Asymmetric Key Cryptosystem and Digital Signature Algorithm Built on Discrete Logarithm Problem (DLP) Ashish Kumar 1 , Jagadeesh Kakarla 2 , and Muzzammil Hussain 1 1 Department of CSE, Central University of Rajasthan, Kishangarh, Ajmer 305817, India {2016mtcse002,mhussain}@curaj.ac.in 2 Department of CSE, IIITD&M Kancheepuram, Chennai 600127, India jagadeeshk@iiitdm.ac.in Abstract. The thoughts of data security prompt the advancement of Cryptog-raphy. At the end of the day, Cryptography is investigation of keeping data secure. In the advanced mark plot a message can be “marked” utilizing a secretly held decoding key. Anybody can confirm this mark utilizing the comparing freely uncovered encryption key. Marks can’t be fashioned, and an endorser can’t later prevent the legitimacy from claiming his mark. This has evident applications in “electronic mail” and “electronic assets exchange” frameworks. Cryptography, notwithstanding give secrecy, authenticity, integrity and non-revocation. The core of cryptography lies in the keys included and mystery of the keys used to encode or decode. Another vital issue is the key size that determines the strength of the key and complexity in executing brute force attack on the texts to recover the key. There have been different cryptographic algorithms suggested. And we give brief overview of mathematical back ground of public key cryptography. A novel the public key scheme and cryptographic signature system has been proposed and the security of system relies on diffi-culty of computing discrete logarithm problem over finite field. Keywords: Cryptography Public key cryptography Brute force Cipher text Digital signature Discrete logarithm problem 1 Introduction Cryptography is a popular way of sending vital information in a secret way. There are many cryptographic techniques available. The state of current information security technique consists of confidentiality, authenticity, integrity, non-repudiation. The security of communication is a crucial issue on World Wide Web. It is about confi- dentiality, integrity, authentication during access or editing of confidential internal documents [1]. Late advances in media communications and PC organizing have carried us into the period of electronic mail. By giving fast and monetary channels to the dispersal of information, electronic mail frameworks are sure to fundamentally lessen our depen-dence on paper as the real medium for exchanges. It is additionally certain that with the © Springer Nature Switzerland AG 2020 A. Abraham et al. (Eds.): ISDA 2018, AISC 940, pp. 401–410, 2020. https://doi.org/10.1007/978-3-030-16657-1_37