Squirrels is a digital signature scheme submitted to the NIST Call for Additional Post-Quantum Signature Schemes. It is designed by Thomas Espitau, Guilhem Niot, Chao Sun and Mehdi Tibouchi.

A short description of Squirrels for the cognoscenti is that it follows the hash-and-sign paradigm of Gentry, Peikert and Vaikuntanathan (GPV), instantiated over unstructured co-cyclic integer lattices. In that sense, it is close in spirit to schemes like Falcon, but avoids the reliance on lattices with an algebraic structure.

This design choice is generally considered more conservative for long term security, as structured lattices may suffer from specific vulnerabilities. This higher security confidence comes at a cost, since unstructured lattices do not admit the very compact description that structured lattices enjoy: this makes keys larger, and signing somewhat less efficient. Nevertheless, our trapdoor generation algorithm mitigates this drawback, and ensures that we reach a high level of security in moderate lattice dimensions.

Design Highlights

Squirrels offers the following features:


On a single core of a Ryzen Pro 7 5850U-based @ 3GHz based laptop, Squirrels achieves the following performance:

Parameter set keygen (s) sign/s vrfy/s pub size sig size
Squirrels-I 34 601.6 13099 666 kB 1019 B
Squirrels-II 52 509.0 11872 854 kB 1147 B
Squirrels-III 127 266.2 6594 1591 kB 1554 B
Squirrels-IV 179 208.7 5766 1844 kB 1676 B
Squirrels-V 351 177.9 3937 2721 kB 2025 B