[Mac] Installation process of cryptography library Miracl

unzip -j -aa -L MIRACL-master.zip

If a prompt similar to the following appears, enter n and press Enter.

replace readme.md? [y]es, [n]o, [A]ll, [N]one, [r]ename: n

The project comes with batch files such as linux, linux64, and linux_cpp. I chose linux64

coalbrother@MacBook-Air miracl % bash linux64
rm: *.exe: No such file or directory
rm: miracl.a: No such file or directory
mrmuldv.c:21:7: error: unknown register name 'eax' in asm
    : "eax","ebx","memory"
      ^
mrmuldv.c:38:7: error: unknown register name 'eax' in asm
    : "eax","ebx","memory"
      ^
mrmuldv.c:56:7: error: unknown register name 'eax' in asm
    : "eax","ebx","memory"
      ^
mrmuldv.c:76:7: error: unknown register name 'eax' in asm
    : "eax","ebx","esi","memory"
      ^
4 errors generated.
ar: mrmuldv.o: No such file or directory
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)
ld: unknown/unsupported architecture name for: -arch armv4t
clang: error: linker command failed with exit code 1 (use -v to see invocation)

Based on the error message provided, it looks like we are trying to link using the ld linker for the -arch armv4t architecture. Obviously, the error message indicates that the schema name is unknown or unsupported. Because the gcc used in this batch file uses the -m32 option, which tells the Clang compiler to generate 32-bit object code, we need to remove this -m32.
In addition, we want to use GNU, so we replace all gcc in it with gcc-13, Be careful not to replace line 54 The gcc was replaced with , and similarly, g++ was replaced with g++ -13. If you want to use the clang compiler, you need to replace clang with gcc, g++ Replace clang++

coalbrother@MacBook-Air miracl % bash linux64
rm: *.exe: No such file or directory
mrmuldv.c: In function 'muldiv':
mrmuldv.c:10:5: error: unknown register name 'ebx' in 'asm'
   10 | __asm__ __volatile__ (
      | ^~~~~~~
mrmuldv.c:10:5: error: unknown register name 'eax' in 'asm'
mrmuldv.c: In function 'muldvm':
mrmuldv.c:29:5: error: unknown register name 'ebx' in 'asm'
   29 | __asm__ __volatile__ (
      | ^~~~~~~
mrmuldv.c:29:5: error: unknown register name 'eax' in 'asm'
mrmuldv.c: In function 'muldvd':
mrmuldv.c:46:5: error: unknown register name 'ebx' in 'asm'
   46 | __asm__ __volatile__ (
      | ^~~~~~~
mrmuldv.c:46:5: error: unknown register name 'eax' in 'asm'
mrmuldv.c: In function 'muldvd2':
mrmuldv.c:63:5: error: unknown register name 'esi' in 'asm'
   63 | __asm__ __volatile__ (
      | ^~~~~~~
mrmuldv.c:63:5: error: unknown register name 'ebx' in 'asm'
mrmuldv.c:63:5: error: unknown register name 'eax' in 'asm'
ar: mrmuldv.o: No such file or directory
Undefined symbols for architecture arm64:
  "_brick_end", referenced from:
      _powers_precomp in cccDVd7k.o
  "_brick_init", referenced from:
      _powers_precomp in cccDVd7k.o
  "_ebrick2_end", referenced from:
      _mult2_precomp in cccDVd7k.o
  "_ebrick2_init", referenced from:
      _mult2_precomp in cccDVd7k.o
  "_ebrick_end", referenced from:
      _mult_precomp in cccDVd7k.o
  "_ebrick_init", referenced from:
      _mult_precomp in cccDVd7k.o
  "_ecurve2_init", referenced from:
      _main in cccDVd7k.o
  "_ecurve2_mult", referenced from:
      _mults2 in cccDVd7k.o
      _mult2_double in cccDVd7k.o
  "_ecurve2_mult2", referenced from:
      _mult2_double in cccDVd7k.o
  "_epoint2_set", referenced from:
      _main in cccDVd7k.o
  "_mul2_brick", referenced from:
      _mult2_precomp in cccDVd7k.o
  "_mul_brick", referenced from:
      _mult_precomp in cccDVd7k.o
  "_muldiv", referenced from:
      _redc in miracl.a(mrmonty.o)
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _xgcd.part.0 in miracl.a(mrxgcd.o)
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
  "_muldvd", referenced from:
      _divide in miracl.a(mrarth2.o)
      _mr_pmul in miracl.a(mrarth1.o)
  "_muldvd2", referenced from:
      _redc in miracl.a(mrmonty.o)
      _multiply in miracl.a(mrarth2.o)
  "_muldvm", referenced from:
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _xgcd.part.0 in miracl.a(mrxgcd.o)
      _mr_sdiv in miracl.a(mrarth1.o)
  "_pow_brick", referenced from:
      _powers_precomp in cccDVd7k.o
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
Undefined symbols for architecture arm64:
  "_muldiv", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
  "_muldvd", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _divide in miracl.a(mrarth2.o)
  "_muldvd2", referenced from:
      _multiply in miracl.a(mrarth2.o)
  "_muldvm", referenced from:
      _mr_sdiv in miracl.a(mrarth1.o)
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
Undefined symbols for architecture arm64:
  "_ecurve2_init", referenced from:
      __Z7ecurve2iiiiRK3BigS1_ii in big.o
  "_muldiv", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
      _egcd in miracl.a(mrgcd.o)
      _mr_dif_fft in miracl.a(mrfast.o)
      ...
  "_muldvd", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _divide in miracl.a(mrarth2.o)
      _fft_mult in miracl.a(mrfast.o)
      _smul in miracl.a(mrsmall.o)
  "_muldvd2", referenced from:
      _multiply in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
  "_muldvm", referenced from:
      _mr_sdiv in miracl.a(mrarth1.o)
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _egcd in miracl.a(mrgcd.o)
      _euclid in miracl.a(mrround.o)
      _xgcd.part.0 in miracl.a(mrxgcd.o)
      _invers in miracl.a(mrsmall.o)
      ...
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
Undefined symbols for architecture arm64:
  "_ecurve2_init", referenced from:
      __Z7ecurve2iiiiRK3BigS1_ii in big.o
  "_muldiv", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
      _egcd in miracl.a(mrgcd.o)
      _mr_dif_fft in miracl.a(mrfast.o)
      ...
  "_muldvd", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _divide in miracl.a(mrarth2.o)
      _fft_mult in miracl.a(mrfast.o)
      _smul in miracl.a(mrsmall.o)
  "_muldvd2", referenced from:
      _multiply in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
  "_muldvm", referenced from:
      _mr_sdiv in miracl.a(mrarth1.o)
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _egcd in miracl.a(mrgcd.o)
      _euclid in miracl.a(mrround.o)
      _xgcd.part.0 in miracl.a(mrxgcd.o)
      _build in miracl.a(mrbuild.o)
      ...
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
Undefined symbols for architecture arm64:
  "_muldiv", referenced from:
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _euclid in miracl.a(mrround.o)
  "_muldvd", referenced from:
      _divide in miracl.a(mrarth2.o)
      _mr_pmul in miracl.a(mrarth1.o)
  "_muldvd2", referenced from:
      _multiply in miracl.a(mrarth2.o)
  "_muldvm", referenced from:
      _build in miracl.a(mrbuild.o)
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _euclid in miracl.a(mrround.o)
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
Undefined symbols for architecture arm64:
  "_ecurve2_init", referenced from:
      __Z7ecurve2iiiiRK3BigS1_ii in big.o
  "_muldiv", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
      _egcd in miracl.a(mrgcd.o)
      _mr_dif_fft in miracl.a(mrfast.o)
      ...
  "_muldvd", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _divide in miracl.a(mrarth2.o)
      _fft_mult in miracl.a(mrfast.o)
      _smul in miracl.a(mrsmall.o)
  "_muldvd2", referenced from:
      _multiply in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
  "_muldvm", referenced from:
      _mr_sdiv in miracl.a(mrarth1.o)
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _egcd in miracl.a(mrgcd.o)
      _euclid in miracl.a(mrround.o)
      _xgcd.part.0 in miracl.a(mrxgcd.o)
      _build in miracl.a(mrbuild.o)
      ...
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
Undefined symbols for architecture arm64:
  "_ecurve2_init", referenced from:
      __Z7ecurve2iiiiRK3BigS1_ii in big.o
  "_muldiv", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
      _egcd in miracl.a(mrgcd.o)
      _mr_dif_fft in miracl.a(mrfast.o)
      ...
  "_muldvd", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _divide in miracl.a(mrarth2.o)
      _fft_mult in miracl.a(mrfast.o)
      _smul in miracl.a(mrsmall.o)
  "_muldvd2", referenced from:
      _multiply in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
  "_muldvm", referenced from:
      _mr_sdiv in miracl.a(mrarth1.o)
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _egcd in miracl.a(mrgcd.o)
      _euclid in miracl.a(mrround.o)
      _xgcd.part.0 in miracl.a(mrxgcd.o)
      _build in miracl.a(mrbuild.o)
      ...
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
Undefined symbols for architecture arm64:
  "_ecurve2_init", referenced from:
      __Z7ecurve2iiiiRK3BigS1_ii in big.o
  "_muldiv", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
      _egcd in miracl.a(mrgcd.o)
      _mr_dif_fft in miracl.a(mrfast.o)
      ...
  "_muldvd", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _divide in miracl.a(mrarth2.o)
      _fft_mult in miracl.a(mrfast.o)
      _smul in miracl.a(mrsmall.o)
  "_muldvd2", referenced from:
      _multiply in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
  "_muldvm", referenced from:
      _mr_sdiv in miracl.a(mrarth1.o)
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _egcd in miracl.a(mrgcd.o)
      _euclid in miracl.a(mrround.o)
      _xgcd.part.0 in miracl.a(mrxgcd.o)
      _build in miracl.a(mrbuild.o)
      ...
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
Undefined symbols for architecture arm64:
  "_ecurve2_init", referenced from:
      __Z7ecurve2iiiiRK3BigS1_ii in big.o
  "_muldiv", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
      _egcd in miracl.a(mrgcd.o)
      _mr_dif_fft in miracl.a(mrfast.o)
      ...
  "_muldvd", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _divide in miracl.a(mrarth2.o)
      _fft_mult in miracl.a(mrfast.o)
      _smul in miracl.a(mrsmall.o)
  "_muldvd2", referenced from:
      _multiply in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
  "_muldvm", referenced from:
      _mr_sdiv in miracl.a(mrarth1.o)
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _egcd in miracl.a(mrgcd.o)
      _euclid in miracl.a(mrround.o)
      _xgcd.part.0 in miracl.a(mrxgcd.o)
      _build in miracl.a(mrbuild.o)
      ...
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
Undefined symbols for architecture arm64:
  "_ecurve2_init", referenced from:
      __Z7ecurve2iiiiRK3BigS1_ii in big.o
  "_muldiv", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _mr_sdiv in miracl.a(mrarth1.o)
      _multiply in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
      _egcd in miracl.a(mrgcd.o)
      _mr_dif_fft in miracl.a(mrfast.o)
      ...
  "_muldvd", referenced from:
      _mr_pmul in miracl.a(mrarth1.o)
      _divide in miracl.a(mrarth2.o)
      _fft_mult in miracl.a(mrfast.o)
      _smul in miracl.a(mrsmall.o)
  "_muldvd2", referenced from:
      _multiply in miracl.a(mrarth2.o)
      _redc in miracl.a(mrmonty.o)
  "_muldvm", referenced from:
      _mr_sdiv in miracl.a(mrarth1.o)
      _normalise in miracl.a(mrarth2.o)
      _divide in miracl.a(mrarth2.o)
      _egcd in miracl.a(mrgcd.o)
      _invers in miracl.a(mrsmall.o)
      _euclid in miracl.a(mrround.o)
      _xgcd.part.0 in miracl.a(mrxgcd.o)
      ...
ld: symbol(s) not found for architecture arm64
collect2: error: ld returned 1 exit status
coalbrother@MacBook-Air miracl %

We encountered many problems again, and we analyzed them in turn.

• Don’t worry if the rm deletion fails. You can delete this sentence.
• unknown register name ebx’ in asm’. Since ebx is not a register in the arm architecture, this operation will report an error. Therefore, we need to replace this operation with standard C language code.
  Change mrmuldv.gcc to mrmuldv.ccc
• ar: mrmuldv.o: No such file or directory, including the following problems, are all caused by mrmuldv.o not being successfully compiled.

coalbrother@MacBook-Air miracl % bash linux64
rm: *.exe: No such file or directory

There is no problem now. According to the program in linux, we have successfully compiled the following files. The explanations come from readme.txt

bmark # Benchmark program for Public Key methods
fact #Factorials
big.o # C++ header for 'big' numbers
zzn.o # C++ header for 'big' numbers mod n
ecn.o # C++ header for GF(p) Elliptic Curves
ec2.o # EC2 function implementations
crt.o # Crt function implementations
mersenne # Mersenne primes
brent # Brent-pollard factoring
flash.o # Flash function implementations
sample # Example C++ source (uses FLASH.H)
ecsgen # DSS (Elliptic Curve GF(p) variation) key generator program
ecsign # DSS (Elliptic Curve GF(p) variation) signature program (static stack-only version)
ecsver # DSS (Elliptic Curve GF(p) variation) verification program (static stack-only version)
pk-demo # Demo of RSA/El Gamal/Diffie-Hellman/Elliptic Curve...
polymod.o # ZZn Polynomial arithmetic wrt a Polynomial Modulus
poly.o # Polynomial Arithmetic with ZZn coefficients

In fact, after having the static library miracl.a, our installation is completed (that is, after all ar operations are completed), all mr* The .o templates are stuffed into miracl.a and used for compiling C language programs.

BLS algorithm based on bilinear pairing

In the miracle manual manual and pairings.txt, it is mentioned that miracl supports pairing-based cryptography, including eta pairing and tate pairing. Unfortunately, GF(2^m) The pairing on is actually broken and is no longer used. Here we use bls.cpp

/*
   Boneh-Lynn-Shacham short signature

   Compile with modules as specified in the selected header file

   For MR_PAIRING_CP curve
   cl /O2 /GX bls.cpp cp_pair.cpp zzn2.cpp big.cpp zzn.cpp ecn.cpp miracl.lib
   (Note this really doesn't make much sense as the signature will not be "short")

   For MR_PAIRING_MNT curve
   cl /O2 /GX bls.cpp mnt_pair.cpp zzn6a.cpp ecn3.cpp zzn3.cpp zzn2.cpp big.cpp zzn.cpp ecn.cpp miracl.lib
\t
   For MR_PAIRING_BN curve
   cl /O2 /GX bls.cpp bn_pair.cpp zzn12a.cpp ecn2.cpp zzn4.cpp zzn2.cpp big.cpp zzn.cpp ecn.cpp miracl.lib

   For MR_PAIRING_KSS curve
   cl /O2 /GX bls.cpp kss_pair.cpp zzn18.cpp zzn6.cpp ecn3.cpp zzn3.cpp big.cpp zzn.cpp ecn.cpp miracl.lib

   For MR_PAIRING_BLS curve
   cl /O2 /GX bls.cpp bls_pair.cpp zzn24.cpp zzn8.cpp zzn4.cpp zzn2.cpp ecn4.cpp big.cpp zzn.cpp ecn.cpp miracl.lib

   Test program
*/

#include <iostream>
#include <ctime>

//********** choose just one of these pairs **********
//#define MR_PAIRING_CP // AES-80 security
//#define AES_SECURITY 80

//#define MR_PAIRING_MNT // AES-80 security
//#define AES_SECURITY 80

#define MR_PAIRING_BN // AES-128 or AES-192 security
#define AES_SECURITY 128
//#define AES_SECURITY 192

//#define MR_PAIRING_KSS // AES-192 security
//#define AES_SECURITY 192

//#define MR_PAIRING_BLS // AES-256 security
//#define AES_SECURITY 256
//************************************************

#include "pairing_3.h"

int main()
{<!-- -->
PFC pfc(AES_SECURITY); // initialise pairing-friendly curve

G2 Q,V;
G1 S,R;
int lsb;
Big s,X;
time_t seed;

time(& amp;seed);
    irand((long)seed);

// Create system-wide G2 constant
pfc.random(Q);

pfc.random(s); // private key
V=pfc.mult(Q,s); // public key

//signature
pfc.hash_and_map(R,(char *)"Test Message to sign");
S=pfc.mult(R,s);

lsb=S.g.get(X); // signature is lsb bit and X

cout << "Signature= " << lsb << " " << X << endl;

// verification - first recover full point S
if (!S.g.set(X,1-lsb))
{<!-- -->
cout << "Signature is invalid" << endl;
exit(0);
}
pfc.hash_and_map(R,(char *)"Test Message to sign");


// Observe that Q is a constant
// Interesting that this optimization doesn't work for the Tate pairing, only the Ate

pfc.precomp_for_pairing(Q);

G1 *g1[2];
G2 *g2[2];
g1[0]= & amp;S; g1[1]= & amp;R;
g2[0]= & amp;Q; g2[1]= & amp;V;

if (pfc.multi_pairing(2,g2,g1)==1)
cout << "Signature verifies" << endl;
else
cout << "Signature is bad" << endl;

    return 0;
}

You can see in the code that the header file pairing_3.h is referenced, and pairing_3.h also references ecn.h,zzn2.h,ecn2.h ,zzn12a.h
Create a new Makefile file and fill in the following content

# Compiler and compilation options
CXX := clang++
CXX_COMPILE_FLAGS := -std=c + + 14 -Wall -O2 -c -I. -L.
CXX_LINK_FLAGS := -std=c + + 14 -Wall -O2 -L. miracl.a
# Source File
CPPS := bls.cpp ecn.cpp zzn2.cpp ecn2.cpp zzn12a.cpp
OS := bls.o ecn.o zzn2.o ecn2.o zzn12a.o
# Target file
OBJ := bls
#Library file path and link options
LIBRARY_PATH := -L.
all:
# compile
$(CXX) $(CXX_COMPILE_FLAGS) $(CPPS) $(LIBRARIES)
# Link
$(CXX) $(CXX_LINK_FLAGS) $(OS) $(LIBRARIES) -o $(OBJ)

I encountered the following error when running, which is also a problem that has troubled me for a long time.

coalbrother@MacBook-Air miracl % make
clang + + -std=c + + 14 -Wall -O2 -c -I. -L. bls.cpp ecn.cpp zzn2.cpp ecn2.cpp zzn12a.cpp
clang: warning: argument unused during compilation: '-L.' [-Wunused-command-line-argument]
zzn2.cpp:146:9: warning: unused variable 'qnr' [-Wunused-variable]
    int qnr=get_mip()->qnr;
        ^
1 warning generated.
clang + + -std=c + + 14 -Wall -O2 -L. miracl.a bls.o ecn.o zzn2.o ecn2.o zzn12a.o -o bls
Undefined symbols for architecture arm64:
  "read_only_error()", referenced from:
      _main in bls.o
  "tx(ZZn4 const & amp;)", referenced from:
      ZZn12::operator*=(ZZn12 const & amp;) in zzn12a.o
      inverse(ZZn12 const & amp;) in zzn12a.o
      tx(ZZn12 const & amp;) in zzn12a.o
  "one()", referenced from:
      ZZn2::operator/=(ZZn const & amp;) in zzn2.o
      ZZn2::operator/=(int) in zzn2.o
      powu(ZZn2 const & amp;, Big const & amp;) in zzn2.o
      pow(ZZn12 const & amp;, Big const & amp;) in zzn12a.o
  "getA()", referenced from:
      is_on_curve(ZZn2 const & amp;) in zzn2.o
  "getB()", referenced from:
      is_on_curve(ZZn2 const & amp;) in zzn2.o
  "randn()", referenced from:
      randn2() in zzn2.o
  "randn4()", referenced from:
      randn12() in zzn12a.o
  "inverse(ZZn4 const & amp;)", referenced from:
      ZZn12::operator/=(ZZn4 const & amp;) in zzn12a.o
      inverse(ZZn12 const & amp;) in zzn12a.o
  "PFC::hash_and_map(G1 & amp;, char*)", referenced from:
      _main in bls.o
  "PFC::multi_pairing(int, G2**, G1**)", referenced from:
      _main in bls.o
  "PFC::precomp_for_pairing(G2 & amp;)", referenced from:
      _main in bls.o
  "PFC::mult(G1 const & amp;, Big const & amp;)", referenced from:
      _main in bls.o
  "PFC::mult(G2 const & amp;, Big const & amp;)", referenced from:
      _main in bls.o
  "PFC::random(G2 & amp;)", referenced from:
      _main in bls.o
  "PFC::random(Big & amp;)", referenced from:
      _main in bls.o
  "PFC::PFC(int, csprng*)", referenced from:
      _main in bls.o
  "PFC::~PFC()", referenced from:
      _main in bls.o
  "ZZn4::powq(ZZn2 const & amp;)", referenced from:
      ZZn12::powq(ZZn2 const & amp;) in zzn12a.o
  "Big::isone() const", referenced from:
      powu(ZZn2 const & amp;, Big const & amp;) in zzn2.o
  "Big::getbig() const", referenced from:
      _main in bls.o
      ECn::get(Big & amp;, Big & amp;) const in ecn.o
      ECn::get(Big &) const in ecn.o
      ECn::getx(Big & amp;) const in ecn.o
      ECn::getxy(Big & amp;, Big & amp;) const in ecn.o
      ECn::getxyz(Big & amp;, Big & amp;, Big & amp;) const in ecn.o
      operator*(Big const & amp;, ECn const & amp;) in ecn.o
      ...
  "Big::iszero() const", referenced from:
      powu(ZZn2 const & amp;, Big const & amp;) in zzn2.o
  "ZZn::getzzn() const", referenced from:
      ZZn2::get(ZZn & amp;, ZZn & amp;) const in zzn2.o
      ZZn2::get(ZZn & amp;) const in zzn2.o
      ZZn2::operator/=(ZZn const & amp;) in zzn2.o
      ZZn2::operator/=(int) in zzn2.o
      operator + (ZZn2 const & amp;, ZZn const & amp;) in zzn2.o
      operator-(ZZn2 const & amp;, ZZn const & amp;) in zzn2.o
      operator*(ZZn2 const & amp;, ZZn const & amp;) in zzn2.o
      ...
  "operator/(ZZn const & amp;, ZZn const & amp;)", referenced from:
      ZZn2::operator/=(ZZn const & amp;) in zzn2.o
  "operator/(ZZn const & amp;, int)", referenced from:
      ZZn2::operator/=(int) in zzn2.o
  "operator<<(std::__1::basic_ostream<char, std::__1::char_traits<char>> & amp;, Big const & amp;)", referenced from:
      _main in bls.o
      operator<<(std::__1::basic_ostream<char, std::__1::char_traits<char>> & amp;, ECn const & amp;) in ecn.o
      operator<<(std::__1::basic_ostream<char, std::__1::char_traits<char>> & amp;, ZZn2 const & amp;) in zzn2.o
  "operator<<(std::__1::basic_ostream<char, std::__1::char_traits<char>> & amp;, ZZn4 const & amp;)", referenced from:
      operator<<(std::__1::basic_ostream<char, std::__1::char_traits<char>> & amp;, ZZn12 const & amp;) in zzn12a.o
  "operator-(ZZn4 const & amp;, ZZn4 const & amp;)", referenced from:
      ZZn12::operator*=(ZZn12 const & amp;) in zzn12a.o
      inverse(ZZn12 const & amp;) in zzn12a.o
  "operator*(ZZn4 const & amp;, ZZn4 const & amp;)", referenced from:
      ZZn12::operator*=(ZZn12 const & amp;) in zzn12a.o
      inverse(ZZn12 const & amp;) in zzn12a.o
  "operator*(int, Big const & amp;)", referenced from:
      powu(ZZn2 const & amp;, Big const & amp;) in zzn2.o
  "operator-(Big const & amp;)", referenced from:
      powu(ZZn2 const & amp;, Big const & amp;) in zzn2.o
      pow(ZZn12 const & amp;, Big const & amp;) in zzn12a.o
  "operator-(ZZn4 const & amp;)", referenced from:
      ZZn12::operator*=(ZZn12 const & amp;) in zzn12a.o
      ZZn12::conj() in zzn12a.o
      operator-(ZZn12 const & amp;) in zzn12a.o
  "operator + (ZZn4 const & amp;, ZZn4 const & amp;)", referenced from:
      ZZn12::operator*=(ZZn12 const & amp;) in zzn12a.o
      inverse(ZZn12 const & amp;) in zzn12a.o
ld: symbol(s) not found for architecture arm64
clang: error: linker command failed with exit code 1 (use -v to see invocation)
make: *** [all] Error 1

ld: symbol(s) not found for architecture arm64
This error message indicates that the linker cannot find a symbol that meets the requirements of the arm64 architecture. In order to solve this problem, I searched all over the Internet and couldn’t find the answer
Finally I saw this sentence in the manual

Combined with the previous article, that is to say, we need to add the modules used to miracl.a! ! !

As for the code after line 69, you can actually delete it. We only need to regenerate miracl.a again.

coalbrother@MacBook-Air miracl % bash linux64
bn_pair.cpp:1439:8: warning: assigning field to itself [-Wself-assign-field]
        mtbits=mtbits;
              ^
1 warning generated.
coalbrother@MacBook-Air miracl % make
clang + + -std=c + + 14 -Wall -O2 -c -I. -L. bls.cpp ecn.cpp zzn2.cpp ecn2.cpp zzn12a.cpp
clang: warning: argument unused during compilation: '-L.' [-Wunused-command-line-argument]
zzn2.cpp:146:9: warning: unused variable 'qnr' [-Wunused-variable]
    int qnr=get_mip()->qnr;
        ^
1 warning generated.
clang + + -std=c + + 14 -Wall -O2 -L. miracl.a bls.o ecn.o zzn2.o ecn2.o zzn12a.o -o bls
coalbrother@MacBook-Air miracl % ./bls
Signature= 0 1296B58E158530D16AABEC2A34D7129EB2337405EA6156725C6EEFE2DB2EE799
Signature verifies

Now you can see that there are no errors and the bls file can be successfully executed!

Conclusion

Creation is not easy, I hope you can like it and support it