International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Trapdoor Functions from the Computational Diffie-Hellman Assumption

Sanjam Garg
Mohammad Hajiabadi
DOI: 10.1007/978-3-319-96881-0_13 (login may be required)
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Presentation: Slides
Conference: CRYPTO 2018
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 Chameleon 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 chameleon 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.
Video from CRYPTO 2018
  title={Trapdoor Functions from the Computational Diffie-Hellman Assumption},
  booktitle={Advances in Cryptology – CRYPTO 2018},
  series={Lecture Notes in Computer Science},
  author={Sanjam Garg and Mohammad Hajiabadi},