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Survey on performance and security problems of countermeasures for passive side-channel attacks on ECC

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Abstract

This paper presents an analysis on the state of the art of several proposals for algorithmic countermeasures to prevent passive side-channel attacks (SCA) on elliptic curve cryptography (ECC) defined over prime fields. One of the main applications of ECC is in the field of Internet of Things, where the interconnection of devices requires public-key technology with small key sizes and high security levels. Since the secure implementation of ECC on embedded devices involves many challenges for security and efficiency, this work evaluates the trade-offs between security and performance of side-channel attack countermeasures for scalar multiplication algorithms without precomputation. The main contribution is to present a panorama of explicit solutions that may be used for the implementation of ECC mechanisms suitable for embedded devices. In addition to the security problems, some countermeasures are also analyzed.

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Notes

  1. When \(m=2\) and the attacker knows whether \(y([2]P)+y(P)=0\), then, \(k_{n-2}=1\); otherwise, \(k_{n-2}=0\).

  2. We consider these ratios for our computing cost and \(S/M=0.8\).

  3. This experimental attack is applied because the implementation does not prevent irregular breaks between Atomic Blocks within the same group operation and distinct group operations.

  4. \(\mathcal {J}\), \(\mathcal {J}^c\) and \(\mathcal {J}^m\), respectively, refer to the Jacobian coordinates, Chudnovsky Jacobian coordinates and the modified Jacobian coordinates

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Acknowledgements

The authors are grateful for the financial support given by Universidad de Santiago de Chile, USACH, through DICYT projects 062033AO, 061513VC (Universidad de Santiago de Chile, Chile), STICAMSUD 19-STIC-02 and STIC-AmSud/CAPES program 88881-198035/2018-01/CAPES (Brazil).

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  1. Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Santiago, Chile

    Rodrigo Abarzúa

  2. Departamento de Ingeniería Eléctrica, Universidad de Santiago de Chile, Santiago, Chile

    Claudio Valencia

  3. Instituto de Computação, Universidade Estadual de Campinas, Campinas, Brazil

    Julio López

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  1. Rodrigo Abarzúa
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  2. Claudio Valencia
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Correspondence to Rodrigo Abarzúa.

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This research was supported by the following research grants: DICYT projects 062033AO, 061513VC (Universidad de Santiago de Chile, Chile), STICAMSUD 19-STIC-02 and STIC-AmSud/CAPES program 88881-198035/2018-01/CAPES (Brazil).

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Abarzúa, R., Valencia, C. & López, J. Survey on performance and security problems of countermeasures for passive side-channel attacks on ECC. J Cryptogr Eng 11, 71–102 (2021). https://doi.org/10.1007/s13389-021-00257-8

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