1

CryptologyDUH BRX UHDGB?

Slides by Raymond Borges

2

Outline

• Background• Ancient Cryptography• Frequency Analysis• Modern Cryptography• Secure Communication• Tools of the trade• Conclusion

3

Background

Cryptology

Cryptography Cryptanalysis

4

Background

Crypto | graphy

hidden/secret writing

5

The Ancient Art of Secret Messages

Cryptography - practice and study of techniques for secure communication

Cypher text Encryption -------------------- Decryption

6

Background

CryptographyPrinciples and methods for:1. Transforming message into unintelligible2. Transforming message back to original form

Secret password #$c*&c!~`fde1 Secret password

1 2

7

Background

Cryptanalysis Principles and methods for:• Retransforming message back to original form• Without knowledge of key

#$c*&c!~`fde1 Secret password

8

Background

Encryption

Transposition Substitution

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

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=D

p = D(k, c) = (c − k) mod 26D=4 (4-3) mod 26 = 1

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 × 1026

Impossible to crack? No….

Polyalphabetic tougher…

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

13

Frequency analysis

• Most frequently occurring trigrams ordered by decreasing frequency are:

14

Polyalphabetic Ciphers

• The Vigenère cipher • First letter use key 1• Second uses key 2• Third uses key 3

To Decrypt go backwards

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

16

Modern Cryptography

Feistel 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

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

18

Modern CryptographyAdvanced Encryption Standard (AES)

1. KeyExpansion2. Initial Round

1. AddRoundKey3. Rounds

1. SubEytes2. ShiftRows3. MixColumns4. AddRoundKey

4.Final Round 1. SubBytes2. ShiftRows3. AddRoundKey

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

20

Public-key cryptography

Encryption Decryption c = me (mod n) m = cd (mod n)

Example:To encrypt m = 65c = 6517 (mod 3233) = 2790

To decrypt c = 2790, we calculatem = 27902753 (mod 3233) = 65

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

22

Some Tools of the trade

File Encryption• Axantum• WinZip

Disk encryption• TrueCrypt

Network• Open SSH

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

24

Questions?