Cryptography on hyperelliptic curves is similar to cryptography on elliptic curves. A hyperelliptic curve is an object of algebraic geometry with appropriate group law to obtain an abelian group on which arithmetic operations are applied.
The use of hyperelliptic curves in cryptography dates from 1989 and is due to Neal Koblitz. Although they were introduced only three years after cryptography on elliptic curves, few cryptosystems implement hyperelliptic curves because the implementation of arithmetic is not as efficient as that of elliptic curves or factorization ( RSA). Since arithmetic on hyperelliptic curves is more complicated than elliptic curve arithmetic, a well-implemented cryptosystem based on hyperelliptic curves may be safer than cryptosystems based on elliptic curves, for the same key size. p>
Hyperelliptic curves are typically shaped Y 2 = f ( x ) {\displaystyle y^{2}=f(x)} where the degree of f {\displaystyle f} is 5 (for a hyperelliptic curve of genus 2) or 7 (for a genus of 3). code
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