Paper 2015/799

Secure Binary Field Multiplication

Hwajeong Seo, Chien-Ning Chen, Zhe Liu, Yasuyuki Nogami, Taehwan Park, Jongseok Choi, and Howon Kim


Binary eld multiplication is the most fundamental building block of binary eld Elliptic Curve Cryptography (ECC) and Galois/Counter Mode (GCM). Both bit-wise scanning and Look-Up Table (LUT) based methods are commonly used for binary eld multiplication. In terms of Side Channel Attack (SCA), bit-wise scanning exploits insecure branch operations which leaks information in a form of timing and power consumption. On the other hands, LUT based method is regarded as a relatively secure approach because LUT access can be conducted in a regular and atomic form. This ensures a constant time solution as well. In this paper, we conduct the SCA on the LUT based binary eld multiplication. The attack exploits the horizontal Correlation Power Analysis (CPA) on weights of LUT. We identify the operand with only a power trace of binary eld multiplication. In order to prevent SCA, we also suggest a mask based binary eld multiplication which ensures a regular and constant time solution without LUT and branch statements.

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Published elsewhere. Minor revision.
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hwajeong84 @ gmail com
2015-08-10: received
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      author = {Hwajeong Seo and Chien-Ning Chen and Zhe Liu and Yasuyuki Nogami and Taehwan Park and Jongseok Choi and Howon Kim},
      title = {Secure Binary Field Multiplication},
      howpublished = {Cryptology ePrint Archive, Paper 2015/799},
      year = {2015},
      note = {\url{}},
      url = {}
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