A morphism from an algebraic curve C to an elliptic curve is called an elliptic subcover of the curve C. Elliptic subcovers provide means of solving discrete logarithm problem in elliptic curves over extension fields. The GHS attack yields only degree 2 minimal elliptic subcovers of hyperelliptic curves of genus 3. In this paper, we study the properties of elliptic subcovers of genus 3 hyperelliptic curves. Using these properties, we find some minimal elliptic subcovers of degree 4, which can not be constructed by GHS attack.
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