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Hashing: SHA256 Tayler Angevine Bachelor of Arts Dr. Ken Blaha 3/13/2014

Hashing: SHA256 Tayler Angevine Bachelor of Arts Dr. Ken Blaha 3/13/2014. Introduction. Review the hash function SHA-256 Goal: understand how SHA-256 computes it’s hash. Why have I decided to focus on Sha-256 algorithms ? Battle tested Considered to be some of the “safest” algorithms

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Hashing: SHA256 Tayler Angevine Bachelor of Arts Dr. Ken Blaha 3/13/2014

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  1. Hashing: SHA256Tayler AngevineBachelor of ArtsDr. Ken Blaha3/13/2014

  2. Introduction • Review the hash function SHA-256 • Goal: understand how SHA-256 computes it’s hash. • Why have I decided to focus on Sha-256algorithms? • Battle tested • Considered to be some of the “safest” algorithms • Bitcoin is based around SHA-256. • The way the algorithm is implemented using MessageDigest left a lot of unknowns. • Was under the impression that I would need to code the algorithm.

  3. More intro • Named after it’s digest length. • Will not focus on • SHA-1 because it has been “broken” • Would rather focus on today’s standard rather than the past. • SHA-384 and SHA-512 because they are essentially the same. • Why go over the code? • I believe it is necessary to understand the code of an algorithm in order to recognize it’s weaknesses or it’s strengths.

  4. What is a hash? • Hash function takes a string of any length, and generates fixed-length output data. • It is not reversible. • Because you are taking a string and basically dividing it. • Therefore, you are losing information. • If you have lost information about the original input, then it is nearly impossible to reverse the hash.

  5. What makes a good hash? • Same input will always lead to the same output. • Avoids collision attacks

  6. A little information… • Sha 256 is more safe from collision attacks than other algorithms. • MD5 = 128 byte output, 64 bits of security • SHA-1 = 160 byte output, 80 bits of security. • SHA 256 = 256 byte output, 128 bits of security • What are collision attacks? • Find two input strings that produce the same hash. • “abc” • “aiieagnea;[sagjeiao;iaeohgao;ejagea” • Hash functions can have infinite input length, but a fixed output.

  7. How does it work? • Padding aka Preprocessing • Block decomposition • Hash Algorithm

  8. Preprocessing • Message (M) is l bits long. • Append message with a 1 • Followed by n zero bits. N is smallest, non-negative solution to the equation. • L + 1 + n = 448 mod 512 • This leaves enough room to append what we have so far with a 64-bit block that equals our message represented in binary. • Message = “abc” • 24 + 1 + N = 448.  N = 423 zero bits

  9. Notation • Algorithm uses AND, XOR, OR, Circular Right Shift, and Logical Right Shifts in order to compute the hash.

  10. AND Produces 1 if both p and q are 1’s.

  11. OR Produces 1 if p or q are 1

  12. XOR Produces 1 if p or q is 1, but not both.

  13. Circular Shift Right ShR(variable, number) • variable: a,b,c,d,e,f,g,h • Number: amount of shift.

  14. Logical Right ShiftRotR(variable, number) • Variable: a,b,c,d,e,f,g,h. • Number: amount of shifts

  15. Equations

  16. Where it starts to get complicated. • Generally H1– H8 are set to the first 32 bits of the fractional parts of the square roots of the first eight primes.

  17. Example • Square root of 2 = 1.414213562373095048801 • Fractional part = 0.41421356237309504. • Hexadecimal = 6A09E667.

  18. Where does our password come into play? • Or original password was padded to 512 bytes. Which is 16 words. • A 64 word array is created we will refer to as W • W0 – W15 are initialized to our padded password. • The rest (W16 – W63) are set to a value determined by this function • J is just the counter in a for loop.

  19. Algorithm Computation(executed 64 times)

  20. A – H are initialized with H1– H8

  21. Last Step • Take your original and H1– H8 add a – h to them.

  22. Issues • Putting together a puzzle • Some things are difficult to find answers to.

  23. Sources • Algorithm • http://csrc.nist.gov/groups/STM/cavp/documents/shs/sha256-384-512.pdf • http://www-ma2.upc.es/~cripto/Q2-06-07/SHA256english.pdf • Actual Implementation • http://www.cs.mcgill.ca/~zcao7/mutls/release/llvm-gcc-4.2-2.9.source/libjava/classpath/gnu/java/security/hash/Sha256.java • http://www.vipan.com/htdocs/bitwisehelp.html • Various Information • wikipedia.org/ • http://www.makeuseof.com/tag/md5-hash-stuff-means-technology-explained/

  24. More Sources • Various Information • http://crypto.stackexchange.com/questions/8636/what-does-message-schedule-mean-in-sha-256 • http://docs.oracle.com/javase/7/docs/api/java/security/MessageDigest.html • Converting bytes to a string • http://www.mkyong.com/java/how-do-convert-byte-array-to-string-in-java/ • Hash Calculator • http://www.xorbin.com/tools/sha256-hash-calculator

  25. QUESTIONS?

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