fe25519.c - security/openssh-library - Rivoreo Source Code Repositories

 /* $OpenBSD: */

 /* Public Domain, from supercop-20130419/crypto_sign/ed25519/ref/fe25519.c */

 #define WINDOWSIZE 1 /* Should be 1,2, or 4 */
 #define WINDOWMASK ((1<<WINDOWSIZE)-1)

 #include "fe25519.h"

 static crypto_uint32 equal(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
 {
   crypto_uint32 x = a ^ b; /* 0: yes; 1..65535: no */
   x -= 1; /* 4294967295: yes; 0..65534: no */
   x >>= 31; /* 1: yes; 0: no */
   return x;
 }

 static crypto_uint32 ge(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
 {
   unsigned int x = a;
   x -= (unsigned int) b; /* 0..65535: yes; 4294901761..4294967295: no */
   x >>= 31; /* 0: yes; 1: no */
   x ^= 1; /* 1: yes; 0: no */
   return x;
 }

 static crypto_uint32 times19(crypto_uint32 a)
 {
   return (a << 4) + (a << 1) + a;
 }

 static crypto_uint32 times38(crypto_uint32 a)
 {
   return (a << 5) + (a << 2) + (a << 1);
 }

 static void reduce_add_sub(fe25519 *r)
 {
   crypto_uint32 t;
   int i,rep;

   for(rep=0;rep<4;rep++)
   {
     t = r->v[31] >> 7;
     r->v[31] &= 127;
     t = times19(t);
     r->v[0] += t;
     for(i=0;i<31;i++)
     {
       t = r->v[i] >> 8;
       r->v[i+1] += t;
       r->v[i] &= 255;
     }
   }
 }

 static void reduce_mul(fe25519 *r)
 {
   crypto_uint32 t;
   int i,rep;

   for(rep=0;rep<2;rep++)
   {
     t = r->v[31] >> 7;
     r->v[31] &= 127;
     t = times19(t);
     r->v[0] += t;
     for(i=0;i<31;i++)
     {
       t = r->v[i] >> 8;
       r->v[i+1] += t;
       r->v[i] &= 255;
     }
   }
 }

 /* reduction modulo 2^255-19 */
 void fe25519_freeze(fe25519 *r)
 {
   int i;
   crypto_uint32 m = equal(r->v[31],127);
   for(i=30;i>0;i--)
     m &= equal(r->v[i],255);
   m &= ge(r->v[0],237);

   m = -m;

   r->v[31] -= m&127;
   for(i=30;i>0;i--)
     r->v[i] -= m&255;
   r->v[0] -= m&237;
 }

 void fe25519_unpack(fe25519 *r, const unsigned char x[32])
 {
   int i;
   for(i=0;i<32;i++) r->v[i] = x[i];
   r->v[31] &= 127;
 }

 /* Assumes input x being reduced below 2^255 */
 void fe25519_pack(unsigned char r[32], const fe25519 *x)
 {
   int i;
   fe25519 y = *x;
   fe25519_freeze(&y);
   for(i=0;i<32;i++)
     r[i] = y.v[i];
 }

 int fe25519_iszero(const fe25519 *x)
 {
   int i;
   int r;
   fe25519 t = *x;
   fe25519_freeze(&t);
   r = equal(t.v[0],0);
   for(i=1;i<32;i++)
     r &= equal(t.v[i],0);
   return r;
 }

 int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y)
 {
   int i;
   fe25519 t1 = *x;
   fe25519 t2 = *y;
   fe25519_freeze(&t1);
   fe25519_freeze(&t2);
   for(i=0;i<32;i++)
     if(t1.v[i] != t2.v[i]) return 0;
   return 1;
 }

 void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b)
 {
   int i;
   crypto_uint32 mask = b;
   mask = -mask;
   for(i=0;i<32;i++) r->v[i] ^= mask & (x->v[i] ^ r->v[i]);
 }

 unsigned char fe25519_getparity(const fe25519 *x)
 {
   fe25519 t = *x;
   fe25519_freeze(&t);
   return t.v[0] & 1;
 }

 void fe25519_setone(fe25519 *r)
 {
   int i;
   r->v[0] = 1;
   for(i=1;i<32;i++) r->v[i]=0;
 }

 void fe25519_setzero(fe25519 *r)
 {
   int i;
   for(i=0;i<32;i++) r->v[i]=0;
 }

 void fe25519_neg(fe25519 *r, const fe25519 *x)
 {
   fe25519 t;
   int i;
   for(i=0;i<32;i++) t.v[i]=x->v[i];
   fe25519_setzero(r);
   fe25519_sub(r, r, &t);
 }

 void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y)
 {
   int i;
   for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i];
   reduce_add_sub(r);
 }

 void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y)
 {
   int i;
   crypto_uint32 t[32];
   t[0] = x->v[0] + 0x1da;
   t[31] = x->v[31] + 0xfe;
   for(i=1;i<31;i++) t[i] = x->v[i] + 0x1fe;
   for(i=0;i<32;i++) r->v[i] = t[i] - y->v[i];
   reduce_add_sub(r);
 }

 void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y)
 {
   int i,j;
   crypto_uint32 t[63];
   for(i=0;i<63;i++)t[i] = 0;

   for(i=0;i<32;i++)
     for(j=0;j<32;j++)
       t[i+j] += x->v[i] * y->v[j];

   for(i=32;i<63;i++)
     r->v[i-32] = t[i-32] + times38(t[i]);
   r->v[31] = t[31]; /* result now in r[0]...r[31] */

   reduce_mul(r);
 }

 void fe25519_square(fe25519 *r, const fe25519 *x)
 {
   fe25519_mul(r, x, x);
 }

 void fe25519_invert(fe25519 *r, const fe25519 *x)
 {
 	fe25519 z2;
 	fe25519 z9;
 	fe25519 z11;
 	fe25519 z2_5_0;
 	fe25519 z2_10_0;
 	fe25519 z2_20_0;
 	fe25519 z2_50_0;
 	fe25519 z2_100_0;
 	fe25519 t0;
 	fe25519 t1;
 	int i;

 	/* 2 */ fe25519_square(&z2,x);
 	/* 4 */ fe25519_square(&t1,&z2);
 	/* 8 */ fe25519_square(&t0,&t1);
 	/* 9 */ fe25519_mul(&z9,&t0,x);
 	/* 11 */ fe25519_mul(&z11,&z9,&z2);
 	/* 22 */ fe25519_square(&t0,&z11);
 	/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t0,&z9);

 	/* 2^6 - 2^1 */ fe25519_square(&t0,&z2_5_0);
 	/* 2^7 - 2^2 */ fe25519_square(&t1,&t0);
 	/* 2^8 - 2^3 */ fe25519_square(&t0,&t1);
 	/* 2^9 - 2^4 */ fe25519_square(&t1,&t0);
 	/* 2^10 - 2^5 */ fe25519_square(&t0,&t1);
 	/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t0,&z2_5_0);

 	/* 2^11 - 2^1 */ fe25519_square(&t0,&z2_10_0);
 	/* 2^12 - 2^2 */ fe25519_square(&t1,&t0);
 	/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
 	/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t1,&z2_10_0);

 	/* 2^21 - 2^1 */ fe25519_square(&t0,&z2_20_0);
 	/* 2^22 - 2^2 */ fe25519_square(&t1,&t0);
 	/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
 	/* 2^40 - 2^0 */ fe25519_mul(&t0,&t1,&z2_20_0);

 	/* 2^41 - 2^1 */ fe25519_square(&t1,&t0);
 	/* 2^42 - 2^2 */ fe25519_square(&t0,&t1);
 	/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); }
 	/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t0,&z2_10_0);

 	/* 2^51 - 2^1 */ fe25519_square(&t0,&z2_50_0);
 	/* 2^52 - 2^2 */ fe25519_square(&t1,&t0);
 	/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
 	/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t1,&z2_50_0);

 	/* 2^101 - 2^1 */ fe25519_square(&t1,&z2_100_0);
 	/* 2^102 - 2^2 */ fe25519_square(&t0,&t1);
 	/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); }
 	/* 2^200 - 2^0 */ fe25519_mul(&t1,&t0,&z2_100_0);

 	/* 2^201 - 2^1 */ fe25519_square(&t0,&t1);
 	/* 2^202 - 2^2 */ fe25519_square(&t1,&t0);
 	/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
 	/* 2^250 - 2^0 */ fe25519_mul(&t0,&t1,&z2_50_0);

 	/* 2^251 - 2^1 */ fe25519_square(&t1,&t0);
 	/* 2^252 - 2^2 */ fe25519_square(&t0,&t1);
 	/* 2^253 - 2^3 */ fe25519_square(&t1,&t0);
 	/* 2^254 - 2^4 */ fe25519_square(&t0,&t1);
 	/* 2^255 - 2^5 */ fe25519_square(&t1,&t0);
 	/* 2^255 - 21 */ fe25519_mul(r,&t1,&z11);
 }

 void fe25519_pow2523(fe25519 *r, const fe25519 *x)
 {
 	fe25519 z2;
 	fe25519 z9;
 	fe25519 z11;
 	fe25519 z2_5_0;
 	fe25519 z2_10_0;
 	fe25519 z2_20_0;
 	fe25519 z2_50_0;
 	fe25519 z2_100_0;
 	fe25519 t;
 	int i;

 	/* 2 */ fe25519_square(&z2,x);
 	/* 4 */ fe25519_square(&t,&z2);
 	/* 8 */ fe25519_square(&t,&t);
 	/* 9 */ fe25519_mul(&z9,&t,x);
 	/* 11 */ fe25519_mul(&z11,&z9,&z2);
 	/* 22 */ fe25519_square(&t,&z11);
 	/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t,&z9);

 	/* 2^6 - 2^1 */ fe25519_square(&t,&z2_5_0);
 	/* 2^10 - 2^5 */ for (i = 1;i < 5;i++) { fe25519_square(&t,&t); }
 	/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t,&z2_5_0);

 	/* 2^11 - 2^1 */ fe25519_square(&t,&z2_10_0);
 	/* 2^20 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); }
 	/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t,&z2_10_0);

 	/* 2^21 - 2^1 */ fe25519_square(&t,&z2_20_0);
 	/* 2^40 - 2^20 */ for (i = 1;i < 20;i++) { fe25519_square(&t,&t); }
 	/* 2^40 - 2^0 */ fe25519_mul(&t,&t,&z2_20_0);

 	/* 2^41 - 2^1 */ fe25519_square(&t,&t);
 	/* 2^50 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); }
 	/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t,&z2_10_0);

 	/* 2^51 - 2^1 */ fe25519_square(&t,&z2_50_0);
 	/* 2^100 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); }
 	/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t,&z2_50_0);

 	/* 2^101 - 2^1 */ fe25519_square(&t,&z2_100_0);
 	/* 2^200 - 2^100 */ for (i = 1;i < 100;i++) { fe25519_square(&t,&t); }
 	/* 2^200 - 2^0 */ fe25519_mul(&t,&t,&z2_100_0);

 	/* 2^201 - 2^1 */ fe25519_square(&t,&t);
 	/* 2^250 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); }
 	/* 2^250 - 2^0 */ fe25519_mul(&t,&t,&z2_50_0);

 	/* 2^251 - 2^1 */ fe25519_square(&t,&t);
 	/* 2^252 - 2^2 */ fe25519_square(&t,&t);
 	/* 2^252 - 3 */ fe25519_mul(r,&t,x);
 }
	/* $OpenBSD: */

	/* Public Domain, from supercop-20130419/crypto_sign/ed25519/ref/fe25519.c */

	#define WINDOWSIZE 1 /* Should be 1,2, or 4 */
	#define WINDOWMASK ((1<<WINDOWSIZE)-1)

	#include "fe25519.h"

	static crypto_uint32 equal(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
	{
	crypto_uint32 x = a ^ b; /* 0: yes; 1..65535: no */
	x -= 1; /* 4294967295: yes; 0..65534: no */
	x >>= 31; /* 1: yes; 0: no */
	return x;
	}

	static crypto_uint32 ge(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
	{
	unsigned int x = a;
	x -= (unsigned int) b; /* 0..65535: yes; 4294901761..4294967295: no */
	x >>= 31; /* 0: yes; 1: no */
	x ^= 1; /* 1: yes; 0: no */
	return x;
	}

	static crypto_uint32 times19(crypto_uint32 a)
	{
	return (a << 4) + (a << 1) + a;
	}

	static crypto_uint32 times38(crypto_uint32 a)
	{
	return (a << 5) + (a << 2) + (a << 1);
	}

	static void reduce_add_sub(fe25519 *r)
	{
	crypto_uint32 t;
	int i,rep;

	for(rep=0;rep<4;rep++)
	{
	t = r->v[31] >> 7;
	r->v[31] &= 127;
	t = times19(t);
	r->v[0] += t;
	for(i=0;i<31;i++)
	{
	t = r->v[i] >> 8;
	r->v[i+1] += t;
	r->v[i] &= 255;
	}
	}
	}

	static void reduce_mul(fe25519 *r)
	{
	crypto_uint32 t;
	int i,rep;

	for(rep=0;rep<2;rep++)
	{
	t = r->v[31] >> 7;
	r->v[31] &= 127;
	t = times19(t);
	r->v[0] += t;
	for(i=0;i<31;i++)
	{
	t = r->v[i] >> 8;
	r->v[i+1] += t;
	r->v[i] &= 255;
	}
	}
	}

	/* reduction modulo 2^255-19 */
	void fe25519_freeze(fe25519 *r)
	{
	int i;
	crypto_uint32 m = equal(r->v[31],127);
	for(i=30;i>0;i--)
	m &= equal(r->v[i],255);
	m &= ge(r->v[0],237);

	m = -m;

	r->v[31] -= m&127;
	for(i=30;i>0;i--)
	r->v[i] -= m&255;
	r->v[0] -= m&237;
	}

	void fe25519_unpack(fe25519 *r, const unsigned char x[32])
	{
	int i;
	for(i=0;i<32;i++) r->v[i] = x[i];
	r->v[31] &= 127;
	}

	/* Assumes input x being reduced below 2^255 */
	void fe25519_pack(unsigned char r[32], const fe25519 *x)
	{
	int i;
	fe25519 y = *x;
	fe25519_freeze(&y);
	for(i=0;i<32;i++)
	r[i] = y.v[i];
	}

	int fe25519_iszero(const fe25519 *x)
	{
	int i;
	int r;
	fe25519 t = *x;
	fe25519_freeze(&t);
	r = equal(t.v[0],0);
	for(i=1;i<32;i++)
	r &= equal(t.v[i],0);
	return r;
	}

	int fe25519_iseq_vartime(const fe25519 x, const fe25519 y)
	{
	int i;
	fe25519 t1 = *x;
	fe25519 t2 = *y;
	fe25519_freeze(&t1);
	fe25519_freeze(&t2);
	for(i=0;i<32;i++)
	if(t1.v[i] != t2.v[i]) return 0;
	return 1;
	}

	void fe25519_cmov(fe25519 r, const fe25519 x, unsigned char b)
	{
	int i;
	crypto_uint32 mask = b;
	mask = -mask;
	for(i=0;i<32;i++) r->v[i] ^= mask & (x->v[i] ^ r->v[i]);
	}

	unsigned char fe25519_getparity(const fe25519 *x)
	{
	fe25519 t = *x;
	fe25519_freeze(&t);
	return t.v[0] & 1;
	}

	void fe25519_setone(fe25519 *r)
	{
	int i;
	r->v[0] = 1;
	for(i=1;i<32;i++) r->v[i]=0;
	}

	void fe25519_setzero(fe25519 *r)
	{
	int i;
	for(i=0;i<32;i++) r->v[i]=0;
	}

	void fe25519_neg(fe25519 r, const fe25519 x)
	{
	fe25519 t;
	int i;
	for(i=0;i<32;i++) t.v[i]=x->v[i];
	fe25519_setzero(r);
	fe25519_sub(r, r, &t);
	}

	void fe25519_add(fe25519 r, const fe25519 x, const fe25519 *y)
	{
	int i;
	for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i];
	reduce_add_sub(r);
	}

	void fe25519_sub(fe25519 r, const fe25519 x, const fe25519 *y)
	{
	int i;
	crypto_uint32 t[32];
	t[0] = x->v[0] + 0x1da;
	t[31] = x->v[31] + 0xfe;
	for(i=1;i<31;i++) t[i] = x->v[i] + 0x1fe;
	for(i=0;i<32;i++) r->v[i] = t[i] - y->v[i];
	reduce_add_sub(r);
	}

	void fe25519_mul(fe25519 r, const fe25519 x, const fe25519 *y)
	{
	int i,j;
	crypto_uint32 t[63];
	for(i=0;i<63;i++)t[i] = 0;

	for(i=0;i<32;i++)
	for(j=0;j<32;j++)
	t[i+j] += x->v[i] * y->v[j];

	for(i=32;i<63;i++)
	r->v[i-32] = t[i-32] + times38(t[i]);
	r->v[31] = t[31]; /* result now in r[0]...r[31] */

	reduce_mul(r);
	}

	void fe25519_square(fe25519 r, const fe25519 x)
	{
	fe25519_mul(r, x, x);
	}

	void fe25519_invert(fe25519 r, const fe25519 x)
	{
	fe25519 z2;
	fe25519 z9;
	fe25519 z11;
	fe25519 z2_5_0;
	fe25519 z2_10_0;
	fe25519 z2_20_0;
	fe25519 z2_50_0;
	fe25519 z2_100_0;
	fe25519 t0;
	fe25519 t1;
	int i;

	/* 2 */ fe25519_square(&z2,x);
	/* 4 */ fe25519_square(&t1,&z2);
	/* 8 */ fe25519_square(&t0,&t1);
	/* 9 */ fe25519_mul(&z9,&t0,x);
	/* 11 */ fe25519_mul(&z11,&z9,&z2);
	/* 22 */ fe25519_square(&t0,&z11);
	/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t0,&z9);

	/* 2^6 - 2^1 */ fe25519_square(&t0,&z2_5_0);
	/* 2^7 - 2^2 */ fe25519_square(&t1,&t0);
	/* 2^8 - 2^3 */ fe25519_square(&t0,&t1);
	/* 2^9 - 2^4 */ fe25519_square(&t1,&t0);
	/* 2^10 - 2^5 */ fe25519_square(&t0,&t1);
	/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t0,&z2_5_0);

	/* 2^11 - 2^1 */ fe25519_square(&t0,&z2_10_0);
	/* 2^12 - 2^2 */ fe25519_square(&t1,&t0);
	/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
	/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t1,&z2_10_0);

	/* 2^21 - 2^1 */ fe25519_square(&t0,&z2_20_0);
	/* 2^22 - 2^2 */ fe25519_square(&t1,&t0);
	/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
	/* 2^40 - 2^0 */ fe25519_mul(&t0,&t1,&z2_20_0);

	/* 2^41 - 2^1 */ fe25519_square(&t1,&t0);
	/* 2^42 - 2^2 */ fe25519_square(&t0,&t1);
	/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); }
	/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t0,&z2_10_0);

	/* 2^51 - 2^1 */ fe25519_square(&t0,&z2_50_0);
	/* 2^52 - 2^2 */ fe25519_square(&t1,&t0);
	/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
	/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t1,&z2_50_0);

	/* 2^101 - 2^1 */ fe25519_square(&t1,&z2_100_0);
	/* 2^102 - 2^2 */ fe25519_square(&t0,&t1);
	/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); }
	/* 2^200 - 2^0 */ fe25519_mul(&t1,&t0,&z2_100_0);

	/* 2^201 - 2^1 */ fe25519_square(&t0,&t1);
	/* 2^202 - 2^2 */ fe25519_square(&t1,&t0);
	/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
	/* 2^250 - 2^0 */ fe25519_mul(&t0,&t1,&z2_50_0);

	/* 2^251 - 2^1 */ fe25519_square(&t1,&t0);
	/* 2^252 - 2^2 */ fe25519_square(&t0,&t1);
	/* 2^253 - 2^3 */ fe25519_square(&t1,&t0);
	/* 2^254 - 2^4 */ fe25519_square(&t0,&t1);
	/* 2^255 - 2^5 */ fe25519_square(&t1,&t0);
	/* 2^255 - 21 */ fe25519_mul(r,&t1,&z11);
	}

	void fe25519_pow2523(fe25519 r, const fe25519 x)
	{
	fe25519 z2;
	fe25519 z9;
	fe25519 z11;
	fe25519 z2_5_0;
	fe25519 z2_10_0;
	fe25519 z2_20_0;
	fe25519 z2_50_0;
	fe25519 z2_100_0;
	fe25519 t;
	int i;

	/* 2 */ fe25519_square(&z2,x);
	/* 4 */ fe25519_square(&t,&z2);
	/* 8 */ fe25519_square(&t,&t);
	/* 9 */ fe25519_mul(&z9,&t,x);
	/* 11 */ fe25519_mul(&z11,&z9,&z2);
	/* 22 */ fe25519_square(&t,&z11);
	/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t,&z9);

	/* 2^6 - 2^1 */ fe25519_square(&t,&z2_5_0);
	/* 2^10 - 2^5 */ for (i = 1;i < 5;i++) { fe25519_square(&t,&t); }
	/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t,&z2_5_0);

	/* 2^11 - 2^1 */ fe25519_square(&t,&z2_10_0);
	/* 2^20 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); }
	/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t,&z2_10_0);

	/* 2^21 - 2^1 */ fe25519_square(&t,&z2_20_0);
	/* 2^40 - 2^20 */ for (i = 1;i < 20;i++) { fe25519_square(&t,&t); }
	/* 2^40 - 2^0 */ fe25519_mul(&t,&t,&z2_20_0);

	/* 2^41 - 2^1 */ fe25519_square(&t,&t);
	/* 2^50 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); }
	/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t,&z2_10_0);

	/* 2^51 - 2^1 */ fe25519_square(&t,&z2_50_0);
	/* 2^100 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); }
	/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t,&z2_50_0);

	/* 2^101 - 2^1 */ fe25519_square(&t,&z2_100_0);
	/* 2^200 - 2^100 */ for (i = 1;i < 100;i++) { fe25519_square(&t,&t); }
	/* 2^200 - 2^0 */ fe25519_mul(&t,&t,&z2_100_0);

	/* 2^201 - 2^1 */ fe25519_square(&t,&t);
	/* 2^250 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); }
	/* 2^250 - 2^0 */ fe25519_mul(&t,&t,&z2_50_0);

	/* 2^251 - 2^1 */ fe25519_square(&t,&t);
	/* 2^252 - 2^2 */ fe25519_square(&t,&t);
	/* 2^252 - 3 */ fe25519_mul(r,&t,x);
	}