HASH FUNCTION AND MESSAGE DIGEST

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Lesson 23

HASH FUNCTION AND MESSAGE DIGEST

There are two terms that you should note here hash function and message digest. Hash function is a one-

way mathematical function applied to a message. Result of the hash function is unique to each message

called Message Digest. A message digest is a single large number typically between 128 to 256 bits in length.

Thus, we can have up to 2256 different messages each having a unique message digest associated with it. This

gives rise to almost an incalculable figure. We can safely assume that each different message that can

possibly be typed would have a unique message digest on applying a hash function. A hash function is said

to be one way because we cannot go back to the original text on applying the hash function to a message

digest. Basically, the concept of hash function and message digest is used to confirm the integrity of a

message. Following is the example of a hash function that can be used in a code (no need to prepare it for

exam)

"char XORhash( char *key, int len)

{

char hash;

int i;

for (hash=0, i=0; i<len; ++i) hash=hash^key[i];

return (hash%101);

/* 101 is prime */

Following example shows how a text message is encrypted and digitally signed using public key

cryptography:

First of all, the sender types a text message "Together, we shall make Pakistan strong...". A hash function is

applied on the message to get the message digest. Assume the message digest comes to be "1967..." in this

case. The message is encrypted using public key of the receiver, thus it becomes scrambled or confidential.

Then the sender adds his private key in the obtained message digest to create his digital signatures. This

digitally singed message is received by the receiver, who applies the pubic key of the sender to decrypt the

digital signature and reveal the message digest. Then the receiver uses his private key to unscramble the

message itself, and applies the same hash function received from the sender to get a message digest. The

receiver compares this message digest with the one sent by the sender through digital signature. If both are

the same it ensures that the message has not been altered during its transmission. Figures 1-4 given below

explain this concept:

Public

Together, we shall make

key

Pakistan strong ....

receiver

Private key

sender

1967....

Fig. 1

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Confidential

message

a7u/b34+...

Block Statement Starts Here

3uk7b/...

Digital

Signature

Block Statement Ends Here

Fig.2

Private Key

Receiver

a7u/b34+...

Public Key

Sender

3uk7b/...

Fig. 3

Together, we shall make

Pakistan strong ....

1967....

Fig. 4

Process of Sending Messages Using Public Key Cryptography

Fig. 5 below shows the working of the digital signature technology:

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How Digital Signature Technology

Works?

The Process of Sending Messages Using Public Key Cryptography

Hash

Public Key receiver

Private Key receiver

Hash

Sender

Receiver

Original

Scrambled

Original

IIneernet

ntt rnet

Scrambled+Signed

Message

Message Digest + Private Key of sender

Public Key sender to reveal Message Digest

Fig. 5

Note that following steps are involved in the digital signature process:

1. Hash function is applied to the original message in order to find the message digest.

2. Public Key of the receiver is used to encrypt the message.

3. A digital signature is attached to the scrambled message by signing the message digest with

Private Key of the sender.

4. The encrypted message, the digital signature and the hash function are sent to the receiver.

5. Public Key of the sender is used by the receiver to reveal the message digest and, thus, to

confirm identity/authenticity of the sender. In this regard, the receiver finds the digital

certificate certifying the public key of the sender and checks whether the digital signature can

be decrypted with the public key on the certificate and whether or not this certificate had been

issued to the sender by a trust-worthy certification authority.

6. Receiver uses his/her Private Key to decrypt the message. Private Key is a secret key only

known to the user.

7. Receiver applies hash function to the received original message and computes the message

digest. If this message digest matches with the one received from the sender, it confirms that

the message has not been altered during transmission. This ensures integrity of the message.

Note that a symmetric key can also be used for encrypting a message instead of using the pair of public and

private keys. The advantage of using symmetric key is that since symmetric algorithms are faster as

compared to asymmetric, therefore, the encryption of a message with the symmetric key takes place quickly.

In order to send the symmetric key to the receiver, however, the asymmetric cryptography has to be used.

PGP uses this system. See Fig. 6 below.

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How Digital Signature Technology

Works?

The Process of Sending Messages Using Public Key Cryptography

Hash

Symmetric Key

Hash

Sender

Receiver

Original

Scrambled

Original

IIneernet

ntt rnet

Scrambled+Signed

Message

Message Digest + Private Key of sender

Public Key sender to reveal Message Digest

Fig. 6

Where only the authenticity is to be ensured and not the integrity, then a name or a piece of text can be

chosen to create the digital signatures. In Fig. 7 below, the word "Imran" has been used to create a digital

signature which can commonly be used for all different messages.

Note that a digital or electronic signature is believed to be more reliable as compared to paper signatures

because it is not ordinarily possible to copy or forge an electronic/digital signature. But, that is very much

possible in case of paper signatures.

Symmetric Key

Original

Scrambled

Inneernet

I tt rnet

Scrambled+Signed

Message

Imran + Private Key of sender

Public Key sender to reveal the word Imran

Fig. 7

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Public Key Infrastructure (PKI)

A PKI is defines as a structured system that provides key management facilities, storage and management

facilities of digital certificates and involves a certification authority. PKI has its application in online

contracts, e-banking, electronic payment systems such as electronic checks, credit card based systems,

electronic cash, micro payment systems etc.

Key Length

A cryptographic key is represented as a string of binary digits 0's & 1's- inside a computer. If a key is 1 bit

in length it means two possible keys, that is, 0 and 1. If a key is 2 bits in length it means four possible key

values, 00, 01, 10 and 11. A Key having 3 bits length means 8 possible values -

000,001,010,011,100,101,110,111. From this, one can derive a general formula, that is, Number of keys =

2(number f bits)

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