{"id":158732,"date":"2009-08-01T00:00:00","date_gmt":"2009-08-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/compact-e-cash-and-simulatable-vrfs-revisited\/"},"modified":"2018-10-16T20:44:48","modified_gmt":"2018-10-17T03:44:48","slug":"compact-e-cash-and-simulatable-vrfs-revisited","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/compact-e-cash-and-simulatable-vrfs-revisited\/","title":{"rendered":"Compact E-Cash and Simulatable VRFs Revisited"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Efficient non-interactive zero-knowledge proofs are a powerful tool for solving many cryptographic problems. We apply the recent Groth-Sahai (GS) proof system for pairing product equations (Eurocrypt 2008) to two related cryptographic problems: compact e-cash (Eurocrypt 2005) and simulatable verifiable random functions (CRYPTO 2007). We present the first efficient compact e-cash scheme that does not rely on a random oracle. To this end we construct efficient GS proofs for signature possession, pseudo randomness and set membership. The GS proofs for pseudorandom functions give rise to a much cleaner and substantially faster construction of simulatable verifiable random functions (sVRF) under a weaker number theoretic assumption. We obtain the first efficient fully simulatable sVRF with a polynomial sized output domain (in the security parameter).<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Efficient non-interactive zero-knowledge proofs are a powerful tool for solving many cryptographic problems. We apply the recent Groth-Sahai (GS) proof system for pairing product equations (Eurocrypt 2008) to two related cryptographic problems: compact e-cash (Eurocrypt 2005) and simulatable verifiable random functions (CRYPTO 2007). We present the first efficient compact e-cash scheme that does not rely [&hellip;]<\/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":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13558],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-158732","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_publishername":"Springer Verlag","msr_edition":"Pairing 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