Brief intro to cryptography

1. Cryptology
DUH BRX UHDGB?
Slides by Raymond Borges
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2. Outline
• Background
• Ancient Cryptography
• Frequency Analysis
• Modern Cryptography
• Secure Communication
• Tools of the trade
• Conclusion
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3. Background
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4. Background
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5. The Ancient Art of Secret Messages
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6. Background
Principles and methods for:
1. Transforming message into unintelligible
2. Transforming message back to original form
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7. Background
Principles and methods for:
• Retransforming message back to original form
• Without knowledge of key
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8. Background
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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
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10. Practice (transposition)
Caesar Cipher
Ciphertext: DUH BRX UHDGB
Solution:
c = E(k, p) = (p + k) mod 26
c = E(3, p) = (p + 3) mod 26 for k=key=3
4 mod 26 = 4 so A=D
p = D(k, c) = (c − k) mod 26
D=4 (4-3) mod 26 = 1
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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 letters
26 ! = 4.03291461 × 1026
Impossible to crack? No….
Polyalphabetic tougher…
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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 
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13. Frequency analysis
• Most frequently occurring trigrams ordered by
decreasing frequency are:
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14. Polyalphabetic Ciphers
• The Vigenère cipher
• First letter use key 1
• Second uses key 2
• Third uses key 3
To Decrypt go backwards
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15. Modern Cryptography
Data Encryption Standard (DES) 1976
• 64 bit key (uses 56bits)
• 16 stages
• Block divided into two 32-bit halves
• XOR
• Subkeys made key schedule
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16. Modern Cryptography
Feistel function:
1. Expansion- the 32-bit half-block is expanded
to 48 bits by duplicating half of the bits
2. 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 boxes
4. Permutation
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17. Modern Cryptography
Advanced Encryption Standard (AES) 2001
• Substitution-permutation network
• Not Feistel
• Fixed block size 128 bits
• Key size of 128, 192, or 256 bits
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18. Modern Cryptography
Advanced Encryption Standard (AES)
1. KeyExpansion
2. Initial Round
1. AddRoundKey
3. Rounds
1. SubEytes
2. ShiftRows
3. MixColumns
4. AddRoundKey
4.Final Round
1. SubBytes
2. ShiftRows
3. AddRoundKey
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19. Public-key cryptography
RSA- Ron Rivest, Adi Shamir, Leonard Adleman 1978
• Uses factoring problem (large primes)
• Two large primes of similar size > 100 digits
Example:
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 = 65
c = 6517 (mod 3233) = 2790
To decrypt c = 2790, we calculate
m = 27902753 (mod 3233) = 65
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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 communication
HTTPS, SSH, SFTP, SSL and TLS and others
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22. Some Tools of the trade
File Encryption
• Axantum
• WinZip
Disk encryption
• TrueCrypt
Network
• Open SSH
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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
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24. Questions?
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