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Lecture 10 Overview

Lecture 10 Overview. 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

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Lecture 10 Overview

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  1. Lecture 10 Overview

  2. 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 10: Hash Functions

  3. 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 10: Hash Functions

  4. 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 10: Hash Functions

  5. A MAC Based on a Block Cipher • M1 • M1 • M1 • XOR • XOR • Encrypt • … • Encrypt • Encrypt • MAC • k • k • k CS 450/650 Lecture 10: Hash Functions

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

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

  15. Lecture 11 Digital Signatures CS 450/650 Fundamentals of Integrated Computer Security Slides are modified from Hesham El-Rewini

  16. Digital Signatures • A digital signature can be interpreted as indicating the signer’s agreement with the contents of an electronic document • Similar to handwritten signatures on physical documents CS 450/650 Lecture 11: Digital Signatures

  17. Digital Signature Properties • Unforgeable: Only the signer can produce his/her signature • Authentic: A signature is produced only by the signer deliberately signing the document CS 450/650 Lecture 11: Digital Signatures

  18. Digital Signature Properties • Non-Alterable: A signed document cannot be altered without invalidating the signature • Non-Reusable: A signature from one document cannot be moved to another document • Signatures can be validated by other users • the signer cannot reasonably claim that he/she did not sign a document bearing his/her signature CS 450/650 Lecture 11: Digital Signatures

  19. Digital Signature Using RSA • The RSA public-key cryptosystem can be used to create a digital signature for a message m • Asymmetric Cryptographic techniques are well suited for creating digital signatures • The signer must have an RSA public/private key pair • c = Me mod n • M = cd mod n CS 450/650 Lecture 11: Digital Signatures

  20. Signature Generation (Signer) Message Redundancy Function Formatted Message Encrypt Private Key Signature CS 450/650 Lecture 11: Digital Signatures

  21. Signature Verification Signature Public Key Decrypt Formatted Message Verify Message CS 450/650 Lecture 11: Digital Signatures

  22. Example • Generate signature S • d = 53 • e = 413 • n = 629 • m = 250 • Assume that R(X) = X • S = R(m)e mod n • S = 25053 mod 629 = 411 CS 450/650 Lecture 11: Digital Signatures

  23. Example • Verify signature with message recovery • Public key (e) = 413 • n = 629 • S = 411 • R(m) = Se mod n • R(m) = 411413 mod 629 = 250 • Verifier checks that R(m) has proper redundancy created by R (none in this case) • m = R-1(m) = 250 CS 450/650 Lecture 11: Digital Signatures

  24. Creating a forged signature • Choose a random number between 0 and n-1 for S • S = 323 • Use the signer’s public key to decrypt S • R(m) = 323413 mod 629 = 85 • Invert R(m) to m: m = 85 • A valid signature (323) has been created for a random message (85) CS 450/650 Lecture 11: Digital Signatures

  25. Redundancy Function • The choice of a poor redundancy function can make RSA vulnerable to forgery • A good redundancy function should make forging signatures much harder CS 450/650 Lecture 11: Digital Signatures

  26. Example • generate signature S • d = 53 • e = 413 • n = 629 • m = 7 • Assume that R(X) = XX • S = R(m)e mod n • S = 7753 mod 629 = 25 CS 450/650 Lecture 11: Digital Signatures

  27. Example • verify signature with message recovery • Public key (e) = 413 • n = 629 • S = 25 • R(m) = Se mod n • R(m) = 25413 mod 629 = 77 • The verifier then checks that R(m) is of the form XX for some message X • m = R-1(m) = 7 CS 450/650 Lecture 11: Digital Signatures

  28. Forging signature (revisited) • Choose a random number between 0 and n-1 for S • S = 323 • Use the signer’s public key to decrypt S • R(m) = 323413 mod 629 = 85 • However, 85 is not a legal value for R(m) • so S = 323 is not a valid signature CS 450/650 Lecture 11: Digital Signatures

  29. Privacy • Signature provides only authenticity. • How can we provide privacy in addition? CS 450/650 Fundamentals of Integrated Computer Security

  30. Simple Scenario of Digital Signature

  31. Getting a Message Digest from a document Hash Message Digest CS 450/650 Lecture 11: Digital Signatures

  32. Generating Signature Message Digest Signature Encrypt using private key CS 450/650 Lecture 11: Digital Signatures

  33. Appending Signature to document Append Signature CS 450/650 Lecture 11: Digital Signatures

  34. Verifying Signature Hash Message Digest Message Digest Decrypt using public key CS 450/650 Lecture 11: Digital Signatures

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