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- 1. CryptologyDUH BRX UHDGB?Slides by Raymond Borges 1
- 2. Outline• Background• Ancient Cryptography• Frequency Analysis• Modern Cryptography• Secure Communication• Tools of the trade• Conclusion 2
- 3. Background 3
- 4. Background 4
- 5. The Ancient Art of Secret Messages 5
- 6. BackgroundPrinciples and methods for:1. Transforming message into unintelligible2. Transforming message back to original form 6
- 7. BackgroundPrinciples and methods for:• Retransforming message back to original form• Without knowledge of key 7
- 8. Background 8
- 9. Encryption• Plaintext: This is what you want to encrypt• Ciphertext: The encrypted output• Enciphering or encryption: process which converts plaintext to ciphertext• Encryption algorithm: Sequence processing steps to transform plaintext into ciphertext• Secret key: Sets some or all parameters used by encryption algorithm 9
- 10. Practice (transposition)Caesar CipherCiphertext: DUH BRX UHDGBSolution:c = E(k, p) = (p + k) mod 26c = E(3, p) = (p + 3) mod 26 for k=key=34 mod 26 = 4 so A=Dp = D(k, c) = (c − k) mod 26D=4 (4-3) mod 26 = 1 10
- 11. Practice (substitution)Monoalphabetic cipher• plaintext letters: a b c d e f .....• substitution letters: t h i j a b .....Key is sequence of substitution letters26 ! = 4.03291461 × 1026Impossible to crack? No….Polyalphabetic tougher… 11
- 12. ETAOIN SHRDLU (Frequency analysis)• ‘E’ is the most common letter in the English language,• ‘Th’ is the most common bigram• ‘The’ most common trigram• Letter frequency English 12
- 13. Frequency analysis• Most frequently occurring trigrams ordered by decreasing frequency are: 13
- 14. Polyalphabetic Ciphers• The Vigenère cipher• First letter use key 1• Second uses key 2• Third uses key 3To Decrypt go backwards 14
- 15. Modern CryptographyData Encryption Standard (DES) 1976• 64 bit key (uses 56bits)• 16 stages• Block divided into two 32-bit halves• XOR• Subkeys made key schedule 15
- 16. Modern CryptographyFeistel function:1. Expansion- the 32-bit half-block is expanded to 48 bits by duplicating half of the bits2. Key mixing — the result is combined with a subkey using an XOR operation.3. Substitution —block divided into eight 6-bit pieces then uses substitution boxes4. Permutation 16
- 17. Modern CryptographyAdvanced Encryption Standard (AES) 2001• Substitution-permutation network• Not Feistel• Fixed block size 128 bits• Key size of 128, 192, or 256 bits 17
- 18. Modern Cryptography Advanced Encryption Standard (AES)1. KeyExpansion2. Initial Round 1. AddRoundKey3. Rounds 1. SubEytes 2. ShiftRows 3. MixColumns 4. AddRoundKey4.Final Round 1. SubBytes 2. ShiftRows 3. AddRoundKey 18
- 19. Public-key cryptographyRSA- Ron Rivest, Adi Shamir, Leonard Adleman 1978• Uses factoring problem (large primes)• Two large primes of similar size > 100 digitsExample:Public (n = 3233, e = 17)Private key is (n = 3233, d = 2753)n=p1*p2,e=coprime number to (p1-1)(p2-1)d =modular multiplicative inverse of e 19
- 20. Public-key cryptography Encryption Decryption c = me (mod n) m = cd (mod n)Example:To encrypt m = 65c = 6517 (mod 3233) = 2790To decrypt c = 2790, we calculatem = 27902753 (mod 3233) = 65 20
- 21. Secure Communication• AES 256 bit key• 15360-bit RSA keys are equivalent 256-bit symmetric keys• 2^256 = 1.15792089 × 1077 brute-force?Use RSA then AES for secure communicationHTTPS, SSH, SFTP, SSL and TLS and others 21
- 22. Some Tools of the tradeFile Encryption• Axantum• WinZipDisk encryption• TrueCryptNetwork• Open SSH 22
- 23. References• http://www.axantum.com/axcrypt/Downloads .html• http://dottech.org/freeware-reviews/15996/• http://technet.microsoft.com/en- us/library/cc757819(v=ws.10).aspx 23
- 24. Questions? 24

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