micro-ecc

A small ECDH and ECDSA implementation for 32-bit microcontrollers. See easy-ecc for a fast and secure pure-C implementation for *nix and Windows.

Features

• Resistant to known side-channel attacks.
• Written in C, with optional inline assembly for ARM and Thumb platforms.
• Small code size: ECDH in as little as 2KB, ECDH + ECDSA in as little as 3KB when compiled for Thumb (eg, Cortex-M0).
• No dynamic memory allocation.
• Reasonably fast: on an LPC1114 at 48MHz (ARM Cortex-M0, 32-cycle 32x32 bit multiply), 192-bit ECDH shared secret calculation takes as little as ~175ms (depending on selected optimizations).
• Support for 4 standard curves: secp128r1, secp192r1, secp256r1, and secp384r1
• BSD 2-clause license.

Usage Notes

Integer Representation

To reduce code size, all large integers are represented using little-endian words - so the least significant word is first. For example, the standard representation of the prime modulus for the curve secp128r1 is FFFFFFFD FFFFFFFF FFFFFFFF FFFFFFFF; in micro-ecc, this would be represented as uint32_t p[4] = {0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffd};.

You can use the ecc_bytes2native() and ecc_native2bytes() functions to convert between the native integer representation and the standardized octet representation.

Generating Keys

You can use the makekeys program in the apps directory to generate keys (on Linux or OS X). You can run make in that directory to build for your native platform (or use emk). To generate a single public/private key pair, run makekeys. It will print out the public and private keys in a representation suitable to be copied into your source code. You can generate multiple key pairs at once using makekeys <n> to generate n keys.

Using the Code

I recommend just copying (or symlink) ecc.h and ecc.c into your project. Then just #include "ecc.h" to use the micro-ecc functions.

See ecc.h for documentation for each function.

Speed and Size

Available optimizations are:

• ECC_SQUARE_FUNC - Use a separate function for squaring.
• ECC_ASM - Choose the type of inline assembly to use. The available options are ecc_asm_none, ecc_asm_thumb, ecc_asm_thumb2, and ecc_asm_arm.

All tests were performed on an LPC1114 running at 48MHz. The listed code sizes include all code and data required by the micro-ecc library (including aebi_lmul when not using assembly), but do not include the sizes of the code using the library functions.

The following compiler options were used (using gcc 4.8):

• Compile: -mcpu=cortex-m0 -mthumb -ffunction-sections -fdata-sections -Os
• Link: -mcpu=cortex-m0 -mthumb -nostartfiles -nostdlib -Wl,--gc-sections

Effect of optimization settings

These tests were performed using the curve secp192r1. Only ECDH code was used (no ECDSA). When enabled, ECC_ASM was defined to ecc_asm_thumb.

ECDH for different curves

In these tests, ECC_ASM was defined to ecc_asm_thumb and ECC_SQUARE_FUNC was defined to 1 in all cases.

ECDSA speed and combined code size

In these tests, the measured speed is the time to verify an ECDSA signature. The measured code size is the combined code size for ECDH and ECDSA. ECC_ASM was defined to ecc_asm_thumb and ECC_SQUARE_FUNC was defined to 1 in all cases.

Maximum stack usage

In these tests, ECC_ASM was defined to ecc_asm_thumb and ECC_SQUARE_FUNC was defined to 1 in all cases. The table values are the maximum possible stack usage for each function, in bytes.