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Lecture 7 Overview

Lecture 7 Overview. Advanced Encryption Standard. 10, 12, 14 rounds for 128, 192, 256 bit keys Regular Rounds (9, 11, 13) Final Round is different (10 th , 12 th , 14 th ) Each regular round consists of 4 steps Byte substitution (BSB) Shift row (SR) Mix column (MC) Add Round key (ARK).

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Lecture 7 Overview

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  1. Lecture 7 Overview

  2. Advanced Encryption Standard • 10, 12, 14 rounds for 128, 192, 256 bit keys • Regular Rounds (9, 11, 13) • Final Round is different (10th, 12th, 14th) • Each regular round consists of 4 steps • Byte substitution (BSB) • Shift row (SR) • Mix column (MC) • Add Round key (ARK) CS 450/650 Lecture 7: AES

  3. AES Overview Plaintext (128) ARK Subkey0 9 rounds BSB SR Ciphertext (128) ARK Subkey10 CS 450/650 Lecture 7: AES

  4. 128-bit block  4 x 4 matrix 128 bits  16 bytes  b0, b1, b2, .., b15 State S0,0 S0,1 CS 450/650 Lecture 7: AES

  5. 128-bit key  4 x 4 matrix 128 bits  16 bytes  k0, k1, k2, .., k15 Key CS 450/650 Lecture 7: AES

  6. Four Operations • Byte Substitution • predefined substitution table s[i,j]  s’[i,j] • Shift Row • left circular shift • Mix Columns • 4 elements in each column are multiplied by a polynomial • Add Round Key • Key is derived and added to each column diffusion confusion diffusion and confusion confusion CS 450/650 Lecture 7: AES

  7. Shift Row (128-bit) CS 450/650 Lecture 7: AES

  8. Mix Column = * Multiplying by 1  no change Multiplying by 2  shift left one bit Multiplying by 3  shift left one bit and XOR with original value More than 8 bits  100011011 is subtracted CS 450/650 Lecture 7: AES

  9. Add Key = b’x bx kx XOR CS 450/650 Lecture 7: AES

  10. 4 bytes 4 bytes 4 bytes 4 bytes 4 bytes 4 bytes 4 bytes 4 bytes Key Generation Circular left shift 1byte S-box XOR Round constant XOR CS 450/650 Lecture 7: AES

  11. DES vs AES CS 450/650 Lecture 7: AES

  12. Cryptographic Hash Functions • Message Digest Functions • Protect integrity • Create a message digest or fingerprint of a digital document • MD4, MD5, SHA • Message Authentication Codes (MACs) • Protect both integrity and authenticity • Produce fingerprints based on both a given document and a secret key CS 450/650 Lecture 7: Hash Functions

  13. Message Digest Functions • Checksums fingerprint of a message • If message changes, checksum will not match • Most checksums are good in detecting accidental changes made to a message • They are not designed to prevent an adversary from intentionally changing a message resulting a message with the same checksum • Message digests are designed to protect against this possibility CS 450/650 Lecture 7: Hash Functions

  14. One-Way Hash Functions Example • M = “Elvis” • H(M) = (“E” + “L” + “V” + “I” + “S”) mod 26 • H(M) = (5 + 12 + 22 + 9 + 19) mod 26 • H(M) = 67 mod 26 • H(M) = 15 M H H(M) = h CS 450/650 Lecture 7: Hash Functions

  15. Collision Example • x = “Viva” • Y = “Vegas” • H(x) = H(y) = 2 x H H(x) = y H H(y) CS 450/650 Lecture 7: Hash Functions

  16. Collision-resistant, One-way hash fnc. • Given M, • it is easy to compute h • Given any h, • it is hard to find any M such that H(M) = h • Given M1, it is difficult to find M2 • such that H(M1) = H(M2) • Functions that satisfy these criteria are called message digest • They produce a fixed-length digest (fingerprint) CS 450/650 Lecture 7: Hash Functions

  17. Message Authentication Codes • A message authentication code (MAC) is a key-dependent message digest function • MAC(M,k) = h CS 450/650 Lecture 7: Hash Functions

  18. A MAC Based on a Block Cipher M1 M1 M1 XOR XOR Encrypt … Encrypt Encrypt MAC k k k CS 450/650 Lecture 7: Hash Functions

  19. Lecture 8 Secure Hash Algorithm CS 450/650 Fundamentals of Integrated Computer Security Slides are modified from Hesham El-Rewini

  20. Secure Hash Algorithm (SHA) • SHA-0 1993 • SHA-1 1995 • SHA-2 2002 • SHA-224, SHA-256, SHA-384, SHA-512 SHA-1 160-bit message digest A message composed of b bits CS 450/650 Lecture 8: Secure Hash Algorithm

  21. Step 1 -- Padding • Padding the total length of a padded message is multiple of 512 • Every message is padded even if its length is already a multiple of 512 • Padding is done by appending to the input • A single bit, 1 • Enough additional bits, all 0, to make the final 512 block exactly 448 bits long • A 64-bit integer representing the length of the original message in bits CS 450/650 Lecture 8: Secure Hash Algorithm

  22. Padding (cont.) Message 1 0…0 Message length 1 bit 64 bits Multiple of 512 CS 450/650 Lecture 8: Secure Hash Algorithm

  23. Example • M = 01100010 11001010 1001 (20 bits) • Padding is done by appending to the input • A single bit, 1 • 427 0s • A 64-bit integer representing 20 • Pad(M) = 01100010 11001010 10011000 … 00010100

  24. Example • Length of M = 500 bits • Padding is done by appending to the input: • A single bit, 1 • 459 0s • A 64-bit integer representing 500 • Length of Pad(M) = 1024 bits

  25. Step 2 -- Dividing Pad(M) • Pad (M) = B1, B2, B3, …, Bn • Each Bi denote a 512-bit block • Each Bi is divided into 16 32-bit words • W0, W1, …, W15 CS 450/650 Lecture 8: Secure Hash Algorithm

  26. Step 3 – Compute W16 – W79 • To Compute word Wj (16<=j<=79) • Wj-3, Wj-8, Wj-14 , Wj-16 are XORed • The result is circularly left shifted one bit CS 450/650 Lecture 8: Secure Hash Algorithm

  27. Step 4 – Initialize A,B,C,D,E • A = H0 • B = H1 • C = H2 • D = H3 • E = H4 CS 450/650 Lecture 8: Secure Hash Algorithm

  28. Initialize 32-bit words • H0 = 67452301 • H1 = EFCDAB89 • H2 = 98BADCFE • H3 = 10325476 • H4 = C3D2E1F0 • K0 – K19 = 5A827999 • K20 – K39 = 6ED9EBA1 • K40 – K49 = 8F1BBCDC • K60 – K79 = CA62C1D6 CS 450/650 Lecture 8: Secure Hash Algorithm

  29. Step 5 – Loop For j = 0 … 79 TEMP = CircLeShift_5 (A) + fj(B,C,D) + E + Wj + Kj E = D; D = C; C = CircLeShift_30(B); B = A; A = TEMP Done +  addition (ignore overflow) CS 450/650 Lecture 8: Secure Hash Algorithm

  30. Four functions • For j = 0 … 19 • fj(B,C,D) = (B AND C) OR ( B AND D) OR (C AND D) • For j = 20 … 39 • fj(B,C,D) = (B XOR C XOR D) • For j = 40 … 59 • fj(B,C,D) = (B AND C) OR ((NOT B) AND D) • For j = 60 … 79 • fj(B,C,D) = (B XOR C XOR D) CS 450/650 Lecture 8: Secure Hash Algorithm

  31. Step 6 – Final • H0 = H0 + A • H1 = H1 + B • H2 = H2 + C • H3 = H3 + D • H4 = H4 + E CS 450/650 Lecture 8: Secure Hash Algorithm

  32. Done • Once these steps have been performed on each 512-bit block (B1, B2, …, Bn) of the padded message, • the 160-bit message digest is given by H0 H1 H2 H3 H4 CS 450/650 Lecture 8: Secure Hash Algorithm

  33. SHA CS 450/650 Lecture 8: Secure Hash Algorithm

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