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Constructing Hyperelliptic Covers for Elliptic Curves over Quadratic Extension Fields
Information Security and PrivacyAbstractElliptic curves and hyperelliptic curves over finite fields are of great interest in public key cryptography. Using much smaller field for same security makes the genus 2 curves more competitive than elliptic curves. However, point counting ...
Hyperelliptic curves of genus three over finite fields of even characteristic
In this paper we classify hyperelliptic curves of genus 3 defined over a finite field k of even characteristic. We consider rational models representing all k-isomorphy classes of curves with a given arithmetic structure for the ramification divisor and ...
Skew-Frobenius Maps on Hyperelliptic Curves
Scalar multiplication methods using the Frobenius maps are known for efficient methods to speed up (hyper)elliptic curve cryptosystems. However, those methods are not efficient for the cryptosystems constructed on fields of small extension degrees due ...
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