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On elliptic curve $L$-functions integrated encryption scheme

Volume 126 / 2023

Sami Omar, Abdulla Eid Banach Center Publications 126 (2023), 53-72 MSC: Primary 94A60; Secondary 11G05, 11T71, 14G50, 14H52. DOI: 10.4064/bc126-4


In this paper, we present a cryptosystem based on the Fourier series coefficients of a modular form attached to an elliptic curve over the rational numbers. More precisely, we show how the techniques of encryption, decryption and digital signature can be integrated in a new authenticated encryption scheme based on the $L$-series of elliptic curves cryptosystem. Finally, we show that our integrated encryption scheme is secure against known plain-text attack, much less vulnerable against key reuse and represents a non-deniable encryption scheme.


  • Sami OmarDepartment of Mathematics
    University of Bahrain
    P.O. Box 32038, Sukhair, Bahrain
  • Abdulla EidDepartment of Mathematics, University of Bahrain
    P.O. Box 32038, Sukhair, Bahrain

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