## Doctoral Theses

### Constructions and Analyses of Efficient Symmetric-Key Primitives for Authentication and Encryption.

8-28-2021

8-28-2022

#### Institute Name (Publisher)

Indian Statistical Institute

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

Cryptology

#### Department

Applied Statistics Unit (ASU-Kolkata)

#### Supervisor

Sarkar, Palash (ASU-Kolkata; ISI)

#### Abstract (Summary of the Work)

In symmetric key cryptography there are two fundamental objectives, viz. 1. confidentiality or secrecy of message from unexpected party and 2. authentication of message which includes authenticating the source of the message as well as integrity of the message against any unwanted modification. Let us first concentrate on confidentiality. In classical symmetric key cryptography two parties, say Alice and Bob, first secretly exchange a key-pair (e, d). Later, if Alice wishes to send a secret message m âˆˆ M to Bob, she computes c = Ee(m) and transmits c to Bob. Upon receiving c, Bob computes Dd(c) = m and gets the original message. Here either e and d are identical or can be derived from each other via a simple transformation. For authentication, if Alice wants to send a message m âˆˆ M to Bob, which is not secret but needs to be conveyed to Bob in its original form, she computes a tag t = He(m) and sends the pair (m, t) to Bob. Upon receiving the pair, Bob runs a verification algorithm on it. He becomes sure that the message was indeed sent by Alice and has not been modified on the way if the pair passes the verification test. In this case Bob accepts it; otherwise he rejects the pair. From the discussion above, it is clear that symmetric-key cryptography involves three sets, viz. key-space, which contains all possible secret keys for the transformations, message space, which contains all possible messages or plaintexts to be conveyed to the other party and output-space which contains the ciphertexts in case of confidentiality and tags (or digests) in case of authentication. In case of confidentiality, the algorithms E and D are called encryption algorithms and decryption algorithms respectively. In case of authentication H is called tag-generation algorithm in general. To construct these algorithms we use some basic cryptographic primitives in a way which will serve our purpose. Block ciphers, stream ciphers and universal hash functions are three of the fundamental primitives in symmetric key cryptography.This thesis is in the areas of universal hash functions and modes of operations. It is structured as follows. Chapter 2 consists of a brief survey of the relevant works present in the literature. In Chapter 3 we set the notation and describe other prerequisite materials required for the rest of the thesis

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28842605

ISILib-TH513