A divisibility sequence associated with multiples of a point on an elliptic curve, using suitably normalized division polynomials. With and , its terms satisfy the Ward identity . Setting nearby indices gives doubling identities, enabling logarithmic-depth evaluation.
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A **divisibility sequence** is a sequence of integers \( (a_n) \) where each term divides the subsequent terms in the sequence according to specific criteria. More formally, a sequence \( (a_n) \) is called a divisibility sequence if for each pair of indices \( m < n \), the term \( a_m \) divides \( a_n \) (denoted as \( a_m \mid a_n \)).