International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Rate-1 Trapdoor Functions from the Diffie-Hellman Problem

Nico Döttling
Sanjam Garg
Mohammad Hajiabadi
Kevin Liu
Giulio Malavolta
DOI: 10.1007/978-3-030-34618-8_20
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Abstract: Trapdoor functions (TDFs) are one of the fundamental building blocks in cryptography. Studying the underlying assumptions and the efficiency of the resulting instantiations is therefore of both theoretical and practical interest. In this work we improve the input-to-image rate of TDFs based on the Diffie-Hellman problem. Specifically, we present: (a)A rate-1 TDF from the computational Diffie-Hellman (CDH) assumption, improving the result of Garg, Gay, and Hajiabadi [EUROCRYPT 2019], which achieved linear-size outputs but with large constants. Our techniques combine non-binary alphabets and high-rate error-correcting codes over large fields.(b)A rate-1 deterministic public-key encryption satisfying block-source security from the decisional Diffie-Hellman (DDH) assumption. While this question was recently settled by Döttling et al. [CRYPTO 2019], our scheme is conceptually simpler and concretely more efficient. We demonstrate this fact by implementing our construction.
  title={Rate-1 Trapdoor Functions from the Diffie-Hellman Problem},
  booktitle={Advances in Cryptology – ASIACRYPT 2019},
  series={Advances in Cryptology – ASIACRYPT 2019},
  author={Nico Döttling and Sanjam Garg and Mohammad Hajiabadi and Kevin Liu and Giulio Malavolta},