Date of Award
Electrical and Computer Engineering
Cryptography, Scalar multiplication, Side channel attack
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Elliptic curve cryptography (ECC) is probably the most popular public key systems nowadays. The classic algorithm for computation of elliptic curve scalar multiplication is Doubling-and-Add. However, it has been shown vulnerable to simple power analysis, which is a type of side channel attacks (SCAs). Among different types of attacks, SCAs are becoming the most important and practical threat to elliptic curve computation. Although Montgomery power ladder (MPL) has shown to be a good choice for scalar multiplication against simple power analysis, it is still subject to some advanced SCAs such like differential power analysis. In this thesis, a new number representation is firstly proposed, then several scalar multiplication algorithms using this new number system are presented. It has also been shown that the proposed algorithms outperform or comparable to the best of existing similar algorithms in terms of against side channel attacks and computational efficiency. Finally we extend both the new number system and the corresponding scalar multiplication algorithms to high radix cases.
Huang, Yue, "Efficient scalar multiplication against side channel attacks using new number representation" (2017). Electronic Theses and Dissertations. 5940.