Basics of Cryptography

For the beginners, by a beginner

 Security Enthusiast
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 Encoding
 Encryption
 Obfuscation
 Cryptography
 Cryptanalysis
 Steganography

 Transposition
 scytale
 Substitution
 Caesar cipher
 Enigma
 Shannon’s law of secrecy
 PGP

 Messages is split in to fixed size blocks.

 Electronic CodeBook (ECB)
 Cipher Block Chaining (CBC)
 Cipher FeedBack(CFB)
 Output Feedback(OFB)
 Counter (CTR)
 Galois Counter Mode (GCM)

 Required to align data to Block length.
 Bit Padding
 Byte Padding
 Zero Padding
 ANSIx.923
 ISO-10126
 PKCS#7
 ISO/IEC 7816-4

 One way function.
 Arbitrary length input, fixed length output.
 Examples:
 CRC(16/32)
 MD(4/5)
 SHA(1/2/3/4)

 Integers
 Prime
 Co-prime
 Modulus
 Congruenc
e
 Group
 Modulus (M)
 Operation
 Identity
 Inverse
 Generator
 Ring
 Order (M-1)
iff M is
prime.

 Diffie-Hellman Key Exchange
 Alice and Bob agree to use a
modulus p = 23 and
generator g = 5.
 Alice chooses a secret
integer a = 6, then sends
Bob A = ga mod p
 A = 56 mod 23 = 8
 Bob chooses a secret
integer b = 15, then sends
Alice B = gb mod p
 B = 515 mod 23 = 19
 Alice computes s = Ba mod p
 s = 196 mod 23 = 2
 Bob computes s = Ab mod p
 s = 815 mod 23 = 2
 Alice and Bob now share a secret
(the number 2).

 Based on intractability principle
 Multiplying two large integers is easy
 Finding prime factors of large integers is an intractable problem.
 Computations are performed in “Group” modulo M.
 M being a very large prime.
 2 keys are generated simultaneously.
 Inverse of each other (modulo M).
 One encrypts (Public Key)
 Other decrypts (Private Key)

Encryption (P=5)
C = Pe
mod n 53 % 33 = 125 % 3 = 26
Decryption
P = Cd mod n 267 % 33 = 8031810176 % 33 = 5 OR
267 % 33 = 26 (3+3+1) % 33 = (263%33)* (263%33)* (26%33) = 5
Key Generation
Select 2 primes: p,q p = 11, q = 3
Calculate: n = p*q n = 33
Calculate: Φ(n) = (p-1)*(q-1) Φ(n) = 20
Choose e : gcd(e, Φ(n)) = 1, (e,n) is public key e = 3; Kpub = (3,33)
Find d : e*d = 1 mod Φ(n), (d,n) is private key d = 7, Kpriv = (7,33)

Basics of Cryptography

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