Blockchain Technology - Week 6 - Role of Cryptography in Blockchain
3 likes499 views
The document discusses the role of cryptography in blockchain, focusing on hashing and the RSA algorithm. It explains key concepts, properties of hashing, and provides detailed examples of encryption and decryption using the RSA methodology, as well as the operation of secure hashing algorithms like SHA-1 and SHA-2. The session concludes with a mention of upcoming topics related to fraud and intrusion detection.
![Fast Computation for xd (mod n)
Let t be the number of bits for integer d, e.g.,
If d=5=1012 , then t=3
y=1;
for (i=t; i≧0; i--) {
y=(y*y)%n;
if (d[i]==1) y=(y*x)%n;
}](https://image.slidesharecdn.com/btweek6-181217085108/85/Blockchain-Technology-Week-6-Role-of-Cryptography-in-Blockchain-21-320.jpg)
Blockchain Technology - Week 6 - Role of Cryptography in Blockchain
- 1. Blockchain Technology Week 6 Unit III – Role of Cryptography in Blockchain Ferdin Joe John Joseph, PhD Faculty of Information Technology Thai-Nichi Institute of Technology, Bangkok Venue: D603
- 2. Week 6 – Unit III Agenda • Role of Cryptography in Blockchain • RSA and SHA 2 Faculty of Information Technology, Thai-Nichi Institute of Technology
- 3. Blockchain’s Encryption Faculty of Information Technology, Thai-Nichi Institute of Technology 3
- 4. Faculty of Information Technology, Thai-Nichi Institute of Technology 4
- 5. Faculty of Information Technology, Thai-Nichi Institute of Technology 5
- 6. Faculty of Information Technology, Thai-Nichi Institute of Technology 6
- 7. Bitcoin Hash • The corresponding SHA-256 of the sentence “How to buy Bitcoin?” looks like this: 156aedcfab1d49f73abddd89faf78d9930e4b523ab804026310c973bf a707d37 • If we remove only one symbol – for example the question mark “?” – the hash of “How to buy Bitcoin” looks like this: 4314d903f04e90e4a5057685243c903fbcfa4f8ec75ec797e1780e d5c891b1bf Faculty of Information Technology, Thai-Nichi Institute of Technology 7
- 8. What is hashing • Hashing means taking an input string of any length and giving out an output of a fixed length. Faculty of Information Technology, Thai-Nichi Institute of Technology 8
- 9. Properties of Hashing • Deterministic • Quick Computation • Pre-image resistance Faculty of Information Technology, Thai-Nichi Institute of Technology 9
- 10. Properties of hashing - Deterministic • No matter how many times you parse a particular input through a hash function you will always get the same result. • This is critical because if you get different hashes every single time it will be impossible to keep track of the input. Faculty of Information Technology, Thai-Nichi Institute of Technology 10
- 11. Properties of hashing – Quick Computation • The hash function should be capable of returning the hash of an input quickly. • If the process isn’t fast enough then the system simply won’t be efficient. Faculty of Information Technology, Thai-Nichi Institute of Technology 11
- 12. Properties of hashing – Pre-image resistance • It is infeasible to determine A, where A is the input and H(A) is the output hash. Faculty of Information Technology, Thai-Nichi Institute of Technology 12
- 13. Faculty of Information Technology, Thai-Nichi Institute of Technology 13
- 14. The RSA Algorithm • Based on the idea that factorization of integers into their prime factors is hard. ★ n=p．q, where p and q are distinct primes • Proposed by Rivest, Shamir, and Adleman in 1977 and a paper was published in The Communications of ACM in 1978 • A public-key cryptosystem
- 15. RSA Algorithm • Bob chooses two primes p,q and compute n=pq • Bob chooses e with gcd(e,(p-1)(q-1))= gcd(e, ψ(n))=1 • Bob solves de≡1 (mod ψ(n)) • Bob makes (e,n) public and (p,q,d) secret • Alice encrypts M as C≡Me (mod n) • Bob decrypts by computing M≡Cd (mod n)
- 16. Proof for the RSA Algorithm • Cd ≡ (Me)d ≡ Med ≡ M1+kφ(n) ≡M (mod n) by Euler’s theorem and Exercise 19 on p.192 • p=885320963, q=238855417, • n=p．q=211463707796206571 • Let e=9007, ∴ d=116402471153538991 • M=“cat”=30120, C=113535859035722866
- 17. Another Example • n=127x193=24511, φ(n)=24192 • e=1307, d=10643 • Encrypt “box” with M=21524, then C=? Encrypt the following message Formosa means a beautiful island
- 18. Selected Problems from P.192-200 (1) n=11413=101x113, so p=101, q=113 ψ(n)=(p-1)x(q-1)=100x112=11200 Choose e=7467, then gcd(e, ψ(n))=1 Solve de≡1 (mod ψ(n)) to get d=3 If the ciphertext C=5859, then the plaintext M≡Cd ≡58593 ≡1415 (mod 11413)
- 19. Fast Computation of xd (mod n) • 1235 mod 511 • 1235 ≡ 28153056843 mod 511 • 1232 ≡ 310 (mod 511) • 1234 ≡ 32 (mod 511) • 1235 ≡ 123101b ≡1234 ×123 ≡ 359 (mod 511)
- 20. Fast Computation for xd (mod n) y=1; while (d != 0) { if ((d%2) != 0) { y=(y*x)%n; d--; } d>>1; x=(x*x)%n; /* x^(2k) */ }
- 21. Fast Computation for xd (mod n) Let t be the number of bits for integer d, e.g., If d=5=1012 , then t=3 y=1; for (i=t; i≧0; i--) { y=(y*y)%n; if (d[i]==1) y=(y*x)%n; }
- 22. The Concept and Criteria 1. Ek(Dk(m))=m and Dk(Ek(m))=m for every message m in M, the set of possible messages, every key k in K, the set of possible keys 2. For every m and every k, then values of Ek(m) and Dk(m) are easy to compute 3. For every k, if someone knows only the function Ek, it is computationally infeasible to find an algorithm to compute Dk 4. Given k, it’s easy to find the functions Ek and Dk
- 23. Secure Hash Algorithm (SHA) • SHA-0 1993 • SHA-1 1995 • SHA-2 2002 • SHA-224, SHA-256, SHA-384, SHA-512 SHA-1 A message composed of b bits 160-bit message digest CS 450/650 Lecture 8: Secure Hash Algorithm 23
- 24. 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 24
- 25. Padding (cont.) Message Message length1 0…0 64 bits Multiple of 512 1 bit CS 450/650 Lecture 8: Secure Hash Algorithm 25
- 26. 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
- 27. 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
- 28. 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 28
- 29. 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 29
- 30. 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 30
- 31. 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 31
- 32. 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 32
- 33. 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 33
- 34. 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 34
- 35. 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 35
- 36. SHA Output size (bits) Internal state size (bits) Block size (bits) Max message size (bits) Word size (bits) Rounds Operations Collisions found SHA-0 160 160 512 264 − 1 32 80 +, and, or, xor, rot Yes SHA-1 160 160 512 264 − 1 32 80 +, and, or, xor, rot None (252 attack) SHA-2 256/224 256 512 264 − 1 32 64 +, and, or, xor, shr, rot None 512/384 512 1024 2128 − 1 64 80 +, and, or, xor, shr, rot None CS 450/650 Lecture 8: Secure Hash Algorithm 36
- 37. Next Week • Fraud and Intrusion Detection 37 Faculty of Information Technology, Thai-Nichi Institute of Technology