{"id":151282,"date":"1999-01-01T00:00:00","date_gmt":"1999-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/limits-on-the-efficiency-of-one-way-permutation-based-hash-functions\/"},"modified":"2018-10-16T21:42:55","modified_gmt":"2018-10-17T04:42:55","slug":"limits-on-the-efficiency-of-one-way-permutation-based-hash-functions","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/limits-on-the-efficiency-of-one-way-permutation-based-hash-functions\/","title":{"rendered":"Limits on the Efficiency of One-Way Permutation-Based Hash Functions"},"content":{"rendered":"
\n

Naor and Yung (1989) show that a one-bit-compressing universal one-way hash function (UOWHF) can be constructed based on a one-way permutation. This construction can be iterated to build a UOWHF which compresses by epsilon n bits, at the cost of epsilon n invocations of the one-way permutation. The show that this construction is not far from optimal, in the following sense, there exists an oracle relative to which there exists a one-way permutation with inversion probability 2\/sup -p(n)\/ (for any p(n) in omega (log n)), but any construction of an epsilon n-bit-compressing UOWHF. Requires Omega ( square root n\/p(n)) invocations of the one-way permutation, on average. (For example, there exists in this relativized world a one-way permutation with inversion probability n\/sup – omega (1)\/, but no UOWHF that involves it fewer than Omega ( square root n\/log n) times.) Thus any proof that a more efficient UOWHF can be derived from a one-way permutation is necessarily non-relativizing; in particular, no provable construction of a more efficient UOWHF can exist based solely on a “black box” one-way permutation. This result can be viewed as a partial justification for the practice of building efficient UOWHFs from stronger primitives (such as collision intractable hash functions), rather than from weaker primitives such as one-way permutations.<\/p>\n<\/div>\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Naor and Yung (1989) show that a one-bit-compressing universal one-way hash function (UOWHF) can be constructed based on a one-way permutation. This construction can be iterated to build a UOWHF which compresses by epsilon n bits, at the cost of epsilon n invocations of the one-way permutation. The show that this construction is not far […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Institute of Electrical and Electronics Engineers, Inc.","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-99-06","msr_organization":"","msr_pages_string":"13","msr_page_range_start":"13","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"\u00a9 1999 IEEE. Personal use of this material is permitted. However, permission to reprint\/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Jeong Han Kim, Daniel R. Simon, Prasad Tetali","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"Microsoft Research","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"1999-04-02","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"http:\/\/www.ieee.org\/","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":1999,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193718],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-151282","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"Institute of Electrical and Electronics Engineers, Inc.","msr_edition":"","msr_affiliation":"","msr_published_date":"1999-04-02","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"13","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"MSR-TR-99-06","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"","msr_publicationurl":"http:\/\/www.ieee.org\/","msr_doi":"","msr_publication_uploader":[{"type":"url","title":"http:\/\/www.ieee.org\/","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[{"id":0,"url":"http:\/\/www.ieee.org\/"}],"msr-author-ordering":[{"type":"text","value":"Jeong Han Kim","user_id":0,"rest_url":false},{"type":"text","value":"Daniel R. Simon","user_id":0,"rest_url":false},{"type":"text","value":"Prasad Tetali","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"techreport","related_content":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/151282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":2,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/151282\/revisions"}],"predecessor-version":[{"id":538385,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/151282\/revisions\/538385"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=151282"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=151282"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=151282"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=151282"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=151282"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=151282"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=151282"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=151282"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=151282"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=151282"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=151282"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=151282"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=151282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}