FourQlib v3.1 (C Edition)

FourQlib implements essential elliptic curve and cryptographic functions based on FourQ, a high-security, high-performance elliptic curve that targets the 128-bit security level [1]. At the high level, FourQlib consists of a set of implementations targeting different platforms with different levels of portability and performance. The cryptographic and elliptic curve API is common to all the implementations.

The library was developed by Microsoft Research and is available under the MIT License.

Contents

Version 3.1 includes the following implementations:

• FourQ_32bit: a portable implementation especially tailored for 32-bit platforms.
• FourQ_64bit_and_portable: a portable implementation for 32-bit and 64-bit platforms with optional optimizations for x64 and 64-bit ARMv8 platforms.
• FourQ_ARM: an optimized implementation for 32-bit ARMv6, ARMv7 and ARMv7-M (Cortex-M4) platforms.
• FourQ_ARM_side_channel: an optimized implementation for 32-bit ARMv6, ARMv7 and ARMv7-M (Cortex-M4), including strong countermeasures against a wide variety of side-channel attacks.
• FourQ_ARM_NEON: an optimized implementation for 32-bit ARM platforms with NEON support.

The elliptic curve and crypto API can be found in FourQ_api.h, which is available per implementation.

The FourQ-Magma folder includes easy-to-read scripts written in Magma.

Complementary cryptographic functions

Random values are generated with /dev/urandom in the case of Linux, and with the function BCryptGenRandom() in the case of Windows. Check the random folder for details.

The library includes an implementation of SHA-512 which is used by default by SchnorrQ signatures (see sha512).

Users can provide their own PRNG and hash implementations by replacing the functions in the random and sha512folders, and applying the corresponding changes to the settings in FourQ.h (in a given implementation). Refer to [2] for the security requirements for the cryptographic hash function.

What's new

In version 3.0

• New support for co-factor ECDH and SchnorrQ signatures.
• New implementations for 32-bit processors, 32-bit ARMv6 and ARMv7 processors, and 32-bit ARM Cortex-M4 microcontroller.
• New implementation for ARMv6/ARMv7/ARMv7-M with strong countermeasures against several side-channel attacks.
• New support for 64-bit ARMv8 processors.

In version 3.1

• New hash to curve functionality (only supported in the portable implementation FourQ_64bit_and_portable).

Main features

• Support for co-factor Elliptic Curve Diffie-Hellman (ECDH) key exchange [3], the SchnorrQ digital signature scheme [2], and hash to curve conversion.
• Support for 3 core elliptic curve operations: variable-base, fixed-base and double-scalar multiplications.
• Support for Windows using Microsoft Visual Studio and Linux using GNU GCC or clang.
• Includes a basic implementation using portable C to enable support on a wide range of platforms including x64, x86 and ARM, Windows and Linux.
• Includes optimized implementations for 64-bit ARMv8 and x64 platforms with optional, high-performance x64 assembly for Linux [1].
• Includes high-performance implementations for 32-bit ARM processors with NEON support [4], for 32-bit ARMv6 and ARMv7 processors, and for 32-bit ARM Cortex-M4 microcontrollers [5].
• Includes side-channel secure implementations for 32-bit ARMv6/ARMv7 and for ARMv7-M (Cortex-M4) microcontrollers [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.

Quick start

Building the library and executing the tests on Linux

One can quickly test a given implementation by executing from the corresponding folder and using a supported architecture:

$ make ARCH=[x64/x86/ARM/ARM64] 

GNU GCC is used by default. After compilation, run fp_tests, ecc_tests or crypto_tests.

Below are the architectures supported by each implementation:

• FourQ_32bit: x86 and ARM
• FourQ_64bit_and_portable: x64, x86, ARM and ARM64
• FourQ_ARM, FourQ_ARM_side_channel and FourQ_ARM_NEON: ARM

For example, to compile the optimized x64 implementation using assembly with GNU GCC, using the efficient endomorphisms on a machine with AVX2 support (e.g, Intel's Haswell or Skylake), execute:

$ cd FourQ_64bit_and_portable
$ make ARCH=x64

Additional compilation options are available. Refer to the README files in a given implementation folder for complete details.

NOTE: the above instructions apply to all the "processor-class" implementations. For instructions on how to compile on an ARM Cortex-M (ARMv7-M) microcontroller, refer to the README files in FourQ_ARM_side_channel or FourQ_ARM.

Building the library and executing the tests on Windows

FourQ_32bit and FourQ_64bit_and_portable include Visual Studio solutions for compilation on Windows. Refer to the corresponding README files for instructions.

License

FourQlib is licensed under the MIT License; see License for details.

Files stm32f4_wrapper.c and stm32f4_wrapper.h in the FourQ_ARM and FourQ_ARM_side_channel folders are by Joost Rijneveld and are released under the CC0 1.0 Universal license.

Files in the folder FourQ_ARM_side_channel/libopencm3 and FourQ_ARM/libopencm3 are from the libopencm3 project and are under the GNU LGPL v3.0 license.

The SHA-512 implementation is by D.J. Bernstein and is released to the public domain.

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.

Contributing

This project has adopted the Microsoft Open Source Code of Conduct. For more information see the Code of Conduct FAQ or contact [email protected] with any additional questions or comments.