Fwd: Elliptic curve point multiplication with libgcrypt

gnu cry gcrypt4 at gmail.com
Thu Dec 7 14:16:41 CET 2017

---------- Forwarded message ----------
From: gnu cry <gcrypt4 at gmail.com>
Date: Thu, Dec 7, 2017 at 12:23 PM
Subject: Elliptic curve point multiplication with libgcrypt
To: gnupg-users at gnupg.org

Hi gpg hackers!

I want to implement an elliptic curve point multiplication (Q=dG) operation
with libgcrypt. I attach my code but my program doesn't work and it has
many errors. I comment the workflow of my program in the attached code.
my question is how do you implement Q=dG in C with libgcrypt? any idea
about my mistakes and how should I fix them?



#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <gcrypt.h>

//select and insert key and curve parameters
char *key521 =
				" (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_mpi_point_t Q,G;      //define and hold two elliptic curve point
	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
	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_mpi_ec_mul(Q,d,G,context);	              // calculate Q=dG

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