Introduction to Cryptography
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The document provides an overview of cryptography, defining it as the practice of secure communication and outlining its two main branches: private key and public key cryptography. It explains private key cryptography with examples like the Caesar cipher and techniques for cracking it, while also detailing public key cryptography, particularly RSA, including its key generation process. The document emphasizes the importance of mathematics in cryptographic techniques and the need for key secrecy.
Introduction to Cryptography
- 1. Introduction to Cryptography by Petre POPESCU
- 2. What is cryptography? "the art of hiding information" OR "the practice and study of techniques for secure communication in the presence of third parties" (wikipedia)
- 3. Modern Cryptography a branch of mathematics and computer science
- 4. Modern Cryptography 2 main branches 1. Private Key Cryptography 2. Public Key Cryptography
- 5. Private Key Cryptography The same key is used for both encryption and decryption
- 6. Private Key Cryptography Examples: - DES - AES - Caesar Cipher - Blowfish
- 7. Caesar Cipher Named after Julius Caesar, who used it in his private and military correspondence.
- 8. Caesar Cipher It is a substitution cipher Each letter is replaced by another letter depending on a "shift" value
- 10. Cracking Caesar Cipher (assuming we know Caesar Cipher is used) 1. Brute Force Attack 2. Word-pattern and letter distribution attack
- 11. Brute Force Attack Since the number of possible shifts is limited, it is feasible to try each shift and discard the results that are not human readable.
- 12. Word-pattern and letter distribution attack Step 1: Find the average distribution of letter in that language. This can be done with ease by analyzing long texts.
- 13. Word-pattern and letter distribution attack Step 2: A Caesar Cipher usually "shifts" this distribution by the shift used for encryption. An error margin is permitted, so now multiple possibilities are generated.
- 14. Word-pattern and letter distribution attack Step 3: Decrypt the text using the possible shifts that were found in step 2. Use word-pattern analysis (and possibly a dictionary of words) to discover the correct variant
- 15. Public Key Cryptography Two keys are needed: - one for encrypting the message - one for decrypting the message
- 16. Public Key Cryptography Key's properties - neither keys can perform both operations - the two keys are mathematically paired - public key - used for encryption - private key - used for decryption
- 17. Public Key Cryptography Examples: - RSA - YAK - Various elliptic curve techniques
- 18. RSA Created by: Ron Rivest Adi Shamir Leonard Adleman Is based on the presumed difficulty of factoring large integers.
- 19. RSA - Generating the two keys (1) Choose two distinct prime numbers: p and q p and q should have high bit-length p and q should be chosen at random
- 20. RSA - Generating the two keys (2) Compute n = pq n is the "modulus" for both the public and private keys
- 21. RSA - Generating the two keys (3) Compute φ(n) = φ(p)φ(q) = (p − 1)(q − 1)
- 22. RSA - Generating the two keys (4) Choose e such that 1 < e < φ(n) and gcd(e, φ(n)) TIP: e and φ(n) are coprime
- 23. RSA - Generating the two keys "e" is the Public Key Exponent
- 24. RSA - Generating the two keys (5) Compute d where d−1 ≡ e (mod φ(n)) or d is the multiplicative inverse of e (modulo φ(n))
- 25. RSA - Generating the two keys To calculate d solve for d given d*e ≡ 1 (mod φ(n))
- 26. RSA - Generating the two keys Public Key: e and n Private Key: d and n d, p, q and φ(n) must be kept secret