Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Applied Statistics Unit (ASU-Kolkata)


Sarkar, Palash (ASU-Kolkata; ISI)

Abstract (Summary of the Work)

Science, it is argued [65], advances through paradigm shifts. Concepts emerge that open-up new vistas of research, fundamentally changing the way we are used to looking at things. Between these paradigm shifts remain the periods of consolidation. Periods when human mind explores the newly found territory, shedding light on hitherto unknown dimensions. If radical changes are the hallmarks of paradigm shifts, the period within witnesses small but continuous developments, occasionally marked by its own milestones. It is in these periods that human faculty tries to grasp the full significance of the new concepts, consolidates its gains and thereby pushes the boundary of our collective knowledge further. The prospects, nevertheless, bring with it new problems too. Perhaps, by the way, making ground for the next paradigm shift. Cryptology, as a branch of science, is no exception to this common story. Though known from the antiquity and not without some shining milestones; it encountered a paradigm shift exactly three decades ago. Diffie and Hellman [37], in 1976 introduced the notion of public key cryptography (PKC) through their work, appropriately titled, New Directions in Cryptography. Prior to this work, cryptology was practiced in the symmetric setting only, i.e., the same secret key was used for encryption as well as decryption. This kind of symmetric key cryptography necessitates a secret channel to be established between the sender and receiver. This is, no doubt, a cumbersome business when a large number of users want to communicate secretly with each other.In the public key setting (also known as asymmetric key cryptography), each user possesses a pair of keys, one public key which is published in a publicly available directory and another private key which is known only to the user concerned. When somebody, say Alice, wants to send an encrypted message to Bob, she looks up in the directory for the public key of Bob, encrypts the message using that public key and sends it to Bob. Bob uses his private key to decrypt the message. Naturally, there should be some mathematical relationship between the two keys, so that given the private key it should be (computationally) easy to decrypt the message encrypted using the public key. On the other hand, it should be (computationally) hard to obtain any information regarding the private key given 1 the public key. In this setting, anybody can send an encrypted message to anybody else, provided the public key is made available, while only the person in possession of the private key can decrypt the message. This way, the problem of key distribution (that we observe in the symmetric setting) can be solved effectively.Within two years of publication of Diffie-Hellman’s work, the field of public key cryptology got a milestone in the form of RSA cryptosystem [79]. Rivest, Shamir and Adleman based their cryptosystem on the hardness of integer factorisation problem. In 1985, ElGamal [41] proposed a public key cryptosystem based on the discrete logarithm problem over cyclic groups. This was soon followed by Koblitz [61] and Miller [73], who independently proposed a public key cryptosystem called the elliptic curve cryptosystem (ECC).


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This work is licensed under a Creative Commons Attribution 4.0 International License.


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