Point Counting on Elliptic and Hyperelliptic Curves
نویسندگان
چکیده
منابع مشابه
Invalid-curve attacks on (hyper)elliptic curve cryptosystems
We extend the notion of an invalid-curve attack from elliptic curves to genus 2 hyperelliptic curves. We also show that invalid singular (hyper)elliptic curves can be used in mounting invalid-curve attacks on (hyper)elliptic curve cryptosystems, and make quantitative estimates of the practicality of these attacks. We thereby show that proper key validation is necessary even in cryptosystems bas...
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Counting rational points on Jacobian varieties of hyperelliptic curves over finite fields is very important for constructing hyperelliptic curve cryptosystems (HCC), but known algorithms for general curves over given large prime fields need very long running times. In this article, we propose an extremely fast point counting algorithm for hyperelliptic curves of type y = x + ax over given large...
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We propose an algorithm to compute the Frobenius polynomial of an ordinary non hyperelliptic curve of genus 3 over F2N . The method is a generalization of Mestre’s AGM-algorithm for hyperelliptic curves and leads to a quasi quadratic time algorithm for point counting. The current methods for point counting on curves over finite fields of small characteristic rely essentially on a p-adic approac...
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The group law on elliptic curves is well-known and gives rise to elliptic curve cryptography systems which find application to government and industry today. However, the generalisation to higher genus requires the manipulation of divisor classes rather than points, and analogues of key genus 1 results have yet to be found. Nonetheless, effective computation within the group is possible, and te...
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With the drastic increase in the number and the use of handheld devices, – mobile phones and smart cards – light weight cryptography has come to the lime light. Elliptic and Hyperelliptic curve cryptosystems (ECC, HECC) are emerging as the best solutions for light weight cryptography. Like in any traditional cryptosystem, the size of the cipher-text space is a significant factor indicating the ...
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