I want to implement an elliptic curve point multiplication (Q=dG) operation with libgcrypt (gcrypt). I write the following code:

#include <stdio.h> #include <string.h> #include <stdlib.h> #include <gcrypt.h>      //select and insert key and curve parameters char *key521 =         "(key-data\n"                 " (public-key\n"                 "  (ecc\n"                 "   (curve NIST P-521)\n"                 "   (q #00F2271E305679EBF9D7673FBF75EEA22E90D100A9E0B5DE30C500411E91710D05826F17F2C33A9527CC6799553C626C015ED666F63A4D5CEB27CDBE61F34DB0AF#)\n"                              "   )\n"                 "  )\n"                 " (private-key\n"                 "  (ecc\n"                 "   (curve NIST P-521)\n"                                "   (d #00BC9D8FD5D0AC1C91C04A1E0A5B6A89229924AAD20E23C5F5E3FE702C3C4633E325D2084DC0CE2005A88FF0512E0CACC271DF3279865DC2C33FCF573F7788278E#)\n"                 "   )\n"                 "  )\n"                 "\n )";                // workflow for calculating of Q=dG  int main() {      gcry_check_version(NULL);     gcry_mpi_point_t Q,G;      //define and hold two elliptic curve point     gcry_mpi_point_release(G);     gcry_mpi_t d;              //define the scalar (d)      gcry_sexp_t dsex;          //define an S-expression variable     gcry_sexp_sscan(&dsex, NULL, key521, strlen(key521));    //set dsex = d in key521 data structure     gcry_sexp_release(dsex);     d= gcry_sexp_nth_mpi(dsex,  1, GCRYMPI_FMT_USG);         // convert from S-exp to MPI format      char curvename= "NIST P-521";         //define curve name       gcry_ctx_t context;                   //define a context (ctx)     gcry_mpi_ec_new(context, dsex, curvename);    //set context     gcry_ctx_release(context);      gcry_mpi_ec_mul(Q,d,G,context);               // calculate Q=dG  } 

first, I select and insert the values of scalar (d) and curve (NIST P521) in S-expression format. then I write the main program (above code with comments).

my program doesn’t work and it has many errors and problems. my question is how do you implement Q=dG in C with libgcrypt library? any idea about my errors?

the below link is Libgcrypt Reference Manual:

https://www.gnupg.org/documentation/manuals/gcrypt