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https://github.com/mratsim/constantine

Constantine: modular, high-performance, zero-dependency cryptography stack for proof systems and blockchain protocols.
https://github.com/mratsim/constantine

barreto-naehrig bigint bignum bls bls-signature bls12-381 constant-time cryptography digital-signature elliptic-curve-arithmetic elliptic-curve-cryptography elliptic-curves finite-fields galois-field hash-to-curve pairing pairing-cryptography public-key-cryptography side-channels zkp

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Constantine: modular, high-performance, zero-dependency cryptography stack for proof systems and blockchain protocols.

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README 

        
# Performance



High-performance is a sought out property.

Note that security and side-channel resistance takes priority over performance.



New applications of elliptic curve cryptography like zero-knowledge proofs or

proof-of-stake based blockchain protocols are bottlenecked by cryptography.



## In blockchain



Ethereum 2 clients spent or use to spend anywhere between 30% to 99% of their processing time verifying the signatures of block validators on R&D testnets

Assuming we want nodes to handle a thousand peers, if a cryptographic pairing takes 1ms, that represents 1s of cryptography per block to sign with a target

block frequency of 1 every 6 seconds.



## In zero-knowledge proofs



According to https://medium.com/loopring-protocol/zksnark-prover-optimizations-3e9a3e5578c0

a 16-core CPU can prove 20 transfers/second or 10 transactions/second.

The previous implementation was 15x slower and one of the key optimizations

was changing the elliptic curve cryptography backend.

It had a direct implication on hardware cost and/or cloud computing resources required.



## Measuring performance



To measure the performance of Constantine



```bash

git clone https://github.com/mratsim/constantine



# Default compiler

nimble bench_fp



# Arithmetic

CC=clang nimble bench_fp  # Using Clang + Assembly (recommended)

CC=clang nimble bench_fp2

CC=clang nimble bench_fp12



# Scalar multiplication and pairings

CC=clang nimble bench_ec_g1_scalar_mul

CC=clang nimble bench_ec_g2_scalar_mul

CC=clang nimble bench_pairing_bls12_381



# And per-curve summaries

CC=clang nimble bench_summary_bn254_nogami

CC=clang nimble bench_summary_bn254_snarks

CC=clang nimble bench_summary_bls12_377

CC=clang nimble bench_summary_bls12_381



# The Ethereum BLS signature protocol

CC=clang nimble bench_ethereum_bls_signatures



# Multi-scalar multiplication

CC=clang nimble bench_ec_g1_msm_bls12_381

CC=clang nimble bench_ec_g1_msm_bn256_snarks

```



The full list of benchmarks is available in the [`benchmarks`](./benchmarks) folder.



As mentioned in the [Compiler caveats](#compiler-caveats) section, GCC is up to 2x slower than Clang due to mishandling of carries and register usage.



#### Ethereum BLS signatures (over BLS12-381 G2)



![Bench Ethereum BLS signature](./media/ethereum_bls_signatures.png)



### BLS12-381 detailed benchmarks



On my machine i9-11980HK (8 cores 2.6GHz, turbo 5GHz), for Clang + Assembly, **all being constant-time** (including scalar multiplication, square root and inversion).



![BLS12-381 perf summary](./media/bls12_381_perf_summary_i9-11980HK.png)



![BLS12-381 Multi-Scalar multiplication 1](./media/bls12_381_msm_i9-11980HK-8cores_1.png)

![BLS12-381 Multi-Scalar multiplication 2](./media/bls12_381_msm_i9-11980HK-8cores_2.png)

![BLS12-381 Multi-Scalar multiplication 3](./media/bls12_381_msm_i9-11980HK-8cores_3.png)



### BN254-Snarks Multi-Scalar-Multiplication benchmarks



On a i9-9980XE (18 cores,watercooled, overclocked, 4.1GHz all core turbo)



![BN254-Snarks multi-scalar multiplication](./media/bn254_snarks_msm-i9-9980XE-18cores.png)



### Parallelism



Constantine multithreaded primitives are powered by a highly tuned threadpool and stress-tested for:

- scheduler overhead

- load balancing with extreme imbalance

- nested data parallelism

- contention

- speculative/conditional parallelism



and provides the following paradigms:

- Future-based task-parallelism

- Data parallelism (nestable and awaitable for loops)

  - including arbitrary parallel reductions

- Dataflow parallelism / Stream parallelism / Graph Parallelism / Pipeline parallelism

- Structured Parallelism



The threadpool parallel-for loops use lazy loop splitting and are fully adaptative to the workload being scheduled, the threads in-flight load and the hardware speed unlike most (all?) runtime, see:

- OpenMP woes depending on hardware and workload: https://github.com/zy97140/omp-benchmark-for-pytorch

- Raytracing ideal runtime, adapt to pixel compute load: ![load distribution](./media/parallel_load_distribution.png)\

  Most (all?) production runtime use scheduling A (split on number of threads like GCC OpenMP) or B (eager splitting, unable to adapt to actual work like LLVM/Intel OpenMP or Intel TBB) while Constantine uses C.



The threadpool provides efficient backoff strategy to conserve power based on:

- eventcounts / futexes, for low overhead backoff

- log-log iterated backoff, a provably optimal backoff strategy used for wireless communication to minimize communication in parallel for-loops



The research papers on high performance multithreading available in Weave repo: https://github.com/mratsim/weave/tree/7682784/research.\

_Note: The threadpool is not backed by Weave but by an inspired runtime that has been significantly simplified for ease of auditing. In particular it uses shared-memory based work-stealing instead of channel-based work-requesting for load balancing as distributed computing is not a target, ..., yet._



## Compiler caveats



Unfortunately compilers and in particular GCC are not very good at optimizing big integers and/or cryptographic code even when using intrinsics like `addcarry_u64`.



Compilers with proper support of `addcarry_u64` like Clang, MSVC and ICC

may generate code up to 20~25% faster than GCC.



This is explained by the GMP team: https://gmplib.org/manual/Assembly-Carry-Propagation.html

and can be reproduced with the following C code.



See https://gcc.godbolt.org/z/2h768y

```C

#include 

#include 



void add256(uint64_t a[4], uint64_t b[4]){

  uint8_t carry = 0;

  for (int i = 0; i < 4; ++i)

    carry = _addcarry_u64(carry, a[i], b[i], &a[i]);

}

```



GCC

```asm

add256:

        movq    (%rsi), %rax

        addq    (%rdi), %rax

        setc    %dl

        movq    %rax, (%rdi)

        movq    8(%rdi), %rax

        addb    $-1, %dl

        adcq    8(%rsi), %rax

        setc    %dl

        movq    %rax, 8(%rdi)

        movq    16(%rdi), %rax

        addb    $-1, %dl

        adcq    16(%rsi), %rax

        setc    %dl

        movq    %rax, 16(%rdi)

        movq    24(%rsi), %rax

        addb    $-1, %dl

        adcq    %rax, 24(%rdi)

        ret

```



Clang

```asm

add256:

        movq    (%rsi), %rax

        addq    %rax, (%rdi)

        movq    8(%rsi), %rax

        adcq    %rax, 8(%rdi)

        movq    16(%rsi), %rax

        adcq    %rax, 16(%rdi)

        movq    24(%rsi), %rax

        adcq    %rax, 24(%rdi)

        retq

```

### Inline assembly



While using intrinsics significantly improve code readability, portability, auditability and maintainability,

Constantine use inline assembly on x86-64 to ensure performance portability despite poor optimization (for GCC)

and also to use dedicated large integer instructions MULX, ADCX, ADOX that compilers cannot generate.



The speed improvement on finite field arithmetic is up 60% with MULX, ADCX, ADOX on BLS12-381 (6 limbs).



Finally assembly is a requirement to ensure constant-time property and to avoid compilers turning careful

branchless code into branches, see [Fighting the compiler (wiki)](https://github.com/mratsim/constantine/wiki/Constant-time-arithmetics#fighting-the-compiler)



In summary, pure C/C++/Nim implies:

- a smart compiler might unravel the constant time bit manipulation and reintroduce branches.

- a significant performance cost with GCC (~50% slower than Clang).

- missed opportunities on recent CPUs that support MULX/ADCX/ADOX instructions (~60% faster than Clang).

- 2.4x perf ratio between using plain GCC vs GCC with inline assembly.



## Sizes: code size, stack usage



Thanks to 10x smaller key sizes for the same security level as RSA, elliptic curve cryptography

is widely used on resource-constrained devices.



Constantine is actively optimize for code-size and stack usage.

Constantine does not use heap allocation.



At the moment Constantine is optimized for 32-bit and 64-bit CPUs.



When performance and code size conflicts, a careful and informed default is chosen.

In the future, a compile-time flag that goes beyond the compiler `-Os` might be provided.