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qDSA is a high-speed, high-security signature scheme that facilitatesimplementations with a very small memory footprint, a crucial requirement forembedded systems and IoT devices, and that uses the same public keys as modernDiffie--Hellman schemes based on Montgomery curves (such as Curve25519) orKummer surfaces. qDSA resembles an adaptation of EdDSA to the world of Kummervarieties, which are quotients of algebraic groups by $\pm$1. Interestingly,qDSA does not require any full group operations or point recovery: allcomputations, including signature verification, occur on the quotient wherethere is no group law. We include details on four implementations of qDSA,using Montgomery and fast Kummer surface arithmetic on the 8-bit AVR ATmega and32-bit ARM Cortex M0 platforms. We find that qDSA significantly outperformsstate-of-the-art signature implementations in terms of stack usage and codesize. We also include an efficient compression algorithm for points on fastKummer surfaces, reducing them to the same size as compressed elliptic curvepoints for the same security level.

qDSA: Small and Secure Digital Signatures with Curve-based Diffie--Hellman Key Pairs