Digital signatures are like electronic “fingerprints.” In the form of a coded message, the digital signature securely associates a signer with a document in a recorded transaction

Where public & private key uses to verify the data integrity and authenticity ,

**RSA Principle**

- n=pqn=pq, where pp and qq are distinct primes.
- ϕ=(p−1)(q−1)
- e<ne<n such that gcd(e,ϕ)=1gcd(e,ϕ)=1
- d=e−1modϕd=e−1modϕ
- c=memodn,1<m<nc=memodn,1<m<n
- m=cdmodn

**Uses of digital signatures**

**Authentication:**Digital signatures can be used to authenticate the**source of messages**. When ownership of a digital signature**secret key**is bound to a specific user, a valid signature shows that the message was sent by that user.**Integrity:**Although encryption hides the contents of a message, it may be possible to change an encrypted message without understanding it. However, if a message is digitally signed, any change in the message after signature will invalidate the signature.**Non-repudiation: Non-repudiation of origin, is an important aspect of**digital signatures. By this property an entity that has signed some information cannot at a later time deny having signed it.

**Digital Signature Properties**

- The digital signature must have the following properties:
- It must
**verify the author** - It must
**authenticate the contents**at the time of the signature. - It must be
**verifiable by third parties**to resolve disputes. - It must
**verify the date and time**of the signature.

- It must
- Thus, the digital signature function includes the authentication function.

**Digital Signature Requirements**

- The signature must be a bit pattern that depends on the message being signed.
- must use some information(Key) unique to the sender
- to prevent both forgery and denial.

- It must be relatively easy to produce the digital signature.
- It must be relatively easy to recognize and verify the digital signature
- It must be
**computationally****infeasible to forge**a digital signature- with fraudulent message for existing signature
- with fraudulent signature for given message

- It could be able to save digital signature for future

**RSA digital signature scheme**

- RSA idea is also used for signing and verifying a message it is called RSA digital signature scheme.
- Digital signature scheme changes the role of the private and public keys
- Private and public keys of only the sender are used
- Sender uses her own private key to sign the document and the receiver uses the sender’s public key to verify it.

- The signing and verifying sets use the same function, but with different parameters. The verifier compares the message and the output of the function for congruence. If the result is two true the message is accepted.

**Key generation in RSA**

Key generation in RSA digital signature scheme is exactly the same as key generation in RSA cryptosystem.

**Working of RSA digital signature scheme:**

Sender A wants to send a message M to the receiver B along with the digital signature S calculated over the message M

Step1: The sender A uses the message digest algorithm to calculate the message digest MD1 over the original message M

Step 2: The sender A now encrypts the message digest with her private key. The output of this process is called the digital signature.

Step 3: Now the sender A sends the original message M along with digital signature DS to receiver B

Step 4: After the receiver B receives the original message M and the sender A’s digital signature, B uses the same message digest algorithm which was used by A and calculate its own message digest MD2 as shown below.

Step 5: The receiver B now uses the sender’s A’s public key to decrypt the digital signature. Note that A had used his private key to decrypt the message digest MD1 to form the digital signature. Therefore only A’s public key can be used to decrypt it. The output of this process is the original message digest which was calculated by A (MD1) in step 1.

Step 6: B now compare the following two message digests.

- MD2, which it had calculated in step 4
- MD1, which is retrieved from A’s digital signature in step 5If MD1 = MD2 the following facts are established:

a. B accepts the original message (M) as the correct, unaltered message from A

b. B is also assured that the message came from A and not from someone else attached, posing as A