys (not bulk data). • Often combined with hybrid encryption (RSA-OAEP + AES).

14. Limitations of OAEP • Only applicable to RSA encryption (not signatures). • Relies on strong hash functions (e.g., SHA-256). • Sensitive to implementation errors. • Still requires proper key management for full security.

15. Summary and References • OAEP strengthens RSA by introducing randomness and masks. • Provides provable security against chosen plaintext attacks. • Essential in modern public-key cryptography. References: 1. Bellare, M., & Rogaway, P. (1994). Optimal Asymmetric Encryption. 2. PKCS #1 v2.2: RSA Cryptography Standard. 3. RFC 8017 - PKCS #1: RSA Cryptography Specifications.