{"id":624786,"date":"2019-12-01T23:49:53","date_gmt":"2019-12-02T07:49:53","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=624786"},"modified":"2019-12-02T00:08:17","modified_gmt":"2019-12-02T08:08:17","slug":"explicit-rate-1-non-malleable-codes-for-local-tampering","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/explicit-rate-1-non-malleable-codes-for-local-tampering\/","title":{"rendered":"Explicit Rate-1 Non-malleable Codes for Local Tampering"},"content":{"rendered":"

This paper constructs high-rate non-malleable codes in the information-theoretic plain model against tampering functions with bounded locality. We consider\u00a0\u03b4<\/mi><\/math>\">\u03b4<\/span><\/span><\/span><\/span><\/span>-local tampering functions; namely, each output bit of the tampering function is a function of (at most)\u00a0\u03b4<\/mi><\/math>\">\u03b4<\/span><\/span><\/span><\/span><\/span> input bits. This work presents the first explicit and efficient rate-1 non-malleable code for \u03b4<\/mi><\/math>\"><\/span><\/span>\u03b4<\/mi><\/math>-local tampering functions, where\u00a0\u03b4<\/mi>=<\/mo>\u03be<\/mi>lg<\/mi>\u2061<\/mo>n<\/mi><\/math>\">\u03b4<\/span>=<\/span>\u03be <\/span>lg<\/span><\/span>n <\/span><\/span><\/span><\/span><\/span>and\u00a0\u03be<\/mi><<\/mo>1<\/mn><\/math>\">\u03be<\/span><<\/span>1<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u03be<\/mi><<\/mo>1<\/mn><\/math><\/p>\n

is any positive constant. As a corollary, we construct the first explicit rate-1 non-malleable code against NC<\/mi>0<\/mn><\/msup><\/math>\"><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/mi>0<\/mn><\/msup><\/math><\/p>\n

tampering functions.<\/p>\n

Before our work, no explicit construction for a constant-rate non-malleable code was known even for the simplest 1-local tampering functions. Ball\u00a0et al. (EUROCRYPT\u20132016), and Chattopadhyay and Li (STOC\u20132017) provided the first explicit non-malleable codes against\u00a0\u03b4<\/mi><\/math>\">\u03b4<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u03b4<\/mi><\/math><\/p>\n

-local tampering functions. However, these constructions are rate-0 even when the tampering functions have 1-locality. In the CRS model, Faust\u00a0et al. (EUROCRYPT\u20132014) constructed efficient rate-1 non-malleable codes for\u00a0\u03b4<\/mi>=<\/mo>O<\/mi>(<\/mo>log<\/mi>\u2061<\/mo>n<\/mi>)<\/mo><\/math>\">\u03b4<\/span>=<\/span>O<\/span>(<\/span>log<\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u03b4<\/mi>=<\/mo>O<\/mi>(<\/mo>log<\/mi>\u2061<\/mo>n<\/mi>)<\/mo><\/math><\/p>\n

local tampering functions.<\/p>\n

Our main result is a general compiler that bootstraps a rate-0 non-malleable code against leaky input and output local tampering functions to construct a rate-1 non-malleable code against\u00a0\u03be<\/mi>lg<\/mi>\u2061<\/mo>n<\/mi><\/math>\">\u03be<\/span>lg<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u03be<\/mi>lg<\/mi>\u2061<\/mo>n<\/mi><\/math><\/p>\n

-local tampering functions, for any positive constant\u00a0\u03be<\/mi><<\/mo>1<\/mn><\/math>\">\u03be<\/span><<\/span>1<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u03be<\/mi><<\/mo>1<\/mn><\/math><\/p>\n

. Our explicit construction instantiates this compiler using an appropriate encoding by Ball\u00a0et al. (EUROCRYPT\u20132016).<\/p>\n","protected":false},"excerpt":{"rendered":"

This paper constructs high-rate non-malleable codes in the information-theoretic plain model against tampering functions with bounded locality. We consider\u00a0\u03b4-local tampering functions; namely, each output bit of the tampering function is a function of (at most)\u00a0\u03b4 input bits. This work presents the first explicit and efficient rate-1 non-malleable code for \u03b4-local tampering functions, where\u00a0\u03b4=\u03be lgn and\u00a0\u03be0 […]<\/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":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"CRYPTO","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","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":"2019-8-16","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"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":[13558],"msr-publication-type":[193716],"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-624786","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2019-8-16","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","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":"","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-030-26948-7_16","label_id":"243109","label":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":[],"msr-author-ordering":[{"type":"user_nicename","value":"Divya 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