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The construction of lattice-based identity-based encryption (IBE) schemes constitutes a fundamental research direction in lattice-based cryptography. The seminal work of Gentry, Peikert, and Vaikuntanathan (STOC 2008) established the first lattice-based IBE (GPV-IBE) scheme, which remains theoretically optimal in contemporary analysis. However, its practical efficiency is constrained by the requirement for discrete Gaussian sampling during user key generation — a process dependent on lattice trapdoors — where both sampling efficiency and trapdoor quality critically impact performance. While subsequent optimizations of GPV-IBE have improved sampling efficiency and reduced security loss, further enhancements are still achievable. In this work, we present a comprehensive analysis of gadget sampling. Concretely, we propose a new non-spherical discrete Gaussian sampling framework to achieve better sampling efficiency over ideal lattice. Then based on Tomita and Shikata’s lattice IBE (PQCrypto 2024), we propose a new lattice IBE, and the proposed scheme offers two advantages: (1) it provides a tight security reduction to the asymmetric version of ring Learning with Errors (RLWE) in the random oracle model; and (2) it improves parameter flexibility compared to existing lattice IBEs.

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Lattice IBE from Non-spherical Gaussian Sampling with Tight Security

  • 会议论文

  • 发表日期：

    2026年

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  • Guotao Chai,
  • Renjie Jin,
  • Shuoqu Jian,
  • Longjiang Qu

摘要

The construction of lattice-based identity-based encryption (IBE) schemes constitutes a fundamental research direction in lattice-based cryptography. The seminal work of Gentry, Peikert, and Vaikuntanathan (STOC 2008) established the first lattice-based IBE (GPV-IBE) scheme, which remains theoretically optimal in contemporary analysis. However, its practical efficiency is constrained by the requirement for discrete Gaussian sampling during user key generation — a process dependent on lattice trapdoors — where both sampling efficiency and trapdoor quality critically impact performance. While subsequent optimizations of GPV-IBE have improved sampling efficiency and reduced security loss, further enhancements are still achievable. In this work, we present a comprehensive analysis of gadget sampling. Concretely, we propose a new non-spherical discrete Gaussian sampling framework to achieve better sampling efficiency over ideal lattice. Then based on Tomita and Shikata’s lattice IBE (PQCrypto 2024), we propose a new lattice IBE, and the proposed scheme offers two advantages: (1) it provides a tight security reduction to the asymmetric version of ring Learning with Errors (RLWE) in the random oracle model; and (2) it improves parameter flexibility compared to existing lattice IBEs.