On discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917514779295744 |
|---|---|
| author | Liu, Ziran Mok, Chung Pang |
| author_facet | Liu, Ziran Mok, Chung Pang |
| contents | This paper studies the problem of discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator, particularly in the non-translational case. Two families of results are obtained. First, in a full-coset regime characterized by a relative maximal period condition (RMPC) on an induced one-dimensional linear congruential generator, one proves bounds of type $q^{1/2}/t$ for the discrepancy $D$, the serial discrepancy $D_s$, and, under the corresponding derived RMPC, the non-overlapping discrepancy $\widetilde D_s$. Second, in the general sub-period regime, one reduces bounds for $D$, $D_s$, and $\widetilde D_s$ to estimation of Fourier $\ell^1$ masses of admissible index sets attached to one-dimensional linear congruential generators. This isolates the arithmetic bottleneck for further improvement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20627 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator Liu, Ziran Mok, Chung Pang Number Theory This paper studies the problem of discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator, particularly in the non-translational case. Two families of results are obtained. First, in a full-coset regime characterized by a relative maximal period condition (RMPC) on an induced one-dimensional linear congruential generator, one proves bounds of type $q^{1/2}/t$ for the discrepancy $D$, the serial discrepancy $D_s$, and, under the corresponding derived RMPC, the non-overlapping discrepancy $\widetilde D_s$. Second, in the general sub-period regime, one reduces bounds for $D$, $D_s$, and $\widetilde D_s$ to estimation of Fourier $\ell^1$ masses of admissible index sets attached to one-dimensional linear congruential generators. This isolates the arithmetic bottleneck for further improvement. |
| title | On discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.20627 |