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arXiv · 1812.09666

A Proof of the Beierle-Kranz-Leander Conjecture related to Lightweight Multiplication in $\mathds{F}_{2^n}$

Sihem Mesnager·Kwang Ho Kim·Dujin Jo·Junyop Choe·Munhyon Han·Dok Nam Lee
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Abstract

Lightweight cryptography is a key tool for building strong security solutions for pervasive devices with limited resources. Due to the stringent cost constraints inherent in extremely large applications (ranging from RFIDs and smart cards to mobile devices), the efficient implementation of cryptographic hardware and software algorithms is of utmost importance to realize the vision of generalized computing. In CRYPTO 2016, Beierle, Kranz and Leander have considered lightweight multiplication in $\mathds{F}_{2^n}$. Specifically, they have considered the fundamental question of optimizing finite field multiplications with one fixed element and investigated which field representation, that is which choice of basis, allows for an optimal implementation. They have left open a conjecture related to two XOR-count. Using the theory of linear algebra, we prove in the present paper that their conjecture is correct. Consequently, this proved conjecture can be used as a reference for further developing and implementing cryptography algorithms in lightweight devices.

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Sihem Mesnager, Kwang Ho Kim, Dujin Jo, Junyop Choe, Munhyon Han, Dok Nam Lee. 2018-12-23. A Proof of the Beierle-Kranz-Leander Conjecture related to Lightweight Multiplication in $\mathds{F}_{2^n}$. https://arxiv.org/abs/1812.09666

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