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Cryptology

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Rupesh Mishra
Rupesh Mishra
Tecnologia
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Cryptography “ You can’t make something secure if you don’t know how to break it” - Marc Weber Tobias
Definition • Cryptography is the science of disguising messages so that only the intended recipient can decipher the received message. • Secret Writing
Scenario
Terminologies • Plain text • Cipher text • Encryption • Decryption • Cryptanalysis • Cryptology
• Encryption: c = Ee(p) • Decryption: p = Dd(c) • Here p is a block of plaintext, c is a block of ciphertext, E is the encryption function, e is the encryption key, D is the decryption function and d is the decryption key. Cryptography
Cryptanalysis • Cryptography is the art and science of creating secret codes. • Cryptanalysis is the art and science of breaking those code.
Cryptanalysis Attack Ciphertext Only Brute-Force Statistical Pattern Known Plaintext Chosen- Plaintext Chosen- Ciphertext
Crypto- graphy Crypt- analysis Cryptology
SymmetricCiphers Substitution Cipher Mono-alphabetic Polyalphabetic Transposition Cipher
Mono-alphabetic Cipher • Additive / Caesar / Shift Cipher • Multiplicative Cipher • Affine Cipher
Caesar Cipher
Representation of Character
Shift Cipher • Encryption o C=(P+K1) Mod 26 • Decryption o P=(C-K1) Mod 26 https://www.youtube.com/watch?v=fEULLhEA4Vk
• The Additive cipher replaces each alphabet in a text by the alphabet k positions away (in the modulo 26 sense). • For k = 3 W H A T I S Y O U R N A M E becomes Z K D W L V BR X U Q D P H
Multiplicative Cipher • Encryption o C=(P * K1) Mod 26 • Decryption o P=(C * K1 -1) Mod 26
Affine Cipher • Combination of Additive and Multiplicative • Encryption o C=(P * K1 + K2) Mod 26 • Decryption o P=((C – K2 )* K1 -1) Mod 26
Cryptanalysis • Brute-Force Attack • Statistical Attack • Frequency of Occurrence of letters.(E,T,A,O,I,N,S,H,R,D……) • Grouping of Di-gram (HE,IN,AN,IS...) and Tri-grams (THE,ING,AND,HER…).
Poly-alphabetic Cipher • Each occurrence of character may have a different substitution. • One to Many • Vigenere Cipher , Play-fair Cipher, Hill Cipher ,Vernam Cipher.
Vigenere Cipher • Blaise de Vigenere, Mathematician • Secret Key of length m (K1,K2.......,Km) is required • Key stream Not depend on plaintext character. • Encryption depends on the position of character in the plaintext.
Example • Plaintext : SHE IS LISTINING • Key : PASCAL • Cipher text : HHW KS WXSLGNTCG
Plaintext S H E I S L I S T I N I N G P Values 18 07 04 08 18 11 08 18 19 04 13 08 13 06 K Values 15 00 18 02 00 11 15 05 08 02 00 11 05 00 C Values 07 07 22 10 18 22 23 23 11 06 13 19 02 06 Cipher text H H W K S W X X L G N T C G
Plaintext S H E I S L I S T I N I N G P Values 18 07 04 08 18 11 08 18 19 04 13 08 13 06 K Values 15 00 18 02 00 11 15 00 08 02 00 11 05 00 C Values 07 07 22 10 18 22 23 18 11 06 13 19 02 06 Cipher text H H W K S W X S L G N T C G
Play-fair Cipher • Used by British army during World war I • Secret key made of 25 alphabet arranged in 5*5 Matrix. • Two step process o Creation of matrix o Encryption
Question (10 Marks) Dec -2012
Solution • Plaintext : SHE IS LISTINING • Key : MORNING M O R N I G A B C D E F H J K L P Q S T U V W X YZ
Solution • SH EI SL IS TI NI NG • SH = QJ H J Q S
Solution • SH EI SL IS TI NI NG • EI = KM M O R N I G A B C D E F H J K
Solution • SH EI SL IS TI NI NG • SL (SAME ROW)= TP L P Q S T
Solution • SH EI SL IS TI NI NG • IS = NT • TI(SAME COLUMN) = YD M O R N I G A B C D E F H J K L P Q S T U V W X YZ
Solution • SH EI SL IS TI NI NG • NI(SAME ROW) = IM • NG = MC M O R N I G A B C D E F H J K L P Q S T U V W X YZ
Hill Cipher • Lester S. Hill • Block Cipher • Key is square matrix of order m*m • Key Matrix need to have multiplicative inverse. • Difficult to break
Example • Plain text = CAT Encryption CAT = FIN • 𝟐 𝟎 𝟏𝟗 × 𝟗 𝟐𝟒 𝟏 𝟏𝟑 𝟏𝟔 𝟏𝟎 𝟏 𝟏𝟎 𝟏𝟓 = 𝟑𝟏 𝟐𝟏𝟔 𝟐𝟑𝟓 𝑴𝒐𝒅 𝟐𝟔 = 𝟓 𝟖 𝟏𝟑 Decryption FIN = CAT • 𝟓 𝟖 𝟏𝟑 × 𝟖 𝟓 𝟏𝟎 𝟐𝟏 𝟖 𝟐𝟏 𝟐𝟏 𝟏𝟐 𝟖 = 𝑴𝒐𝒅 𝟐𝟔 = 𝟐 𝟎 𝟏𝟗
One-Time Pad • Vernam Cipher. • Key used once can not be reused. • Key length is equal to message length. • Book cipher / Running Key cipher
Plaintext V E R N E M C I P H E R Numeric Code 21 04 17 13 00 12 02 08 15 07 04 17 Key 76 48 06 82 44 03 58 11 60 05 48 88 Sum 97 52 33 95 44 15 60 19 75 12 52 105 Mod 26 19 00 07 17 18 15 08 19 23 12 00 01 Ciphertext T A H R S P I T X M A B
Book Cipher • Running Key cipher.
Cipher Block Cipher Polygram Substitution Stream Cipher Homophonic Substitution
Transposition • Permutation of position of Plaintext alphabet. • Rail Fence Technique • Simple Columnar Transposition • Simple Columnar Transposition with Multiple Round
Cryptography Encryption Decryption
Cryptography Create secret Code • Encryption o CT = Ek (PT) • Decryption o PT=Dk (CT) = Dk (Ek (PT))
Cryptography • Input to the process o Algorithm o Key
Cryptography Symmetric Key Asymmetric Key
Symmetric Key • Same key is used for encryption and decryption of message. • Key Exchange Problem
Diffie-Hellman Algorithm 1. Pick random, secret x 2. Compute A = gx mod n 3. Send A to Bob 4. K1 = Bx Mod n 1. Pick random, secret y 2. Compute B = gy mod n 3. Send B to Alice 4. K2 = Ay Mod n Alice and Bob agree on two prime number n and g
Diffie – Hellman K1 = (gx mod n)y = gxy mod n K2 = (gy mod n)x = gxy mod n • Let n = 11 and g = 7 • Let x = 3 and compute A • Let y = 6 and compute B • Calculate K1 and K2
Solution 1. N = 11 , g = 7 2. x = 3 then A = 73 Mod 11 = 2 3. y = 6 then B = 76 Mod 11 = 4 4. K1 = 43 Mod 11 = 9 5. K2 = 26 Mod 11 = 9
Problem with Algorithm • Man in Middle attack
Asymmetric Key
Cryptology

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Cryptology

Notas do Editor

  1. Breaking Code
  2. KAISISKI TEST IS USED TO BREAK THE CODE
  3. Pattern Attack is Possible 25! Ways if applying Brute-force attack
  4. Making Code