1. Secured Hash Algorithm(SHA)
By – Debanjan Sadhya
(iwc )
Mayank Swarnkar
(iwc )

2. Contents Introduction Definition Properties of SHA SHA Functions
SHA Constants
Preprocessing in SHA
Hashing in SHA
Example (SHA-1)

3. Introduction SHA – Secure Hash Algorithm
Used for Authentication(Eg of Maths Problem)
Types of SHA-
SHA 0
SHA 1
SHA 2 – SHA 256, SHA 384, SHA 512
SHA 3

4. Secured Hash Function(SHF)

5. A cryptographic hash function takes an arbitrary block of data and returns a fixed-size bit string.
The data to be encoded is often called the "message," and the hash value is sometimes called the message digest or simply digest.
Used in digital signatures and message authentication codes.

6. Properties of SHA
It is easy to compute the hash value for any given message
It is infeasible to generate a message that has a given hash
It is infeasible to modify a message without changing the hash
It is infeasible to find two different messages with the same hash

7. Pre-image resistance
Given a hash h it should be difficult to find any message m such that
h = hash(m)
This concept is related to that of one-way . Functions that lack this property are vulnerable to preimage attacks.

8. Second pre-image resistance
Given an input m1 it should be difficult to find another input m2 where m1 ≠ m2 such that
hash(m1) = hash(m2)
This property is sometimes referred to as weak collision resistance, and functions that lack this property are vulnerable to second-preimage attacks.

9. Collision resistance
It should be difficult to find two different messages m1 and m2 such that
hash(m1) = hash(m2)
Such a pair is called a cryptographic hash collision. This property is sometimes referred to as strong collision resistance. It requires a hash value at least twice as long as that required for preimage-resistance, otherwise collisions may be found by a birthday attack.

10. SHA-1 Function

11. SHA 256 Function

12. SHA 384 and SHA 512 Functions

13. SHA 1 Constants

14. SHA 256 Constants

15. SHA 384 and SHA 512 Constants

16. Steps involved in SHA
Preprocessing
Hashing

17. Preprocessing It consists of three steps- Padding Parsing
Setting initial hash value

18. Padding
The message, M, shall be padded before hash computation begins. The purpose of this padding is to ensure that the padded message is a multiple of 512 or 1024 bits, depending on the algorithm.
SHA-1 and SHA-256 (l k = 448mod512 )
SHA-384 and SHA-512 (l k ” 896mod1024 )

19. Parsing the Padded Message
After a message has been padded, it must be parsed into Nm-bit blocks before the hash computation can begin.
SHA-1 and SHA-256
SHA-384 and SHA-512

20. Setting the Initial Hash Value (H(0))
SHA-1 For SHA-1, the initial hash value, H(0), shall consist of the following five 32-bit words, in hex: H 0(0) = H1(0 ) = efcdab89 H2(0) = 98badcfe H 3(0) = H4(0) = c3d2e1f0.

21. SHA-256
For SHA-256, the initial hash value, H(0), shall consist of the following eight 32-bit words, in hex:
H 0(0) = 6a09e667
H1(0) = bb67ae85
H2(0) = 3c6ef372
H 3(0 )= a54ff53a
H4(0 )= 510e527f
H 5(0) = 9b05688c
H 6(0) = 1f83d9ab
H 7(0) = 5be0cd19.

22. SHA-384
For SHA-384, the initial hash value, H(0), shall consist of the following eight 64-bit words, in hex:
H 0(0) = cbbb9d5dc1059ed8
H1(0) = 629a292a367cd507
H2(0) = a3070dd17
H 3(0) = 152fecd8f70e5939
H4(0 ) = ffc00b31
H 5(0) = 8eb44a
H 6(0) = db0c2e0d64f98fa7
H 7(0) = 47b5481dbefa4fa4.

23. SHA-512
For SHA-512, the initial hash value, H(0), shall consist of the following eight 64-bit words, in hex:
H 0(0) = 6a09e667f3bcc908
H1(0) = bb67ae8584caa73b
H2(0) = 3c6ef372fe94f82b
H 3(0 ) = a54ff53a5f1d36f1
H4(0) = 510e527fade682d1
H 5(0) = 9b05688c2b3e6c1f
H 6(0 ) = 1f83d9abfb41bd6b
H 7(0) = 5be0cd19137e2179.

24. To Summarize until now…
Basics -> Hex Digits(4 bit) and Words(32 and 64 bits)
Operations on Words -> SHR, ROTR, ROTL
Functions -> ch, parity, maj, Σ0(x), Σ1(x), σ0(x), σ1(x)
Constants ->
Eighty 32-bit words K0, K1,…, K79 (SHA-1)
Sixty-four 32-bit words K0, K1 , …K (SHA-256)
Eighty 64-bit words K0, K1,…K79 (SHA-384 & SHA-512)
Initial Hash Value H(0)

25. SHA-1
The algorithm uses 1) a message schedule of eighty 32-bit words, 2) five working variables of 32 bits each, and 3) a hash value of five 32-bit words. The final result of SHA-1 is a 160-bit message digest.
SHA-1 Preprocessing
1. Pad the message M
2. Parse the padded message into N 512-bit message blocks, M(1), M(2), …, M(N)
3. Set the initial hash value, H(0)

26. SHA-1
SHA-1 Hash Computation

28. After repeating steps one through four a total of N times (i. e
After repeating steps one through four a total of N times (i.e., after processing M(N)), the resulting 160-bit message digest of the message, M, is

29. SHA-256
The algorithm uses 1) a message schedule of sixty- four 32-bit words, 2) eight working variables of 32 bits each, and 3) a hash value of eight 32-bit words. The final result of SHA-256 is a 256-bit message digest. SHA-256 Preprocessing 1. Pad the message M 2. Parse the padded message into N 512-bit message blocks, M(1), M(2)…M(N) 3. Set the initial hash value, H(0)

30. SHA-256
SHA-256 Hash Computation

33. After repeating steps one through four a total of N times (i. e
After repeating steps one through four a total of N times (i.e., after processing M(N)), the resulting 256-bit message digest of the message, M, is

34. SHA-512
The algorithm uses 1) a message schedule of eighty 64-bit words, 2) eight working variables of 64 bits each, and 3) a hash value of eight 64-bit words. The final result of SHA-512 is a 512-bit message digest.
SHA-512 Preprocessing
1. Pad the message, M
2. Parse the padded message into N 1024-bit message blocks, M(1), M(2),…M(N)
3. Set the initial hash value, H(0)

35. SHA-512
SHA-512 Hash Computation Exceptions from SHA-256(else same as SHA-256)…

36. After repeating steps one through four a total of N times (i. e
After repeating steps one through four a total of N times (i.e., after processing M(N)), the resulting 512-bit message digest of the message, M, is

37. Example (SHA-1)
Let the message, M, be the 24-bit (l = 24) ASCII string "abc ", which is equivalent to the following binary string: The message is padded by appending a "1" bit, followed by 423 “0" bits, and ending with the hex value (the 2X32-bit word representation of the length, 24). Thus, the final padded message consists of one block (N = 1).

39. The following schedule shows the hex values for a, b, c, d, and e after pass t of the “for t = 0 to 79” loop

42. The final hash value, H(1), is calculated to be:
The resulting 160-bit message digest is:

43. Comparison of SHA Family

44. THANK YOU…