Asymmetric key Cryptography using Laplace Transform
G. Nagalakshmi1, A. Chandra Sekhar2, D. Ravi Sankar3

1G.Nagalakshmi*, Asst. Professor, Department of Mathematics, GIS, GITAM (Deemed to be University), Visakhapatnam, India.
2A. Chandra Sekhar, Professor, Dept of Mathematics, GIS, GITAM (Deemed to be University), Andhra Pradesh, India.
3N. Ravi Shankar, Professor, Dept of Mathematics, GIS, GITAM (Deemed to be University), Andhra Pradesh, India.
Manuscript received on January 12, 2020. | Revised Manuscript received on January 23, 2020. | Manuscript published on February 10, 2020. | PP: 3083-3087 | Volume-9 Issue-4, February 2020. | Retrieval Number: D2007029420/2020©BEIESP | DOI: 10.35940/ijitee.D2007.029420
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Abstract: This paper presents a method of Asymmetric key cryptography using Laplace transform and inverse Laplace transform respectively on Maclaurin’s series to attain information and network Security. The public key and private key are used to encrypt and decrypt data in Asymmetric cryptography. Public and private key are generated using Encryption and Decryption algorithms with a numerical example. Frequency allocations of characters in plain text file and cipher text file with proposed algorithm are analyzed using bar diagrams. It has been observed that the repeated character in encipher file has same frequency while running ElGamal and RSA encryption algorithms but differ in proposed algorithm. Time complexity of each algorithm is tested for distinct file size and is presented in a suitable table. Statistical analysis for the proposed algorithm is performed using coefficient correlation and compared with ElGamal, RSA algorithms. All these tests ensure that the proposed algorithm provide network security and key recovery attack. 
Keywords: Cryptography, Laplace Transform, Inverse Laplace Transform, public key, private key, Maclaurin’s expansion.
Scope of the Article: Cryptography and Applied Mathematics