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Jacobians of hyperelliptic curves for cryptography

Angelo Sonnino

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Abstract

Jacobians of hyperelliptic curves defined over a finite field are used in constructing cryptosystems based on discrete logarithm. The aim of this paper is to present some hyperelliptic curves defined over $\mathbb{F}_{4}$ whose Jacobians provide cryptosystems resisting the currently known attacks. The key tool for this purpose is the classification of $L$-polynomials of hyperelliptic curves defined over $\mathbb{F}_{4}$.

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What this paper is about

Jacobians of hyperelliptic curves defined over a finite field are used in constructing cryptosystems based on discrete logarithm. The aim of this paper is to present some hyperelliptic curves defined over $\mathbb{F}_{4}$ whose Jacobians provide cryptosystems resisting the currently known attacks. The key tool for this purpose is the classification of $L$-polynomials of hyperelliptic curves defined over $\mathbb{F}_{4}$.

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Available abstract

Jacobians of hyperelliptic curves defined over a finite field are used in constructing cryptosystems based on discrete logarithm. The aim of this paper is to present some hyperelliptic curves defined over $\mathbb{F}_{4}$ whose Jacobians provide cryptosystems resisting the currently known attacks. The key tool for this purpose is the classification of $L$-polynomials of hyperelliptic curves defined over $\mathbb{F}_{4}$.

Key concepts: Hyperelliptic curve cryptography, Hyperelliptic curve, Cryptography, Mathematics, Computer science, Elliptic curve cryptography, Algebra over a field, Computer security

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