1. 引言
Salleras和Daza 2021年论文《 ZPiE: Zero-Knowledge Proofs in Embedded Systems》。
代码实现：
- https://github.com/xevisalle/zpie（C语言）
可以跨平台编译为X86/X64/ARM-32/ARM-64，从而支持在嵌入式平台上运行。
zyd@zyd-VirtualBox:~/zyd/zpie$ ./zpie
******************* ZPiE v0.2 *******************
USAGE: ./zpie [ACTIONS] [OPTIONS]
[ACTIONS]:
-s : Perform setup.
-p : Generate proof.
-v : Verify proof.
-pbp : Generate bulletproof where Nb is the bit size and Mc the number of aggregated proofs.
-vbp : Verify bulletproof where Nb is the bit size and Mc the number of aggregated proofs.
[OPTIONS]
-l : Activate operation logs.
zyd@zyd-VirtualBox:~/zyd/zpie$ ./zpie -s
******************* ZPiE v0.2 *******************
--- Starting ZPiE - Groth'16...
|--- # of constraints: 456
|--- # of variables: 650
|--- # of public outputs: 2
|--- Multi-core execution: OFF
|--- Elliptic curve: BN128
[SUCCESS] : Setup generated successfully in 1.095185s
zyd@zyd-VirtualBox:~/zyd/zpie$ ./zpie -p
******************* ZPiE v0.2 *******************
--- Starting ZPiE - Groth'16...
|--- # of constraints: 456
|--- # of variables: 650
|--- # of public outputs: 2
|--- Multi-core execution: OFF
|--- Elliptic curve: BN128
|--- Mode: Prove
|--- FFT constraints size : 512
[SUCCESS] : ZPiE started successfully in 1.101788s
--- Computing proof...
|--- Circuit evaluation: [0.000170s]
|--- Compute h coefficients: [0.002513s]
|--- G1, G2 multiexponentiations: [0.448896s]
|--- Bos-Coster: [0.109755s]
|--- Heap sorting: [0.003515s]
[SUCCESS] : Proof generated successfully in 0.488291s
zyd@zyd-VirtualBox:~/zyd/zpie$ ./zpie -v
******************* ZPiE v0.2 *******************
--- Starting ZPiE - Groth'16...
|--- # of constraints: 456
|--- # of variables: 650
|--- # of public outputs: 2
|--- Multi-core execution: OFF
|--- Elliptic curve: BN128
[SUCCESS] : Proof verified in 0.003520s
zyd@zyd-VirtualBox:~/zyd/zpie$ ./zpie -pbp 128 10
******************* ZPiE v0.2 *******************
--- Starting ZPiE - Bulletproofs...
|--- # of bits : 128
|--- # of aggregated proofs: 10
|--- Multi-core execution: OFF
|--- Elliptic curve: BN128
[ERROR] : Input values must be powers of two.
zyd@zyd-VirtualBox:~/zyd/zpie$ ./zpie -pbp 128 8
******************* ZPiE v0.2 *******************
--- Starting ZPiE - Bulletproofs...
|--- # of bits : 128
|--- # of aggregated proofs: 8
|--- Multi-core execution: OFF
|--- Elliptic curve: BN128
[SUCCESS] : Bulletproof created in 2.851989s
zyd@zyd-VirtualBox:~/zyd/zpie$ ./zpie -vbp 128 8
******************* ZPiE v0.2 *******************
--- Starting ZPiE - Bulletproofs...
|--- # of bits : 128
|--- # of aggregated proofs: 8
|--- Multi-core execution: OFF
|--- Elliptic curve: BN128
[SUCCESS] : Bulletproof verified in 1.147386s
zyd@zyd-VirtualBox:~/zyd/zpie$
[1] ZPiE: Zero-Knowledge Proofs in Embedded Systems
