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SQIsign

Post-quantum digital signature scheme From Wikipedia, the free encyclopedia

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SQIsign is a post-quantum signature scheme submitted to first round of the post-quantum standardisation process. It is based around a proof of knowledge of an elliptic curve[a] endomorphism that can be transformed to a signature scheme using the Fiat–Shamir transform.

Quick Facts General, Designers ...
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It promises small key sizes between 64 and 128 bytes and small signature sizes between 177 and 335 bytes, which outperforms other post-quantum signature schemes that have a trade-off between signature and key sizes. SQIsign, however, has higher signing and verification times.[4] The original paper concluded that their C implementation takes 0.6 s for key generation, 2.5 s for a sign operation and 0.05 s or 50 ms for a verification operation.[5]

These times have been improved with new variations like SQIsign-east.[6]

The name stands for "Short Quaternion and Isogeny Signature" as it makes use of isogenies and quaternions.

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Security

SQIsign's security relies on the hardness of the endomorphism ring problem, which is currently considered hard.[7][8]

The authors also provide a rationale for the chosen parameters in the last chapter of the specification.[1]

While SQIsign makes use of a similar construction, the weaknesses of SIDH do not translate to it.[1]

There is a security proof for SQIsign.[9]

Implementations

There is a reference implementation hosted on GitHub.

SQIsign 2.0

The team behind SQIsign improved the original design in their round 2 submission and incorporated improvements from the SQIsign2D-West variant.[10]

This has improved the signing time by a factor of 20 and the verification time by a factor of 6 while increasing the security level and reducing the signature size by 14%.[10]:6

Variants

There are a couple of variants based on the original SQIsign:[11]

  • SQIsignHD: New dimensions in cryptography[12]
  • SQIsign2D-West: The fast, the small, and the safer[13]
  • SQIsign2D‑East: A new signature scheme using 2-dimensional isogenies[3]
  • SQIPrime: A dimension 2 variant of SQISignHD with non-smooth challenge isogenies[14]

References

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