FourQ on AVR

This is a state-of-the-art, 128-bit secure ECC library based on the elliptic curve FourQ [1] for 8-bit AVR microcontrollers.

The library was built upon FourQlib (https://github.com/Microsoft/FourQlib).

The current version contains AVR assembly code that is only compatible with the IAR C compiler.

The library was written by Zhe Liu (zhelu.liu@uwaterloo.ca), Geovandro Pereira (geovandro.pereira@uwaterloo.ca) and Hwajeong Seo (hwajeong84@gmail.com).

Contents

• iar-ide: project files for compilation with the IAR Workbench.
• License.txt: MIT License file.
• README.md: this readme file.

The source folder src contains:

• Main .c and .h files: library and header files. Public API for ECC scalar multiplication, key exchange and signatures is in src/FourQ_api.h.
• src/AVR/: folder with library files implementing low-level arithmetic for AVR.
• src/blake2b/: folder with implementation of hash function BLAKE2b.
• src/random/: folder with pseudo-random generation function (ONLY FOR TESTING).
• src/tests/: test files for AVR.

IMPORTANT SECURITY NOTE

Random values are generated with rand(). This is NOT a cryptographically secure function. Users should replace this function with a cryptographically-secure PRNG (see random.c) .

Complementary cryptographic functions

The library includes an implementation of BLAKE2b which is used by default by SchnorrQ signatures (see blake2b/).

Users can provide their own hash implementations by replacing the functions in blake2b/, and applying the corresponding changes to the settings in FourQ.h. Refer to [2] for the security requirements for the cryptographic hash function.

Main features

• Support for co-factor Elliptic Curve Diffie-Hellman (ECDH) key exchange [3].
• Support for the SchnorrQ digital signature scheme [2].
• Support for 3 core elliptic curve operations: variable-base, fixed-base and double-scalar multiplications.
• Includes an optimized implementation for 8-bit AVR microcontrollers with support for the IAR C compiler [5].
• Includes testing and benchmarking code for field arithmetic, elliptic curve and cryptographic functions.
• All functions evaluating secret data have regular, constant-time execution, protecting against timing and cache attacks.
• Includes an option to disable the use of the fast endomorphisms.

Instructions

Download the IAR Workbench for AVR (https://www.iar.com/iar-embedded-workbench/).

Open the project file microFourQ_AVR.eww and click on Project > Rebuild All.

Project settings can be accessed and modified by going to Project > Options....

License

This library is licensed under the MIT License; see License.txt for details.

It is based on the Microsoft library FourQlib (https://github.com/Microsoft/FourQlib), which is also licensed under MIT.

The BLAKE2b implementation, written by Thomas Pornin, is under an MIT-like open source license (see blake.c).

The files mp_add.s and mp_sub.s, written by Johann Groszschaedl and copyrighted by University of Luxembourg, are licensed under GPLv3.

References

[1] Craig Costello and Patrick Longa, "FourQ: four-dimensional decompositions on a Q-curve over the Mersenne prime". Advances in Cryptology - ASIACRYPT 2015, 2015. The extended version is available here.

[2] Craig Costello and Patrick Longa. "SchnorrQ: Schnorr signatures on FourQ". MSR Technical Report, 2016. Available here.

[3] Watson Ladd, Patrick Longa and Richard Barnes, "Curve4Q". Internet-Draft, draft-ladd-cfrg-4q-01, 2017. Available here.

[4] Patrick Longa, "FourQNEON: faster elliptic curve scalar multiplications on ARM processors". Selected Areas in Cryptography (SAC 2016), 2016. Preprint available here.

[5] Zhe Liu, Patrick Longa, Geovandro Pereira, Oscar Reparaz and Hwajeong Seo, "FourQ on embedded devices with strong countermeasures against side-channel attacks". Preprint available here.