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Journal Articles Journal of Symbolic Computation Year : 2023

## Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields

Elie Eid
• Function : Author

#### Abstract

Let $p$ be an odd prime number. We propose an algorithm for computing rational representations of isogenies between Jacobians of hyperelliptic curves via-adic differential equations with a sharp analysis of the loss of precision. Consequently, after having possibly lifted the problem in the $p$-adics, we derive fast algorithms for computing explicitly Cantor's division polynomials of hyperelliptic curves defined over finite fields.

### Dates and versions

hal-03588288 , version 1 (02-03-2022)

### Identifiers

• HAL Id : hal-03588288 , version 1
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### Cite

Elie Eid. Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields. Journal of Symbolic Computation, 2023, 117, pp.68 - 100. ⟨10.1016/j.jsc.2022.10.006⟩. ⟨hal-03588288⟩

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