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We construct a public-key encryption scheme whose security follows from the hardness of the (planted) MinRank problem over uniformly random instances. This corresponds to the hardness of decoding random linear rank-metric codes. In contrast, existing constructions of public-key encryption from such problems require the hardness of decoding specific families of structured codes. Central to our construction is the development of a new notion of duality for rank-metric codes.

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Public-Key Encryption from the MinRank Problem

  • 会议论文

  • 发表日期：

    2026年

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  • Rohit Chatterjee,
  • Changrui Mu,
  • Prashant Nalini Vasudevan

摘要

We construct a public-key encryption scheme whose security follows from the hardness of the (planted) MinRank problem over uniformly random instances. This corresponds to the hardness of decoding random linear rank-metric codes. In contrast, existing constructions of public-key encryption from such problems require the hardness of decoding specific families of structured codes. Central to our construction is the development of a new notion of duality for rank-metric codes.