What Provisions have been made regarding authentication of electronic Records under the information technology act?

A digital signature is a mathematical scheme to verify the authenticity of digital documents or messages. Also, a valid digital signature allows the recipient to trust the fact that a known sender sent the message and it was not altered in transit. 
Section 3 of the Information technology act 

Authentication of electronic records.-
(1) Subject to the provisions of this section, any subscriber may authenticate an electronic record by affixing his digital signature.
(2) The authentication of the electronic record shall be effected by the use of the asymmetric cryptosystem and hash function which envelopes and transform the initial electronic record into another electronic record. Explanation.-For the purposes of this sub-section, "hash function" means an algorithm mapping or translation of one sequence of bits into another, generally smaller, set known as "hash result" such that an electronic record yields the same hash result every time the algorithm is executed with the same electronic record as its input making it computationally infeasible-
(a) to derive or reconstruct the original electronic record from the hash result produced by the algorithm;
(b) that two electronic records can produce the same hash result using the algorithm.
(3) Any person by the use of a public key of the subscriber can verify the electronic record.
(4) The private key and the public key are unique to the subscriber and constitute a functioning key pair.

What is Hash? 

Hash Function means an algorithm mapping or translation of one sequence of bits into another, generally smaller, set known as “hash Result” 
UNIQUENESS OF KEYS - According to Subsection(4) The private key and the public key is unique to the subscriber and constitute a functioning key pair. Such as section 3 has provisions regarding authentication and verification of electronic records.