Revisiting Atomic Patterns for Elliptic Curve Scalar Multiplication Revealing Inherent Vulnerability to Simple SCA
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909415467122688 |
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| author | Sigourou, Alkistis Aikaterini Dyka, Zoya Li, Sze Hei Langendoerfer, Peter Kabin, Ievgen |
| author_facet | Sigourou, Alkistis Aikaterini Dyka, Zoya Li, Sze Hei Langendoerfer, Peter Kabin, Ievgen |
| contents | Elliptic Curve Scalar Multiplication denoted as kP operation is the basic operation in all Elliptic Curve based cryptographic protocols. The atomicity principle and different atomic patterns for kP algorithms were proposed in the past as countermeasures against simple side-channel analysis. In this work, we investigated the resistance of a kP algorithm implemented in hardware using Longa's atomic patterns. We analysed its simulated power trace. We show in the example of our kP implementation for the NIST EC P-256 that the field squaring operations are distinguishable from the field multiplications even if they are performed by the same field multiplier, due to the addressing of the second multiplicand. This inherent vulnerability of atomic patterns can be successfully exploited for revealing the scalar k. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03218 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting Atomic Patterns for Elliptic Curve Scalar Multiplication Revealing Inherent Vulnerability to Simple SCA Sigourou, Alkistis Aikaterini Dyka, Zoya Li, Sze Hei Langendoerfer, Peter Kabin, Ievgen Cryptography and Security Elliptic Curve Scalar Multiplication denoted as kP operation is the basic operation in all Elliptic Curve based cryptographic protocols. The atomicity principle and different atomic patterns for kP algorithms were proposed in the past as countermeasures against simple side-channel analysis. In this work, we investigated the resistance of a kP algorithm implemented in hardware using Longa's atomic patterns. We analysed its simulated power trace. We show in the example of our kP implementation for the NIST EC P-256 that the field squaring operations are distinguishable from the field multiplications even if they are performed by the same field multiplier, due to the addressing of the second multiplicand. This inherent vulnerability of atomic patterns can be successfully exploited for revealing the scalar k. |
| title | Revisiting Atomic Patterns for Elliptic Curve Scalar Multiplication Revealing Inherent Vulnerability to Simple SCA |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2412.03218 |