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Updated features and size/speed numbers for new point multiplication algorithm.
This commit is contained in:
Ken MacKay
@@ -11,19 +11,17 @@ A small ECDH and ECDSA implementation for 32-bit microcontrollers.
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Features
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--------
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* BSD 2-clause license.
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* Resistant to known side-channel attacks.
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* Written in C, with optional inline assembly for ARM and Thumb platforms.
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* Small code size: as low as 1800 bytes when compiled for Thumb (eg, Cortex-M0).
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* Small code size: ECDH in as little as 2KB, ECDH + ECDSA in as little as 3KB when compiled for Thumb (eg, Cortex-M0).
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* No dynamic memory allocation.
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* 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 ~150ms (depending on selected optimizations).
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* 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).
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* Support for 4 standard curves: secp128r1, secp192r1, secp256r1, and secp384r1
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* Optional optimizations so you can choose between code size and speed.
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* BSD 2-clause license.
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Usage Notes
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-----------
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**NOTE:** This implementation is not designed to be resistant to timing attacks or other side-channel attacks. To thwart timing attacks, you can use a timer to ensure that all ECDH operations take the same amount of time (ie, the longest time it would ever take). You can determine the maximum time for ECDH by using a private key that is all 0xffffffff.
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#### Integer Representation ####
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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};`.
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@@ -43,7 +41,6 @@ Speed and Size
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Available optimizations are:
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* `ECC_SQUARE_FUNC` - Use a separate function for squaring.
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* `ECC_USE_NAF` - Use a non-adjacent form for scalar representation when doing point multiplication.
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* `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`.
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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),
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@@ -55,9 +52,7 @@ The following compiler options were used (using gcc 4.8):
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### Effect of optimization settings ###
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These tests were performed using the curve secp192r1. Only ECDH code was used (no ECDSA).
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#### ECC_ASM defined to ecc_asm_none ####
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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`.
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<table>
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<tr>
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@@ -67,61 +62,29 @@ These tests were performed using the curve secp192r1. Only ECDH code was used (n
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</tr>
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<tr>
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<td>none</td>
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<td>431.9</td>
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<td>1948</td>
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<td>438.9</td>
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<td>2212</td>
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</tr>
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<tr>
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<td>ECC_SQUARE_FUNC</td>
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<td>393.0</td>
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<td>2152</td>
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</tr>
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<tr>
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<td>ECC_USE_NAF</td>
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<td>369.5</td>
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<td>2208</td>
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</tr>
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<tr>
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<td>both</td>
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<td>337.2</td>
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<td>406.7</td>
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<td>2412</td>
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</tr>
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</table>
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#### ECC_ASM defined to ecc_asm_thumb ####
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<table>
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<tr>
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<th>Optimizations</th>
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<th>ECDH time (ms)</th>
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<th>Code size (bytes)</th>
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</tr>
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<tr>
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<td>none</td>
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<td>183.9</td>
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<td>1772</td>
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</tr>
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<tr>
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<td>ECC_SQUARE_FUNC</td>
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<td>172.6</td>
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<td>1920</td>
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</tr>
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<tr>
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<td>ECC_USE_NAF</td>
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<td>158.2</td>
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<td>2032</td>
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<td>ECC_ASM</td>
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<td>186.3</td>
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<td>2036</td>
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</tr>
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<tr>
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<td>both</td>
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<td>147.7</td>
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<td>2180</td>
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<td>175.7</td>
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<td>2170</td>
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</tr>
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</table>
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### ECDH for different curves ###
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In these tests, `ECC_ASM` was defined to `ecc_asm_thumb` in all cases.
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#### No other optimizations (smallest code size) ####
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In these tests, `ECC_ASM` was defined to `ecc_asm_thumb` and `ECC_SQUARE_FUNC` was defined to `1` in all cases.
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<table>
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<tr>
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@@ -133,51 +96,23 @@ In these tests, `ECC_ASM` was defined to `ecc_asm_thumb` in all cases.
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</tr>
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<tr>
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<td><em>ECDH time (ms):</em></td>
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<td>85.5</td>
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<td>183.9</td>
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<td>473.6</td>
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<td>1405.8</td>
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<td>89.9</td>
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<td>175.7</td>
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<td>465.1</td>
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<td>1370.3</td>
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</tr>
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<tr>
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<td><em>Code size (bytes):</em></td>
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<td>1908</td>
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<td>1772</td>
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<td>2104</td>
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<td>1832</td>
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</tr>
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</table>
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#### All optimizations (fastest) ####
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<table>
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<tr>
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<th></th>
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<th>secp128r1</th>
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<th>secp192r1</th>
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<th>secp256r1</th>
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<th>secp384r1</th>
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</tr>
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<tr>
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<td><em>ECDH time (ms):</em></td>
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<td>75.9</td>
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<td>147.7</td>
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<td>385.8</td>
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<td>1128.2</td>
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</tr>
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<tr>
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<td><em>Code size (bytes):</em></td>
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<td>2332</td>
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<td>2180</td>
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<td>2516</td>
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<td>2324</td>
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<td>2170</td>
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<td>2512</td>
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<td>2244</td>
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</tr>
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</table>
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### ECDSA speed and combined code size ###
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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` in all cases.
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#### No other optimizations (smallest code size) ####
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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.
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<table>
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<tr>
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@@ -189,51 +124,23 @@ In these tests, the measured speed is the time to verify an ECDSA signature. The
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</tr>
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<tr>
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<td><em>ECDSA verify time (ms):</em></td>
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<td>108.6</td>
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<td>230.6</td>
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<td>590.2</td>
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<td>1729.7</td>
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<td>106.7</td>
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<td>217.1</td>
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<td>555.2</td>
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<td>1576.1</td>
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</tr>
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<tr>
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<td><em>Code size (bytes):</em></td>
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<td>2638</td>
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<td>2526</td>
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<td>2846</td>
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<td>2674</td>
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</tr>
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</table>
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#### All optimizations (fastest) ####
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<table>
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<tr>
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<th></th>
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<th>secp128r1</th>
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<th>secp192r1</th>
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<th>secp256r1</th>
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<th>secp384r1</th>
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</tr>
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<tr>
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<td><em>ECDSA verify time (ms):</em></td>
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<td>108.0</td>
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<td>219.0</td>
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<td>558.5</td>
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<td>1615.0</td>
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</tr>
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<tr>
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<td><em>Code size (bytes):</em></td>
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<td>3046</td>
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<td>2918</td>
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<td>3248</td>
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<td>3062</td>
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<td>3138</td>
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<td>3014</td>
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<td>3334</td>
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<td>3158</td>
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</tr>
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</table>
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### Maximum stack usage ###
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In these tests, `ECC_ASM` was defined to `ecc_asm_thumb` in all cases. The table values are the maximum possible stack usage for each function, in bytes.
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#### No other optimizations (smallest code size) ####
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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.
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<table>
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<tr>
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@@ -245,57 +152,10 @@ In these tests, `ECC_ASM` was defined to `ecc_asm_thumb` in all cases. The table
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</tr>
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<tr>
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<td><em>ecc_make_key()</em></td>
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<td>392</td>
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<td>488</td>
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<td>624</td>
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<td>848</td>
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</tr>
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<tr>
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<td><em>ecc_valid_public_key()</em></td>
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<td>184</td>
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<td>224</td>
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<td>304</td>
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<td>416</td>
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</tr>
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<tr>
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<td><em>ecdh_shared_secret()</em></td>
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<td>336</td>
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<td>416</td>
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<td>528</td>
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<td>680</td>
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<td>936</td>
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</tr>
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<tr>
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<td><em>ecdsa_sign()</em></td>
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<td>448</td>
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<td>568</td>
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<td>728</td>
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<td>1000</td>
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</tr>
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<tr>
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<td><em>ecdsa_verify()</em></td>
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<td>480</td>
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<td>616</td>
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<td>792</td>
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<td>1096</td>
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</tr>
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</table>
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#### All optimizations (fastest) ####
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<table>
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<tr>
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<th></th>
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<th>secp128r1</th>
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<th>secp192r1</th>
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<th>secp256r1</th>
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<th>secp384r1</th>
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</tr>
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<tr>
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<td><em>ecc_make_key()</em></td>
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<td>472</td>
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<td>600</td>
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<td>760</td>
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<td>1056</td>
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</tr>
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<tr>
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<td><em>ecc_valid_public_key()</em></td>
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@@ -306,23 +166,23 @@ In these tests, `ECC_ASM` was defined to `ecc_asm_thumb` in all cases. The table
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</tr>
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<tr>
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<td><em>ecdh_shared_secret()</em></td>
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<td>496</td>
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<td>640</td>
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<td>360</td>
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<td>456</td>
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<td>584</td>
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<td>816</td>
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<td>1144</td>
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</tr>
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<tr>
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<td><em>ecdsa_sign()</em></td>
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<td>528</td>
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<td>680</td>
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<td>864</td>
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<td>1208</td>
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<td>400</td>
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<td>504</td>
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<td>640</td>
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<td>888</td>
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</tr>
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<tr>
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<td><em>ecdsa_verify()</em></td>
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<td>488</td>
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<td>624</td>
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<td>792</td>
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<td>1104</td>
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<td>400</td>
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<td>520</td>
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<td>672</td>
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<td>952</td>
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</tr>
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</table>
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