Cryptology ePrint Archive: Report 2018/529

Trapdoor Functions from the Computational Diffie-Hellman Assumption

Sanjam Garg and Mohammad Hajiabadi

Abstract: Trapdoor functions (TDFs) are a fundamental primitive in cryptography. Yet, the current set of assumptions known to imply TDFs is surprisingly limited, when compared to public-key encryption. We present a new general approach for constructing TDFs. Specifically, we give a generic construction of TDFs from any Hash Encryption (Döttling and Garg [CRYPTO '17]) satisfying a novel property which we call recyclability. By showing how to adapt current Computational Diffie-Hellman (CDH) based constructions of hash encryption to yield recyclability, we obtain the first construction of TDFs with security proved under the CDH assumption. While TDFs from the Decisional Diffie-Hellman (DDH) assumption were previously known, the possibility of basing them on CDH had remained open for more than 30 years.

Category / Keywords: public-key cryptography / Trapdoor Functions, Computational Diffie-Hellman Assumption

Original Publication (with minor differences): IACR-CRYPTO-2018

Date: received 29 May 2018, last revised 29 Jun 2018

Contact author: mdhajiabadi at berkeley edu, sanjamg at berkeley edu

Available format(s): PDF | BibTeX Citation

Note: Fixed a typo in the abstract.

Version: 20180629:192910 (All versions of this report)

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