{"component": "clause", "props": {"groups": [{"size": 3, "snippet_links": [{"key": "the-argument", "type": "clause", "offset": [0, 12]}, {"key": "similar-to", "type": "definition", "offset": [49, 59]}, {"key": "the-function", "type": "clause", "offset": [132, 144]}, {"key": "distribution-of", "type": "clause", "offset": [376, 391]}, {"key": "close-to", "type": "definition", "offset": [454, 462]}, {"key": "lemma-3", "type": "clause", "offset": [501, 508]}], "snippet": "The argument that R is nearly uniform given P is similar to the errorless case, except s has to be taken into account. For every s, the function Hi(c) = (\u03c3, R) is universal, because for every c1, c2, there is at most one i such that Hi(c1) = Hi(c2) (because i(a1 \u2212 a2) is fixed, like in the errorless case). Because H\u02dc \u221e(W | SS(W )) \u2265 m \u2212 k, applying Lemma 1, we see that the distribution of (R, P ) = (R, (i, \u03c3, s)) is 2(n\u2032\u2212v\u2212(m\u2212k))/2\u22121 = 2(n\u2212v\u2212m)/2\u22121 -close to (Un\u2032\u22122v \u00d7Un\u2032\u2212v \u00d7U2v\u00d7SS(W )). Applying Lemma 3 to A = R, B = P , C = Un\u2032\u22122v , D = Un\u2032\u2212v \u00d7 U2v \u00d7 SS(W ), we get that (n\u2032\u2212v\u2212m)/2 (R, P ) is \u03b5-close to Un\u2032\u22122v \u00d7 P , for \u03b5 = 2 .", "samples": [{"hash": "ewxZaYyzX6h", "uri": "/contracts/ewxZaYyzX6h#extraction", "label": "Robust Fuzzy Extractors and Authenticated Key Agreement", "score": 24.1348391513, "published": true}, {"hash": "1kOWJ1J61kw", "uri": "/contracts/1kOWJ1J61kw#extraction", "label": "Robust Fuzzy Extractors and Authenticated Key Agreement", "score": 19.7993113334, "published": true}, {"hash": "5K0SDtjcTwz", "uri": "/contracts/5K0SDtjcTwz#extraction", "label": "Robust Fuzzy Extractors and Authenticated Key Agreement", "score": 17.632331911, "published": true}], "hash": "62440d2eab7ad7c183cc96884a93cbed", "id": 1}, {"size": 1, "snippet_links": [{"key": "further-support", "type": "clause", "offset": [0, 15]}, {"key": "the-agreement", "type": "clause", "offset": [20, 33]}], "snippet": "Further support for the agreement marker hypothesis comes from island effects. In the focus raising construction, a subconstituent of an embedded complement such as holnap \u2018tomorrow\u2019 in (45a) raises (potentially over multiple finite clause boundaries) to the matrix focus position, immediately preceding the verb, as in (45b) (E\u00b4 . Kiss 1990: exx. (6) and (7)).\n(45) a. Ja\u00b4nos mond-t-a [ hogy holnap e\u00b4rkez-ik ]. \u2587\u2587\u2587\u2587.NOM say-PAST-3SG.DEF that tomorrow \u2587\u2587\u2587\u2587\u2587\u2587-\u2587\u2587\u2587.\u2587\u2587 \u2018\u2587\u2587\u2587\u2587 said that he is arriving tomorrow.\u2019", "samples": [{"hash": "dQJnv1fVdfJ", "uri": "/contracts/dQJnv1fVdfJ#extraction", "label": "Objective Conjugation", "score": 21.0913488312, "published": true}], "hash": "6d303db8c650fcb9bf40e6ca03dc3629", "id": 9}, {"size": 3, "snippet_links": [{"key": "final-provisions", "type": "clause", "offset": [0, 16]}], "snippet": "Final provisions", "samples": [{"hash": "huYBMpTrt04", "uri": "/contracts/huYBMpTrt04#extraction", "label": "Voluntary Partnership Agreement", "score": 21.5156408062, "published": true}, {"hash": "hliKO6H86uJ", "uri": "/contracts/hliKO6H86uJ#extraction", "label": "Voluntary Partnership Agreement", "score": 20.8590006845, "published": true}, {"hash": "3sUmqB9qKSk", "uri": "/contracts/3sUmqB9qKSk#extraction", "label": "Voluntary Partnership Agreement", "score": 20.2537143517, "published": true}], "hash": "d6769aa02cb67fa5d09eb106f0e4d37c", "id": 2}, {"size": 2, "snippet_links": [{"key": "the-tenant-will-not", "type": "clause", "offset": [0, 19]}, {"key": "materials-provided", "type": "clause", "offset": [149, 167]}, {"key": "for-the-benefit-of", "type": "definition", "offset": [185, 203]}, {"key": "the-tenants", "type": "definition", "offset": [204, 215]}], "snippet": "The Tenant will not take, sell or carry away any soil, mineral, gravel, turf, sand or clay. This includes any top-soil, compost, manure or any other materials provided and/or purchased for the benefit of the Tenants on the allotments.", "samples": [{"hash": "2izUFKUM1sV", "uri": "/contracts/2izUFKUM1sV#extraction", "label": "Tenancy Agreement", "score": 31.7013855719, "published": true}, {"hash": "3MqzhZKuFv8", "uri": "/contracts/3MqzhZKuFv8#extraction", "label": "Tenancy Agreement", "score": 31.5289314143, "published": true}], "hash": "7cf33257803f280e00acc1ec4fd9db96", "id": 3}, {"size": 2, "snippet_links": [{"key": "for-purposes-hereof", "type": "definition", "offset": [0, 19]}, {"key": "mineral-extraction", "type": "clause", "offset": [21, 39]}, {"key": "executive-order-no", "type": "clause", "offset": [102, 120]}, {"key": "mining-code", "type": "definition", "offset": [131, 142]}, {"key": "for-the-purpose-of", "type": "definition", "offset": [146, 164]}, {"key": "volume-and-quality", "type": "clause", "offset": [178, 196]}, {"key": "contained-in", "type": "definition", "offset": [228, 240]}, {"key": "covered-by", "type": "definition", "offset": [275, 285]}, {"key": "mineral-rights", "type": "definition", "offset": [290, 304]}], "snippet": "For purposes hereof, mineral extraction (\u201cExtraction\u201d) means mineral prospection works, as defined in Executive Order No. 227/69 (\u201cMining Code\u201d), for the purpose of defining the volume and quality of gold, silver and byproducts contained in the soil and subsoil of the areas covered by the Mineral Rights.", "samples": [{"hash": "bDCrtBWfjEx", "uri": "/contracts/bDCrtBWfjEx#extraction", "label": "Quota Purchase Agreement", "score": 28.340862423, "published": true}, {"hash": "7IdZbjDyn5J", "uri": "/contracts/7IdZbjDyn5J#extraction", "label": "Quota Purchase Agreement (Ardent Mines LTD)", "score": 20.6618754278, "published": true}], "hash": "f3815641c782006cb8de5e3acdb86114", "id": 4}, {"size": 2, "snippet_links": [{"key": "an-appropriate", "type": "clause", "offset": [6, 20]}, {"key": "cleaning-equipment", "type": "clause", "offset": [43, 61]}, {"key": "safe-condition", "type": "definition", "offset": [100, 114]}, {"key": "carpet-cleaning", "type": "definition", "offset": [127, 142]}, {"key": "floor-care", "type": "clause", "offset": [158, 168]}], "snippet": "Using an appropriate chemical solution and cleaning equipment, carpet will be cleaned and left in a safe condition. (Extensive carpet cleaning will require a floor care request to be submitted)", "samples": [{"hash": "eVXgjsOSKI1", "uri": "/contracts/eVXgjsOSKI1#extraction", "label": "Service Level Agreement", "score": 22.1704312115, "published": true}, {"hash": "b7iAwQb9sYi", "uri": "/contracts/b7iAwQb9sYi#extraction", "label": "Service Level Agreement", "score": 22.1704312115, "published": true}], "hash": "d930d1f4ed3864bddfce86ee4b16b9dd", "id": 5}, {"size": 2, "snippet_links": [{"key": "for-the-avoidance-of-doubt", "type": "clause", "offset": [0, 26]}, {"key": "right-to-commercialize", "type": "clause", "offset": [48, 70]}, {"key": "shuffled-genes", "type": "clause", "offset": [71, 85]}, {"key": "the-right", "type": "clause", "offset": [144, 153]}, {"key": "agricultural-products", "type": "clause", "offset": [178, 199]}, {"key": "extraction-rights", "type": "clause", "offset": [234, 251]}, {"key": "agreed-by", "type": "clause", "offset": [297, 306]}, {"key": "research-committee", "type": "definition", "offset": [311, 329]}], "snippet": "For the avoidance of doubt, Zeneca's ---------- right to commercialize Shuffled Genes for [*******] for Agricultural Applications shall include the right to commercialize Zeneca Agricultural Products obtained by extraction. Any other extraction rights for Zeneca Agricultural Products shall be as agreed by the Research Committee.", "samples": [{"hash": "hzrOuCPBtZl", "uri": "/contracts/hzrOuCPBtZl#extraction", "label": "Collaboration Agreement (Maxygen Inc)", "score": 18.0, "published": true}, {"hash": "chqJrJOqilr", "uri": "/contracts/chqJrJOqilr#extraction", "label": "Collaboration Agreement (Maxygen Inc)", "score": 18.0, "published": true}], "hash": "749317e1d0615968243c2712a97f1d0b", "id": 6}, {"size": 2, "snippet_links": [{"key": "a-portion", "type": "definition", "offset": [4, 13]}, {"key": "organic-solvent", "type": "definition", "offset": [64, 79]}, {"key": "scope-of-accreditation", "type": "definition", "offset": [209, 231]}, {"key": "certified-reference-material", "type": "definition", "offset": [269, 297]}, {"key": "analytical-batch", "type": "definition", "offset": [334, 350]}], "snippet": "6.1 A portion of the homogenized sample must be extracted in an organic solvent that is suitable for recovering cannabinoids.\n6.2 The preparation method utilized must be the one specified in the ISO17025:2017 scope of accreditation for cannabinoid analysis.\n6.3 A hemp Certified Reference Material (CRM) should be processed with each analytical batch.", "samples": [{"hash": "1Iqsj6F7mMs", "uri": "/contracts/1Iqsj6F7mMs#extraction", "label": "Designated Laboratory Compliance Agreement", "score": 30.3819743982, "published": true}, {"hash": "iUShMeLaVxv", "uri": "/contracts/iUShMeLaVxv#extraction", "label": "Designated Laboratory Compliance Agreement", "score": 30.1549376627, "published": true}], "hash": "d012f856299294692fbbb8bf8c205327", "id": 7}, {"size": 2, "snippet_links": [{"key": "the-protocol", "type": "clause", "offset": [41, 53]}, {"key": "send-to", "type": "definition", "offset": [432, 439]}, {"key": "in-order-to", "type": "clause", "offset": [571, 582]}, {"key": "mac-key", "type": "definition", "offset": [764, 771]}, {"key": "number-of", "type": "clause", "offset": [1281, 1290]}, {"key": "in-the-case", "type": "clause", "offset": [1515, 1526]}, {"key": "security-parameters", "type": "clause", "offset": [1686, 1705]}, {"key": "details-of-the", "type": "clause", "offset": [1823, 1837]}, {"key": "the-context", "type": "clause", "offset": [2238, 2249]}, {"key": "in-section-4", "type": "clause", "offset": [2368, 2380]}, {"key": "space-over", "type": "clause", "offset": [2476, 2486]}, {"key": "an-exchange", "type": "clause", "offset": [2701, 2712]}, {"key": "the-o", "type": "clause", "offset": [2778, 2783]}, {"key": "loss-of", "type": "definition", "offset": [3046, 3053]}, {"key": "section-32", "type": "definition", "offset": [3099, 3110]}], "snippet": "Letting C denote an active \u2587\u2587\u2587\u2019s view of the protocol, SD ((kA, C,E | kA /=\u22a5), (U\u03bbk , C, E)) \u2264 \u03f5 and SD ((kB, C,E | kB /=\u22a5), (U\u03bbk , C, E)) \u2264 \u03f5. Our Protocol Before going into details in subsequent sections, we present here a high-level overview of our protocol. We start with an authentication sub-protocol Auth presented in [RW03] that achieves the following: using the secret w that is common to \u2587\u2587\u2587\u2587\u2587 and \u2587\u2587\u2587, it allows \u2587\u2587\u2587\u2587\u2587 to send to \u2587\u2587\u2587 an authentic (but nonsecret) message M of length \u03bbM bit-by-bit in 2\u03bbM messages. \u2587\u2587\u2587\u2587\u2587 and \u2587\u2587\u2587 [RW03] can use this sub-protocol in order to agree on a key k as follows: they use Auth to get an extractor seed s from \u2587\u2587\u2587\u2587\u2587 to \u2587\u2587\u2587, and then extract k from w using s.1 We modify this protocol by using Auth to authenticate a MAC key instead of an extractor seed. The MAC key, in turn, is used to authenticate the extractor seed s (which can be done very efficiently using simple information-theoretic MACs). This seems counterintuitive, because \u2587\u2587\u2587\u2587 reveals what is being authenticated, while MAC keys need to remain secret. The insight is to use the MAC key before Auth begins.2 Our modification is beneficial for three reasons. First, MAC keys can be made shorter than extractor keys, so Auth is used on a shorter string, thus reducing the number of rounds and the entropy loss. Second, this modification allows us to use the same MAC key to authenticate not only the extractor seed s, but also the error-correction information (the so-called \u201csecure sketch\u201d of w [DORS08]) in the case \u2587\u2587\u2587\u2019s w' is different from \u2587\u2587\u2587\u2587\u2587\u2019s w. Third, because there are MACs that are secure even against (limited) key modification [DKRS06, CDF+08], we can lower the security parameters in Auth, further increasing efficiency and reducing entropy loss. The rest of the paper is devoted to filling in the details of the above overview, including smaller improvements not discussed here, and proving the following theorem. 1For technical reasons, since the adversary can modify message of Auth, she may have some information about the string extracted from w; this problem is easily handled, see Section 4. 2This idea has been used before in several contexts; to the best of our knowledge it was first used in [Che97] in the context of secure link state routing. Theorem 1. Given an [n, \u03ba, 2\u03b7 +1]2 linear error correcting code, the protocol presented in Section 4 is an ( , hW , \u03bbk, \u03b7, \u03b4, \u03f5)-interactive robust fuzzy extraction protocol, where is the Hamming space over 0, 1 n with the following parameters: Setting security \u03b4 = 2\u2212L, the protocol can extract \u03bbk = hW (n \u03ba) 2 log 1 (L2/2 + O(L(log n + log L))) bits (assuming n < 2L and \u03bbk (n \u03ba)+ 2 log 1 > 10L). The protocol involves an exchange of L + log n + 5 messages between the two The constant hidden by the O in the entropy loss is small, with O(L(log n + log L)) really being less than 3L log 2L + 1 L log n + 3(log 8L)(log 16n). We obtain similar results for other metric spaces, with the only difference being that n \u03ba in the entropy loss gets replaced by the entropy loss of the secure sketch for that metric space (see Section 3.2).", "samples": [{"hash": "9IIMAqGXcxC", "uri": "/contracts/9IIMAqGXcxC#extraction", "label": "Key Agreement", "score": 19.0, "published": true}], "hash": "50b34340fc2c54c8797df9fc030ef144", "id": 8}, {"size": 1, "snippet_links": [{"key": "the-protocol", "type": "clause", "offset": [41, 53]}], "snippet": "Letting C denote an active \u2587\u2587\u2587\u2019s view of the protocol, SD ((kA, C,E | kA /=\u22a5), (U\u03bbk , C, E)) \u2264 \u03f5 and SD ((kB, C,E | kB /=\u22a5), (U\u03bbk , C, E)) \u2264 \u03f5.", "samples": [{"hash": "UcAmMEqhdo", "uri": "/contracts/UcAmMEqhdo#extraction", "label": "Key Agreement", "score": 22.5421536487, "published": true}], "hash": "6ee0f99187d039484c41591520dc5ef3", "id": 10}], "next_curs": "ClMSTWoVc35sYXdpbnNpZGVyY29udHJhY3Rzci8LEhZDbGF1c2VTbmlwcGV0R3JvdXBfdjU2IhNleHRyYWN0aW9uIzAwMDAwMDBhDKIBAmVuGAAgAA==", "clause": {"size": 40, "children": [["", ""], ["security-of-gen", "Security of Gen"], ["error-tolerance", "Error-Tolerance"], ["security-of-rep", "Security of Rep"], ["extractors", "Extractors"]], "parents": [["introduction", "Introduction"], ["tenancy", "Tenancy"], ["authentic-texts", "Authentic texts"], ["counterparts", "COUNTERPARTS"], ["compensation-and-payment", "Compensation and Payment"]], "title": "Extraction", "id": "extraction", "related": [["production", "Production", "Production"], ["plant", "Plant", "Plant"], ["storage", "Storage", "Storage"], ["wastewater", "Wastewater", "Wastewater"], ["fabrication", "Fabrication", "Fabrication"]], "related_snippets": [], "updated": "2025-07-07T12:37:55+00:00", "also_ask": [], "drafting_tip": "Define permitted extraction methods to prevent unauthorized activities; specify quantity limits to control resource depletion; require compliance with laws to ensure enforceability.", "explanation": "The Extraction clause defines the rights and obligations related to the removal or retrieval of resources, materials, or data from a specified location or system. Typically, this clause outlines what can be extracted, under what conditions, and any limitations or permissions required, such as environmental regulations for mineral extraction or data privacy rules for information retrieval. Its core practical function is to clearly allocate rights and responsibilities regarding extraction activities, thereby preventing disputes and ensuring compliance with applicable laws or agreements."}, "json": true, "cursor": ""}}