Regular SPA Resistant Fixed-base Comb Method for Elliptic Curve Scalar Multiplication
| Main Authors: | Nashwa A. F. Mohammed, Mohsin H. A. Hashim |
|---|---|
| Format: | Article Journal |
| Bahasa: | eng |
| Terbitan: |
, 2021
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/5669240 |
Daftar Isi:
- Abstract—Side Channel Attack(SCA) allow an adversary to reveal partial information or exact value of the secret key in a cryptographic device by observing side channel information such as the computing times or the power consumptions. Two main kinds of SCA attacks are Simple Power Analysis(SPA) and Differential Power Analysis(DPA) attacks. In elliptic curve cryptography a particular target of SCA attacks is the secret scalar k in scalar multiplication algorithm. In this paper, we prove that the length of the recoding of the odd scalar k using Joye and Tunstall regular signed-digit recoding with m = 2 is equal to the length of the binary representation of the scalar k. Then, we propose a regular SPA resistant elliptic curve scalar multiplication algorithm using the fixed base comb method. Our proposed method represents the odd scalar k in base 2 using Joye and Tunstall regular signed-digit recoding. Then, the scalar k is divided into ! d blocks according to the method of Lim and Lee and processes columnwise. All the columns are non-zero, so our method regularly repeat the same pattern (one point doubling and one point addition(or subtraction)) in each iteration, therefore, SPA cannot extract any information about the secret key k by observing the power consumption. The proposed method has a constant run time which ensure the resistance against timing attacks. Moreover, the proposed method dose not make use of any dummy operation, therefore, it is resistant to safe error fault attacks. In addition to that, our proposed method resistant to DPA, Okeya and Sakurai’s secondorder DPA, RPA, ZPA and Geiselmann-Steinwandt’s attacks. Index Terms—Scalar multiplication, Simple power analysis, Differential power analysis