SOFIA: MQ-based signatures in the QROM

Ming-Shing Chen, Andreas Hülsing, Joost Rijneveld, Simona Samardjiska and Peter Schwabe

Abstract: We propose SOFIA, the first MQ-based signature scheme provably secure in the quantum-accessible random oracle model (QROM). Our construction relies on an extended version of Unruh's transform for 5-pass identification schemes that we describe and prove secure both in the ROM and QROM.

Based on a detailed security analysis, we provide concrete parameters for SOFIA that achieve 128 bit post-quantum security. The result is SOFIA-4-128 with parameters that are carefully optimized to minimize signature size and maximize performance. SOFIA-4-128 comes with an implementation targeting recent Intel processors with the AVX2 vector-instruction set; the implementation is fully protected against timing attacks.

Paper: 2017-07-07

Source code: Available on GitHub

Related talks:
SOFIA: MQ-based signatures in the QROM
2018-03-28 – PKC 2018
2018-02-01 – PQCRYPTO research retreat

  author       = {Ming-Shing Chen and Andreas H\"ulsing and Joost Rijneveld and Simona Samardjiska and Peter Schwabe},
  title        = {SOFIA: MQ-based signatures in the QROM},
  booktitle    = {Public Key Cryptography -- {PKC 2018}},
  year         = {2018},
  publisher    = {Springer-Verlag Berlin Heidelberg},
  series       = {Lecture Notes in Computer Science},
  volume       = {10770},
  editor       = {Michel Abdalla and Ricardo Dahab},
  pages        = {3--33},
  url          = {},