Preparedby:KMAkkasAli,AssociateProfessor,IIT,JU
PGDIT, JU
Lecture-9: Cryptographic Hash Function
 To introduce general ideas behind hashing and hash functions.
 Cryptographic hash function and its importance.
 Use and application of hash function.
 Desirable properties of a hash function.
 Simple hash functions.
Objectives of this Lecture:
9.2

PGDIT, JU9.3
What is Hashing?
 Hashing is the transformation of a string of characters into a
usually shorter fixed-length value or key that represents the
original string.
 Hashing is a cryptographic technique that produces hash values
using an algorithm or hash function for accessing data or for
security purposes.
 A hash value (or simply hash), also called a message digest, is a
number generated from a string of text. The hash is substantially
smaller than the text itself.
 In hashing, a fixed-length message digest is created out of a
variable-length message. The digest is normally much smaller than
the message.
 It plays a vital role in security system that creates a unique, fixed-
length signature for a message or data set.
 People commonly use them to compare sets of data. Since a hash
is unique to a specific message, even minor changes to that
message result in a dramatically different hash. Therefore it is very
resistant to tampering.

PGDIT, JU9.4
What is Hashing (cont…)
 Hashing also refers to a search technique or a method of accessing data records,
where search time is independent of the number of the elements in the
collection.
 Hashing is used to index and retrieve items in a database because it is faster to
find the item using the shorter hashed key than to find it using the original value.
 For example, consider a list of names in a database:
 Rassel Akram
 Asif Afzal Khan
 Khan Ataus Samad
 Anuradha Mondol
 Each of these names would be the key in the database for that person's data. A
database search mechanism would first have to start looking character-by-
character across the name for matches until it found the match.
 But if each of the names were hashed, it might be possible to generate a unique
four-digit key or index for each name. So you might get something like:
 1345 Rassel Akram
 3097 Asif Afzal Khan
 4060 Khan Ataus Samad
 7350 Anuradha Mondol
 A search for any name would first consist of computing the hash value (using the
same hash function used to store the item) and then comparing for a match
using that value. This is much more efficient than searching through all the
records till the matching record is found. Because, to find a match across four
digits, each having only 10 possibilities is faster, than across an unpredictable
value length where each character had 26 possibilities.

PGDIT, JU9.5
Importance of Hashing
 Hashing is used to index and retrieve items in a database
because it is faster to find the item using the shorter hashed
key than to find it using the original value.
 In addition to faster data retrieval, hashing is also used to
encrypt and decrypt digital signatures (used to authenticate
message senders and receivers).
 Hashing plays vital a role in security systems where it is used
to ensure that transmitted messages have not been tampered
with.
 The sender generates a hash of the message, encrypts it, and
sends it with the message itself. The recipient then decrypts
both the message and the hash, produces another hash from
the received message, and compares the two hashes. If they
are the same, there is a very high probability that the
message was transmitted intact.

PGDIT, JU9.6
Hash Function
 A hash function is a formula or an algorithm that-
 takes large data sets of variable length as input, and
 returns smaller data sets of fixed length as output.
 Since, the output is smaller than the input data, a hash
function compresses an n-bit message string to create an m-
bit string where n is normally greater than m.
 The values returned by a hash function are called hash values,
hash codes, hash sums, checksums or simply hashes.
 Hash function creates hash value in such a way that it is
extremely unlikely that some other text will produce the same
hash value.
 A hash table (also called hash map) is used
to implement an associative array that can
map keys to values. A hash table uses a
hash function to compute an index into an
array of buckets or slots, from which the
correct value can be found.

PGDIT, JU9.7
 A cryptographic hash function is a hash function that takes an
arbitrary block of data as input and returns a fixed-size bit
string as output. The returned value is called the cryptographic
hash value.
 Cryptographic hash function creates hash value in such a way
that any (accidental or intentional) change to the data will
change the hash value. Therefore, it is extremely unlikely that
some other text will produce the same hash value.
 The data to be encoded are often called the message, and the
hash value is sometimes called the message digest or simply
digest.

PGDIT, JU9.8
 In cryptographic hash function, even a small changes in the input
would cause a large change in the output.
 Figure below shows how the slight changes input (here in the
word "over") drastically change the resulting output.

PGDIT, JU9.9
Illustration: Cryptographic Hash Function
 An illustration of the potential use of a cryptographic hash is as
follows:
 Alice poses a tough math problem to Bob and claims she has solved it.
 Bob would like to try it himself, but would yet like to be sure that Alice
is not bluffing. Therefore, Alice writes down her solution, computes its
hash and tells Bob the hash value (whilst keeping the solution secret).
Then, when Bob comes up with the solution himself a few days later,
Alice can prove that she had the solution earlier by revealing it and
having Bob hash it and check that it matches the hash value given to
him before.

PGDIT, JU9.10
Use of Hash Function
 Cryptographic hash functions have many information security
applications, such as in-
 digital signatures
 message authentication codes (MACs)
 other forms of authentication
 Hash functions are primarily used to generate fixed-length
output data that acts as a shortened reference to the original
data. This is useful when the output data is too cumbersome
to use in its entirety.
 For example, consider a list of person’s names. Here, name of each
person is of variable length. Searching for a person's name in the list is
slow; time required to retrieve each name may also vary. But if each
name could be hashed to a fixed length integer, then searching and
retrieving each name will be performed in faster with constant time.
 Hash functions are also used to accelerate table lookup or
data comparison tasks such as finding items in a database,
detecting duplicated or similar records in a large file, finding
similar stretches in DNA sequences, and so on.

PGDIT, JU9.11
Hash Functions Used in Cryptography
 The two commonly used hash functions are MD5 and SHA-1.
 MD5:
 MD stands for Message Digest.
 Several MD hash algorithms designed by Ron Rivest are MD2, MD4
and MD5.
 The last version MD5 is more secured than the previous versions.
 It divides the message into blocks of 512 bits and creates a 128-bit
digest.
 SHA-1:
 SHA stands for Secure Hash Algorithm.
 This standard was developed by NIST (National Institute of
Standards and Technology).
 This standard is mostly based on MD5.
 Several versions of SHA standard were realsed: SHA-1, SHA-224,
SHA-256, SHA-384 and SHA-512.
 SHA-1 returns a string of 160 bits.
 Both MD5 and SHA-1 hash functions are built with the Merkle-
Damgard construction.

PGDIT, JU9.12
Hash Functions Used in Cryptography
Merkle-Damgard Scheme:
 The Merkle-Damgard construction method takes an arbitrary
sized input and breaks the input into fixed size blocks of the
same size as the output. It applies a one way compression
function to each of the blocks in turn, combining a block of
input with the output of the previous block. The last block has
bits representing the length of the entire message.
 A one way compression function takes two fixed size inputs - the key
and the plain text - and returns one single output - the cipher text
which is the same size as the plain text.
 An example of such a function is the Davis-Meyer compression function.
It feeds the previous hash value (Hi-1) as the plaintext to be encrypted.
It uses the each block of the message (mi) as the key. The output
ciphertext is then XORed with the previous hash value (Hi-1) to produce
the next hash value (Hi). In the first round when there is no previous
hash value it uses a predefined inital value (H0).

PGDIT, JU9.13
Application of Hash Function in Cryptography
Hash functions are used for:
 Verifying the integrity of message and file
 Verifying password for secure login
 fingerprints of keys
 authentication
 digital signatures
 Verifying the integrity of files or messages:
 An important application of secure hashes is verification of
message integrity. Determining whether any changes have been
made to a message (or a file), for example, can be accomplished
by comparing message digests calculated before, and after,
transmission (or any other event).
 For this reason, most digital signature algorithms only confirm the
authenticity of a hashed digest of the message to be "signed".
Verifying the authenticity of a hashed digest of the message is
considered proof that the message itself is authentic.

PGDIT, JU9.14
 Verifying password for secure login:
 A related application of hash function is password verification.
 Storing all user passwords as plaintext character can result in a massive
security breach if the password file is compromised.
 One way to reduce this danger is to only store the hash digest of each
password instead of the plaintext password in the table (a file) that is
stored by user identification.
 Any user can read the contents of the file, but, because the hash
function is a one-way function, it is almost impossible to guess the
value of the password.
 When the password is created , the system hashes it and stores the
hash in the password file.
 When the user sends her user ID and password, the system creates a
hash of the password and then compare the hash value with the one
stored in the file.
 If there is a match, the user is granted access; otherwise, access is
denied.

PGDIT, JU9.15
 File or data identifier:
 A message digest can also serve as a means of reliably identifying
a file;
 One of the main applications of a hash function is to allow the fast
look-up of a data in a hash table. Being hash functions of a
particular kind, cryptographic hash functions lend themselves well
to this application too.
 Authentication:
 Authentication is the assurance that the communicating entity is
the one that it claims to be.
 Cryptographic hash function can be used for provide
authentication.

PGDIT, JU9.16
 Digital Signature:
 Digital signature, first proposed in 1976 by Whitfield Diffie of
Stanford University, is a digital code (encrypted message digest)
that can be attached to an electronically transmitted message that
uniquely identifies the sender.
 Like a written signature, the purpose of a digital signature is to
guarantee that the individual sending the message really is who he
or she claims to be. It is linked to the data in such a manner that if
the data is changed, the digital signature is invalidated.
 When making a digital signature, cryptographic hash functions are
generally used to construct the message digest.
 A digital signature servers three important purposes:
 Verifies data integrity.
 Provides authentication of the sender.
 Provides non-repudiation

PGDIT, JU9.17
Properties of Cryptographic Hash Function
 A cryptographic hash function must be able to withstand all
known types of cryptanalytic attack.
 A desirable cryptographic hash function should have the following
properties:
 A hash function produces a fixed length value from a variable length source.
 It is easy to compute the hash value for any given message.
 Pre-image resistance: Given a hash h, it should be difficult to find any message
m such that h = hash(m). That is, it is infeasible to generate a message that has a
given hash.
 A function with this property is called a one-way function.
 Functions that lack this property are vulnerable to preimage attacks.
 Second pre-image resistance: Given a message m1, it should be difficult to find
another message m2 such that m1 ≠ m2 and hash(m1) = hash(m2).
 Functions that lack this property are vulnerable to second-preimage attacks.
 It is infeasible to modify a message without changing the hash.

PGDIT, JU9.18
Properties of Cryptographic Hash Function
 Collision resistance: It should be difficult to find two different messages
m1 and m2 with the same hash h. 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.
 A hash function must be referentially transparent, i.e., if called twice on
input that is "equal" (for example, strings that consist of the same sequence
of characters), it should give the same result.
 A hash procedure must be deterministic—meaning that for a given input
value, it must always generate the same hash value.
 Hash functions are destructive, as the original data is lost when hashed.
 A small change in the input m would cause a large change in the output of
the hash function.
 It should be impossible for an adversary to find two messages with
substantially similar digests; or to infer any useful information about the
data, given only its digest. Therefore, a cryptographic hash function should
behave as much as possible like a random function while still being
deterministic and efficiently computable.
 The above properties of a cryptographic hash function imply that a
malicious adversary cannot replace or modify the input data without
changing its digest. Thus, if two strings have the same digest, one can be
very confident that they are identical.

PGDIT, JU9.19
Simple Hash Function
Division-remainder method:
 Using this method, choose a number m that is larger than
the number n of keys in K (K is a set of keys). Generally,
the number m is chosen to be a prime number. The hash
function H is defined as:
H(k)= k (mod m) or, H(k)= k (mod m)+1
 Here k (mod m) denotes the remainder when k is divided
by m.
 The second formula is used when we want the hash
addresses to range from 1 to m rather than from 0 to m-1.
Some Popular Hash Function:
Here are some relatively simple hash functions that have been
used:
 Division-remainder method
 Mid-square method
 Folding method

PGDIT, JU9.20
Example: Division-remainder method:
Suppose a company with 68 employees assigned a 4-digit employee number
to each employee which is used as the primary key. Apply the division
method of hash function to each of the following employee number:
3205, 7148, 2345
Solution:
 Since, there are 68 employees in the company, two digit employee
number is sufficient to represent them.
 Highest 2 digit number is 99 and 97 is the nearest 2 digit prime
number of 99. So, we divide each of the 4 digit employee number by
97.
H(3205)= 3205 (mod 97)= 04.
H(7148)= 7148 (mod 97)= 67
H(2345)= 2345 (mod 97)= 17
 In the case that the memory addresses begin with 01 rather than 00,
we choose that the function H(k) = k(mod m)+1 to obtain. H(3205)=
3205 (mod 97)+1= 4+1=05

PGDIT, JU9.21
Mid-square method:
 Using this method, the key k is squared. Then the hash
function H is defined by:
H(k)=l,
Where l is obtained by deleting digits from both ends of k2.
Example: Mid-square method
Suppose a company with 68 employees assigned a 4-digit employee number
to each employee which is used as the primary key. Apply the mid-square
method of hash function to each of the following employee number:
3205, 7148, 2345
Solution:
 Observe that the 4th and 5th digits counting from right are chosen for
the hash address.
K 3205 7148 2345
K2 10272025 51093904 5499025
H(k) = I 72 93 99

PGDIT, JU9.22
Folding method:
 Using this method, the key k is portioned into a number of parts, k1, k2,
k3, …..kr, where each part, except possibly the last, has the same number
of digits as the required address. Then the parts are added together,
ignoring the last carry if any. That is:
 H(k)=k1+k2+k3+…..+kr , where the leading-digit carries, if any, are
ignored.
Example: Folding method
Suppose a company with 68 employees assigned a 4-digit employee number to
each employee which is used as the primary key. Apply the folding method of
hash function to each of the following employee number:
3205, 7148, 2345
Solution:
Chop the key into two parts and then add them.
 Observed that the leading digit from the 2nd function is ignored.
 Alternatively, reverse folding method may be used as:
H(3205)= 32+50=82
K 3205 7148 2345
H(k)=K1+k2 32+05=37 71+48=119 23+45=77
H(k) 37 19 77

Network security cryptographic hash function

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