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For a point $G\\in\\mathbf{E}(\\mathbb{F}_p)$ the elliptic curve congruential generator (with respect to the first coordinate) is a sequence $(x_n)$ defined by the relation $x_n=x(W_n)=x(W_{n-1}\\oplus G)=x(nG\\oplus W_0)$, $n=1,2,\\dots$, where $\\oplus$ denotes the group operation in $\\mathbf{E}$ and $W_0$ is an initial point. In this paper, we show that if some consecutive elements of the sequence $(x_n)$ are given as integers, then one can compute in polynomial time an ellipt"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.03305","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-09-12T08:39:27Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"59d61bcab608fc1177f90d4fe4a3cc752869f18c23675e99959818ad8f60f6b1","abstract_canon_sha256":"dbec3127672fd0345e79f1bb450db8b216c13e62fc9841c7102a788c56b29195"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:47.253981Z","signature_b64":"WjNEfvXO+zC8sn+gjlRAaKlpdp/tuLOCrZAuOYeGVlxN4YVIMBlE9EDCfQHL0TljLYt2YS8FZdPHtta2R2ecCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"057c48a25da8ca2a3328f76f8e64ebabbae85176b048f11aff70c911ea9a4aa0","last_reissued_at":"2026-05-18T01:04:47.253376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:47.253376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Predicting the elliptic curve congruential generator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CR","authors_text":"L\\'aszl\\'o M\\'erai","submitted_at":"2016-09-12T08:39:27Z","abstract_excerpt":"Let $p$ be a prime and let $\\mathbf{E}$ be an elliptic curve defined over the finite field $\\mathbb{F}_p$ of $p$ elements. 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