An improved hybrid scheme for e-payment security using elliptic curve cryptography
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ORIGINAL RESEARCH
An improved hybrid scheme for e-payment security using elliptic curve cryptography O. M. Lawal1 • O. R. Vincent1 • A. A. A. Agboola2 • O. Folorunso1
Received: 13 December 2019 / Accepted: 22 September 2020 Bharati Vidyapeeth’s Institute of Computer Applications and Management 2020
Abstract This paper presents an improved security scheme using a hybrid of elliptic curve integrated encryption and provably secure elliptic curve with cyclotomic points. The proposed scheme uses Weierstrass form of an elliptic curve and cyclotomic polynomial, by creating a relationship to uniquely generate a hash function to form a structure from a coordinate in the curve and variable in the polynomial. The scheme was tested using e-payment information for mutual agreement and transaction authentication. The scheme is secured for encryption of information with low computational time and useful to fight against small subgroup, chosen ciphertext attacks and ensures data confidentiality and integrity. Keywords Elliptic curve cryptography Cyclotomic polynomials Hybridisation and key agreement Mutual authentication E-payment security
1 Introduction In information security, the elliptic curve integrated encryption scheme (ECIES) is one of the best-known encryption schemes. ECIES derives its two symmetric keys from Diffie–Hellman and symmetric algorithms such as advanced encryption standard (AES). ECIES is an
& O. R. Vincent [email protected] 1
Department of Computer Science, College of Physical Sciences, Federal University of Agriculture, Abeokuta, Nigeria
2
Department of Mathematics, College of Physical Sciences, Federal University of Agriculture, Abeokuta, Nigeria
excellent alternative to RSA-AES for encrypting data that must be sent through insecure communication networks [37]. However, it was found with adaptive chosen ciphertext and session key attacks when an opponent intentionally provides an invalid public key in the elliptic curve point which may belong to the elliptic curve selected by the user, ECIES becomes weak to small subgroup attack [25, 28]. Thus, improvements on the key derivation function of the elliptic curve is important [12, 24, 32, 42]. On the other hand, provably secure elliptic curve scheme (PSECS) is identity-based encryption with regards to elliptic curve discrete logarithm and integer factorization problems. The PSECS essentially depends on the security of a secret key, and it is a twin algorithm of ECIES, which enhances the function of key and data encapsulation mechanisms. However, it has also been found to struggle with chosen ciphertext and small subgroup attacks [4, 51]. Some studies have argued that for information exchange, PSECS can be harnessed against small subgroup attack without increasing the computational time [19, 30]. In the e-payment system, information is exchanged over open networks in the form of e-cash with the use of smart card information. Therefore, financial transactions owners have given high priority to security concentration because huge electr
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