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We introduce improved constructions of trapdoor hash (TDH) schemes under either DDH or DCR. Compared with the original construction of (Döttling et al., Crypto 2019), our new schemes are more expressive and feature more compact encoding keys. Expressivity: Our TDH scheme allows computing arbitrary functions of the form \(f(x,y) = \sum _i f_i(x)\cdot g_i(y)\) , where \(f_i, g_i\) are logarithmic-depth functions. This improves over the original construction that was restricted to computing the inner product between x and y. Compactness: Our TDH scheme has encoding keys of length \(|y|\cdot (1+o(1))\) , shaving an \(\varOmega (\lambda )\) factor compared to the original construction. Equipped with our new scheme, we revisit numerous applications of TDH and construct various low-communication cryptographic primitives that improve over the state of the art, including:

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Enhanced Trapdoor Hashing from DDH and DCR

  • 会议论文

  • 发表日期：

    2025年

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  • Geoffroy Couteau,
  • Aditya Hegde,
  • Sihang Pu

摘要

We introduce improved constructions of trapdoor hash (TDH) schemes under either DDH or DCR. Compared with the original construction of (Döttling et al., Crypto 2019), our new schemes are more expressive and feature more compact encoding keys. Expressivity: Our TDH scheme allows computing arbitrary functions of the form \(f(x,y) = \sum _i f_i(x)\cdot g_i(y)\) , where \(f_i, g_i\) are logarithmic-depth functions. This improves over the original construction that was restricted to computing the inner product between x and y. Compactness: Our TDH scheme has encoding keys of length \(|y|\cdot (1+o(1))\) , shaving an \(\varOmega (\lambda )\) factor compared to the original construction. Equipped with our new scheme, we revisit numerous applications of TDH and construct various low-communication cryptographic primitives that improve over the state of the art, including: