X-Git-Url: https://git.cryptolib.org/?p=avr-crypto-lib.git;a=blobdiff_plain;f=bigint%2Fbigint.c;h=6db0389d693490bdc818b4688e88b29370c6e4f7;hp=3e2f0eb295241651d679faa9f04f3df723db01d1;hb=997bf1010de28a0a7246b792254a1ec6a59d5d4d;hpb=f947a91725d102074386e84dc98d819d7f935611

diff --git a/bigint/bigint.c b/bigint/bigint.c
index 3e2f0eb..6db0389 100644
--- a/bigint/bigint.c
+++ b/bigint/bigint.c
@@ -1,6 +1,6 @@
 /* bigint.c */
 /*
-    This file is part of the AVR-Crypto-Lib.
+    This file is part of the ARM-Crypto-Lib.
     Copyright (C) 2008  Daniel Otte (daniel.otte@rub.de)
 
     This program is free software: you can redistribute it and/or modify
@@ -32,10 +32,14 @@
 
 #include "bigint.h"
 #include <string.h>
-/*
+
+#define DEBUG 0
+
+#if DEBUG
 #include "cli.h"
 #include "bigint_io.h"
-*/
+#endif
+
 #ifndef MAX
  #define MAX(a,b) (((a)>(b))?(a):(b))
 #endif
@@ -44,14 +48,14 @@
  #define MIN(a,b) (((a)<(b))?(a):(b))
 #endif
 
-#define SET_FBS(a, v) do{(a)->info &=0xF8; (a)->info |= (v);}while(0)
+#define SET_FBS(a, v) do{(a)->info &=~BIGINT_FBS_MASK; (a)->info |= (v);}while(0)
 #define GET_FBS(a)   ((a)->info&BIGINT_FBS_MASK)
 #define SET_NEG(a)   (a)->info |= BIGINT_NEG_MASK
 #define SET_POS(a)   (a)->info &= ~BIGINT_NEG_MASK
 #define XCHG(a,b)    do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0)
-#define XCHG_PTR(a,b)    do{ a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
-	                         b = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
-	                         a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b)));}while(0)
+#define XCHG_PTR(a,b)    do{ a = (void*)(((bigint_ptr_int_t)(a)) ^ ((bigint_ptr_int_t)(b))); \
+	                         b = (void*)(((bigint_ptr_int_t)(a)) ^ ((bigint_ptr_int_t)(b))); \
+	                         a = (void*)(((bigint_ptr_int_t)(a)) ^ ((bigint_ptr_int_t)(b)));}while(0)
 
 #define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
 
@@ -64,10 +68,10 @@ void bigint_adjust(bigint_t* a){
 		a->info=0;
 		return;
 	}
-	uint8_t t;
-	uint8_t i = 0x07;
+	bigint_word_t t;
+	uint8_t i = BIGINT_WORD_SIZE-1;
 	t = a->wordv[a->length_B-1];
-	while((t&0x80)==0 && i){
+	while((t&(1L<<(BIGINT_WORD_SIZE-1)))==0 && i){
 		t<<=1;
 		i--;
 	}
@@ -76,31 +80,81 @@ void bigint_adjust(bigint_t* a){
 
 /******************************************************************************/
 
+uint16_t bigint_length_b(bigint_t* a){
+	if(!a->length_B || a->length_B==0){
+		return 0;
+	}
+	return (a->length_B-1) * BIGINT_WORD_SIZE + GET_FBS(a);
+}
+
+/******************************************************************************/
+
+uint16_t bigint_length_B(bigint_t* a){
+	return a->length_B * sizeof(bigint_word_t);
+}
+
+/******************************************************************************/
+
+uint32_t bigint_get_first_set_bit(bigint_t* a){
+	if(a->length_B==0){
+		return (uint32_t)(-1);
+	}
+	return (a->length_B-1)*sizeof(bigint_word_t)*8+GET_FBS(a);
+}
+
+
+/******************************************************************************/
+
+uint32_t bigint_get_last_set_bit(bigint_t* a){
+	uint32_t r=0;
+	uint8_t b=0;
+	bigint_word_t x=1;
+	if(a->length_B==0){
+		return (uint32_t)(-1);
+	}
+	while(a->wordv[r]==0 && r<a->length_B){
+		++r;
+	}
+	if(a->wordv[r] == 0){
+		return (uint32_t)(-1);
+	}
+	while((x&a->wordv[r])==0){
+		++b;
+		x <<= 1;
+	}
+	return r*BIGINT_WORD_SIZE+b;
+}
+
+/******************************************************************************/
+
 void bigint_copy(bigint_t* dest, const bigint_t* src){
+	memcpy(dest->wordv, src->wordv, src->length_B*sizeof(bigint_word_t));
 	dest->length_B = src->length_B;
 	dest->info = src->info;
-	memcpy(dest->wordv, src->wordv, src->length_B);
 }
 
 /******************************************************************************/
 
 /* this should be implemented in assembly */
 void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
-	uint16_t t=0, i;
+	uint16_t i;
+	bigint_wordplus_t t=0LL;
 	if(a->length_B < b->length_B){
 		XCHG_PTR(a,b);
 	}
 	for(i=0; i<b->length_B; ++i){
-		t = a->wordv[i] + b->wordv[i] + t;
-		dest->wordv[i] = (uint8_t)t;
-		t>>=8;
+//		t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t;
+		t += a->wordv[i];
+		t += b->wordv[i];
+		dest->wordv[i] = (bigint_word_t)t;
+		t>>=BIGINT_WORD_SIZE;
 	}
 	for(; i<a->length_B; ++i){
-		t = a->wordv[i] + t;
-		dest->wordv[i] = (uint8_t)t;
-		t>>=8;
+		t += a->wordv[i];
+		dest->wordv[i] = (bigint_word_t)t;
+		t>>=BIGINT_WORD_SIZE;
 	}
-	dest->wordv[i++] = t;
+	dest->wordv[i++] = (bigint_word_t)t;
 	dest->length_B = i;
 	bigint_adjust(dest);
 }
@@ -109,30 +163,54 @@ void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 
 /* this should be implemented in assembly */
 void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
-	uint16_t i,j=0;
-	uint16_t t=0;
-	if(scale>dest->length_B)
-		memset(dest->wordv+dest->length_B, 0, scale-dest->length_B);
-	for(i=scale; i<a->length_B+scale; ++i,++j){
-		t = a->wordv[j] + t;
+	bigint_t x;
+#if BIGINT_WORD_SIZE == 8
+	memset(dest->wordv + dest->length_B, 0, MAX(dest->length_B, a->length_B + scale) - dest->length_B);
+	x.wordv = dest->wordv + scale;
+	x.length_B = dest->length_B - scale;
+	if((int16_t)x.length_B < 0)
+		x.length_B = 0;
+	x.info = dest->info;
+	bigint_add_u(&x, &x, a);
+	dest->length_B = x.length_B + scale;
+	dest->info = 0;
+	bigint_adjust(dest);
+#else
+#error unimplemented!
+#endif
+
+
+/*	uint16_t i,j=0;
+	uint16_t scale_w;
+	bigint_word_t *dst;
+	bigint_wordplus_t t=0;
+	scale_w = (scale+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t);
+	if(scale>dest->length_B*sizeof(bigint_word_t)){
+		memset(((uint8_t*)dest->wordv)+dest->length_B*sizeof(bigint_word_t), 0, scale-dest->length_B*sizeof(bigint_word_t));
+	}
+	// a->wordv = (const uint32_t*)(((uint8_t*)a->wordv)+(scale&3));
+	dst  = dest->wordv + (scale&(sizeof(bigint_word_t)-1));
+	for(i=scale/sizeof(bigint_word_t); i<a->length_B+scale_w; ++i,++j){
+		t += a->wordv[j];
 		if(dest->length_B>i){
-			t += dest->wordv[i];
+			t += dst[i];
 		}
-		dest->wordv[i] = (uint8_t)t;
-		t>>=8;
+		dst[i] = (bigint_word_t)t;
+		t>>=BIGINT_WORD_SIZE;
 	}
 	while(t){
 		if(dest->length_B>i){
-			t = dest->wordv[i] + t;
+			t += dst[i];
 		}
-		dest->wordv[i] = (uint8_t)t;
-		t>>=8;
+		dst[i] = (bigint_word_t)t;
+		t>>=BIGINT_WORD_SIZE;
 		++i;
 	}
 	if(dest->length_B < i){
 		dest->length_B = i;
 	}
 	bigint_adjust(dest);
+	*/
 }
 
 /******************************************************************************/
@@ -141,60 +219,46 @@ void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
 void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 	int8_t borrow=0;
 	int8_t  r;
-	int16_t t;
+	bigint_wordplus_signed_t t=0LL;
 	uint16_t i, min, max;
 	min = MIN(a->length_B, b->length_B);
 	max = MAX(a->length_B, b->length_B);
 	r = bigint_cmp_u(a,b);
 	if(r==0){
-		dest->length_B = 0;
-		dest->wordv[0] = 0;
-		bigint_adjust(dest);
+		bigint_set_zero(dest);
 		return;
 	}
 	if(b->length_B==0){
-		dest->length_B = a->length_B;
-		memcpy(dest->wordv, a->wordv, a->length_B);
-		dest->info = a->info;
+		bigint_copy(dest, a);
 		SET_POS(dest);
 		return;
 	}
 	if(a->length_B==0){
-			dest->length_B = b->length_B;
-			memcpy(dest->wordv, b->wordv, b->length_B);
-			dest->info = b->info;
-			SET_NEG(dest);
-			return;
+		bigint_copy(dest, b);
+		SET_NEG(dest);
+		return;
 	}
 	if(r<0){
 		bigint_sub_u(dest, b, a);
 		SET_NEG(dest);
-	}else{
-		for(i=0; i<min; ++i){
-			t = a->wordv[i] - b->wordv[i] - borrow;
-			if(t<0){
-				borrow = 1;
-				dest->wordv[i]=(uint8_t)t;
-			}else{
-				borrow = 0;
-				dest->wordv[i]=(uint8_t)t;
-			}
+		return;
+	}
+	for(i=0; i<max; ++i){
+		t = a->wordv[i];
+		if(i<min){
+			t -= b->wordv[i];
 		}
-		for(;i<max; ++i){
-			t = a->wordv[i] - borrow;
-			if(t<0){
-				borrow = 1;
-				dest->wordv[i]=(uint8_t)t;
-			}else{
-				borrow = 0;
-				dest->wordv[i]=(uint8_t)t;
-			}
-
+		t -= borrow;
+		dest->wordv[i]=(bigint_word_t)t;
+		if(t<0){
+			borrow = 1;
+		}else{
+			borrow = 0;
 		}
-		SET_POS(dest);
-		dest->length_B = i;
-		bigint_adjust(dest);
 	}
+	SET_POS(dest);
+	dest->length_B = i;
+	bigint_adjust(dest);
 }
 
 /******************************************************************************/
@@ -212,8 +276,8 @@ int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
 	uint16_t i;
 	i = a->length_B-1;
 	do{
-		if(a->wordv[i]!=b->wordv[i]){
-			if(a->wordv[i]>b->wordv[i]){
+		if(a->wordv[i] != b->wordv[i]){
+			if(a->wordv[i] > b->wordv[i]){
 				return 1;
 			}else{
 				return -1;
@@ -307,34 +371,35 @@ int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){
 /******************************************************************************/
 
 void bigint_shiftleft(bigint_t* a, uint16_t shift){
-	uint16_t byteshift;
-	uint16_t i;
+	uint16_t byteshift, word_alloc;
+	int16_t i;
 	uint8_t bitshift;
-	uint16_t t=0;
-	byteshift = (shift+3)/8;
+	bigint_word_t *p;
+	bigint_wordplus_t t=0;
+	if(shift==0){
+		return;
+	}
+	byteshift = shift/8;
 	bitshift = shift&7;
-	memmove(a->wordv+byteshift, a->wordv, a->length_B);
-	memset(a->wordv, 0, byteshift);
+	for(i=0;i<=byteshift/sizeof(bigint_word_t); ++i){
+		a->wordv[a->length_B+i] = 0;
+	}
+	if(byteshift){
+		memmove(((uint8_t*)a->wordv)+byteshift, a->wordv, a->length_B*sizeof(bigint_word_t));
+		memset(a->wordv, 0, byteshift);
+	}
+	p = (bigint_word_t*)(((uint8_t*)a->wordv)+byteshift);
+	word_alloc = a->length_B+(byteshift+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t)+1;
+	a->wordv[word_alloc-1]=0;
 	if(bitshift!=0){
-		if(bitshift<=4){ /* shift to the left */
-			for(i=byteshift; i<a->length_B+byteshift; ++i){
-				t |= (a->wordv[i])<<bitshift;
-				a->wordv[i] = (uint8_t)t;
-				t >>= 8;
-			}
-			a->wordv[i] = (uint8_t)t;
-			byteshift++;
-		}else{ /* shift to the right */
-			for(i=a->length_B+byteshift-1; i>byteshift-1; --i){
-				t |= (a->wordv[i])<<(bitshift);
-				a->wordv[i] = (uint8_t)(t>>8);
-				t <<= 8;
-			}
-			t |= (a->wordv[i])<<(bitshift);
-			a->wordv[i] = (uint8_t)(t>>8);
+		for(i=0; i<a->length_B; ++i){
+			t |= ((bigint_wordplus_t)p[i])<<bitshift;
+			p[i] = (bigint_word_t)t;
+			t >>= BIGINT_WORD_SIZE;
 		}
+		p[i] = (bigint_word_t)t;
 	}
-	a->length_B += byteshift;
+	a->length_B = word_alloc;
 	bigint_adjust(a);
 }
 
@@ -344,32 +409,33 @@ void bigint_shiftright(bigint_t* a, uint16_t shift){
 	uint16_t byteshift;
 	uint16_t i;
 	uint8_t bitshift;
-	uint16_t t=0;
+	bigint_wordplus_t t=0;
 	byteshift = shift/8;
 	bitshift = shift&7;
-	if(byteshift >= a->length_B){ /* we would shift out more than we have */
+	if(byteshift >= a->length_B*sizeof(bigint_word_t)){ /* we would shift out more than we have */
 		bigint_set_zero(a);
 		return;
 	}
-	if(byteshift == a->length_B-1 && bitshift>GET_FBS(a)){
+	if(byteshift == a->length_B*sizeof(bigint_word_t)-1 && bitshift>GET_FBS(a)){
 		bigint_set_zero(a);
 		return;
 	}
 	if(byteshift){
-		memmove(a->wordv, a->wordv+byteshift, a->length_B-byteshift);
-		memset(a->wordv+a->length_B-byteshift, 0,  byteshift);
+		memmove(a->wordv, (uint8_t*)a->wordv+byteshift, a->length_B-byteshift);
+		memset((uint8_t*)a->wordv+a->length_B-byteshift, 0,  byteshift);
 	}
+	byteshift /= sizeof(bigint_word_t);
 	if(bitshift!=0){
 	 /* shift to the right */
 		for(i=a->length_B-byteshift-1; i>0; --i){
-			t |= (a->wordv[i])<<(8-bitshift);
-			a->wordv[i] = (uint8_t)(t>>8);
-			t <<= 8;
+			t |= ((bigint_wordplus_t)(a->wordv[i]))<<(BIGINT_WORD_SIZE-bitshift);
+			a->wordv[i] = (bigint_word_t)(t>>BIGINT_WORD_SIZE);
+			t <<= BIGINT_WORD_SIZE;
 		}
-		t |= (a->wordv[0])<<(8-bitshift);
-		a->wordv[0] = (uint8_t)(t>>8);
+		t |= ((bigint_wordplus_t)(a->wordv[0]))<<(BIGINT_WORD_SIZE-bitshift);
+		a->wordv[0] = (bigint_word_t)(t>>BIGINT_WORD_SIZE);
 	}
-	a->length_B -= byteshift;
+    a->length_B -= ((shift/8)+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t);
 	bigint_adjust(a);
 }
 
@@ -400,7 +466,7 @@ void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 	}
 	if(dest==a || dest==b){
 		bigint_t d;
-		uint8_t d_b[a->length_B+b->length_B];
+		bigint_word_t d_b[a->length_B+b->length_B];
 		d.wordv = d_b;
 		bigint_mul_u(&d, a, b);
 		bigint_copy(dest, &d);
@@ -410,78 +476,80 @@ void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 		if(a->length_B!=1){
 			XCHG_PTR(a,b);
 		}
-		uint16_t i, t=0;
-		uint8_t x = a->wordv[0];
-		for(i=0; i<b->length_B; ++i){
-			t += b->wordv[i]*x;
-			dest->wordv[i] = (uint8_t)t;
-			t>>=8;
+		bigint_wordplus_t t=0;
+		uint16_t i;
+		bigint_word_t x = a->wordv[0];
+		for(i=0; i < b->length_B; ++i){
+			t += ((bigint_wordplus_t)b->wordv[i])*((bigint_wordplus_t)x);
+			dest->wordv[i] = (bigint_word_t)t;
+			t>>=BIGINT_WORD_SIZE;
 		}
-		dest->wordv[i] = (uint8_t)t;
-		dest->length_B=i+1;
+		dest->wordv[i] = (bigint_word_t)t;
+		dest->length_B = i+1;
+		dest->info = 0;
 		bigint_adjust(dest);
 		return;
 	}
-	if(a->length_B<=4 && b->length_B<=4){
+	if(a->length_B * sizeof(bigint_word_t) <= 4 && b->length_B * sizeof(bigint_word_t) <= 4){
 		uint32_t p=0, q=0;
 		uint64_t r;
-		memcpy(&p, a->wordv, a->length_B);
-		memcpy(&q, b->wordv, b->length_B);
-		r = (uint64_t)p*(uint64_t)q;
-		memcpy(dest->wordv, &r, a->length_B+b->length_B);
-		dest->length_B =  a->length_B+b->length_B;
+		memcpy(&p, a->wordv, a->length_B*sizeof(bigint_word_t));
+		memcpy(&q, b->wordv, b->length_B*sizeof(bigint_word_t));
+		r = (uint64_t)p * (uint64_t)q;
+		memcpy(dest->wordv, &r, (dest->length_B = a->length_B + b->length_B)*sizeof(bigint_word_t));
 		bigint_adjust(dest);
 		return;
 	}
 	bigint_set_zero(dest);
 	/* split a in xh & xl; split b in yh & yl */
-	uint16_t n;
-	n=(MAX(a->length_B, b->length_B)+1)/2;
+	const uint16_t n = (MAX(a->length_B, b->length_B)+1)/2;
 	bigint_t xl, xh, yl, yh;
 	xl.wordv = a->wordv;
 	yl.wordv = b->wordv;
 	if(a->length_B<=n){
-		xh.info=0;
-		xh.length_B = 0;
+		bigint_set_zero(&xh);
 		xl.length_B = a->length_B;
-		xl.info = 0;
+		xl.info = a->info;
 	}else{
 		xl.length_B=n;
 		xl.info = 0;
 		bigint_adjust(&xl);
-		xh.wordv = a->wordv+n;
+		xh.wordv = &(a->wordv[n]);
 		xh.length_B = a->length_B-n;
-		xh.info = 0;
+		xh.info = a->info;
 	}
 	if(b->length_B<=n){
-		yh.info=0;
-		yh.length_B = 0;
+		bigint_set_zero(&yh);
 		yl.length_B = b->length_B;
 		yl.info = b->info;
 	}else{
 		yl.length_B=n;
 		yl.info = 0;
 		bigint_adjust(&yl);
-		yh.wordv = b->wordv+n;
+		yh.wordv = &(b->wordv[n]);
 		yh.length_B = b->length_B-n;
-		yh.info = 0;
+		yh.info = b->info;
 	}
 	/* now we have split up a and b */
-	uint8_t  tmp_b[2*n+2], m_b[2*(n+1)];
+	/* remember we want to do:
+	 * x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl
+	 *          5          9     2   4   3    7   5   6   1         8   1
+	 */
+	bigint_word_t  tmp_b[2*n+2], m_b[2*(n+1)];
 	bigint_t tmp, tmp2, m;
 	tmp.wordv = tmp_b;
-	tmp2.wordv = tmp_b+n+1;
+	tmp2.wordv = &(tmp_b[n+1]);
 	m.wordv = m_b;
 
-	bigint_mul_u(dest, &xl, &yl);  /* dest <= xl*yl     */
-	bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl     */
-	bigint_add_u(&tmp, &yh, &yl);  /* tmp  <= yh+yl     */
-	bigint_mul_u(&m, &tmp2, &tmp); /* m    <= tmp2*tmp  */
-	bigint_mul_u(&tmp, &xh, &yh);  /* h    <= xh*yh     */
-	bigint_sub_u(&m, &m, dest);    /* m    <= m-dest    */
-    bigint_sub_u(&m, &m, &tmp);    /* m    <= m-h       */
-	bigint_add_scale_u(dest, &m, n);
-	bigint_add_scale_u(dest, &tmp, 2*n);
+	bigint_mul_u(dest, &xl, &yl);  /* 1: dest <= xl*yl     */
+	bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh+xl     */
+	bigint_add_u(&tmp, &yh, &yl);  /* 3: tmp  <= yh+yl     */
+	bigint_mul_u(&m, &tmp2, &tmp); /* 4: m    <= tmp2*tmp  */
+	bigint_mul_u(&tmp, &xh, &yh);  /* 5: h    <= xh*yh     */
+	bigint_sub_u(&m, &m, dest);    /* 6: m    <= m-dest    */
+    bigint_sub_u(&m, &m, &tmp);    /* 7: m    <= m-h       */
+	bigint_add_scale_u(dest, &m, n*sizeof(bigint_word_t)); /* 8: dest <= dest+m**n*/
+	bigint_add_scale_u(dest, &tmp, 2*n*sizeof(bigint_word_t)); /* 9: dest <= dest+tmp**(2*n) */
 }
 
 /******************************************************************************/
@@ -517,11 +585,11 @@ void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 /* square */
 /* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
 void bigint_square(bigint_t* dest, const bigint_t* a){
-	if(a->length_B<=4){
+	if(a->length_B*sizeof(bigint_word_t)<=4){
 		uint64_t r=0;
-		memcpy(&r, a->wordv, a->length_B);
+		memcpy(&r, a->wordv, a->length_B*sizeof(bigint_word_t));
 		r = r*r;
-		memcpy(dest->wordv, &r, 2*a->length_B);
+		memcpy(dest->wordv, &r, 2*a->length_B*sizeof(bigint_word_t));
 		SET_POS(dest);
 		dest->length_B=2*a->length_B;
 		bigint_adjust(dest);
@@ -529,7 +597,7 @@ void bigint_square(bigint_t* dest, const bigint_t* a){
 	}
 	if(dest==a){
 		bigint_t d;
-		uint8_t d_b[a->length_B*2];
+		bigint_word_t d_b[a->length_B*2];
 		d.wordv = d_b;
 		bigint_square(&d, a);
 		bigint_copy(dest, &d);
@@ -538,79 +606,115 @@ void bigint_square(bigint_t* dest, const bigint_t* a){
 	uint16_t n;
 	n=(a->length_B+1)/2;
 	bigint_t xh, xl, tmp; /* x-high, x-low, temp */
-	uint8_t buffer[2*n+1];
+	bigint_word_t buffer[2*n+1];
 	xl.wordv = a->wordv;
 	xl.length_B = n;
-	xh.wordv = a->wordv+n;
+	xl.info = 0;
+	xh.wordv = &(a->wordv[n]);
 	xh.length_B = a->length_B-n;
+	xh.info = 0;
+	bigint_adjust(&xl);
+	bigint_adjust(&xh);
 	tmp.wordv = buffer;
+/* (xh * b**n + xl)**2 = xh**2 * b**2n + 2 * xh * xl * b**n + xl**2 */
+
+//	cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl);
+//	cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh);
 	bigint_square(dest, &xl);
+//	cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest);
 	bigint_square(&tmp, &xh);
-	bigint_add_scale_u(dest, &tmp, 2*n);
+//	cli_putstr("\r\nDBG (2): xh**2: "); bigint_print_hex(&tmp);
+	bigint_add_scale_u(dest, &tmp, 2*n*sizeof(bigint_word_t));
+//	cli_putstr("\r\nDBG (3): xl**2 + xh**2*n**2: "); bigint_print_hex(dest);
 	bigint_mul_u(&tmp, &xl, &xh);
+//	cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp);
 	bigint_shiftleft(&tmp, 1);
-	bigint_add_scale_u(dest, &tmp, n);
+//	cli_putstr("\r\nDBG (5): xl*xh*2: "); bigint_print_hex(&tmp);
+	bigint_add_scale_u(dest, &tmp, n*sizeof(bigint_word_t));
+//	cli_putstr("\r\nDBG (6): x**2: "); bigint_print_hex(dest);
+//	cli_putstr("\r\n");
 }
 
 /******************************************************************************/
-
 void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
-	bigint_t tmp;
-	uint8_t tmp_b[b->length_B+1];
-	uint16_t i,j,byteshift=bitscale/8;
-	uint8_t borrow=0;
-	int16_t t;
+	bigint_t tmp, x;
+	bigint_word_t tmp_b[b->length_B + 1];
+	const uint16_t word_shift = bitscale / BIGINT_WORD_SIZE;
 
-	if(a->length_B < b->length_B+byteshift){
+	if(a->length_B < b->length_B + word_shift){
+#if DEBUG
+		cli_putstr("\r\nDBG: *bang*\r\n");
+#endif
 		bigint_set_zero(a);
 		return;
 	}
-
 	tmp.wordv = tmp_b;
 	bigint_copy(&tmp, b);
-	bigint_shiftleft(&tmp, bitscale&7);
+	bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE);
 
-	for(j=0,i=byteshift; i<tmp.length_B+byteshift; ++i, ++j){
-		t = a->wordv[i] - tmp.wordv[j] - borrow;
-		a->wordv[i] = (uint8_t)t;
-		if(t<0){
-			borrow = 1;
-		}else{
-			borrow = 0;
-		}
-	}
-	while(borrow){
-		if(i+1 > a->length_B){
-			bigint_set_zero(a);
-			return;
-		}
-		a->wordv[i] -= borrow;
-		if(a->wordv[i]!=0xff){
-			borrow=0;
-		}
-		++i;
-	}
+	x.info = a->info;
+	x.wordv = &(a->wordv[word_shift]);
+	x.length_B = a->length_B - word_shift;
+
+	bigint_sub_u(&x, &x, &tmp);
 	bigint_adjust(a);
+	return;
 }
 
 /******************************************************************************/
 
 void bigint_reduce(bigint_t* a, const bigint_t* r){
-//	bigint_adjust(r);
+//	bigint_adjust((bigint_t*)r);
 	uint8_t rfbs = GET_FBS(r);
-
+#if DEBUG
+	cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
+#endif
 	if(r->length_B==0 || a->length_B==0){
 		return;
 	}
-	while(a->length_B > r->length_B){
-		bigint_sub_u_bitscale(a, r, (a->length_B-r->length_B)*8+GET_FBS(a)-rfbs-1);
+	if((r->length_B*sizeof(bigint_word_t)<=4) && (a->length_B*sizeof(bigint_word_t)<=4)){
+		uint32_t p=0, q=0;
+		memcpy(&p, a->wordv, a->length_B*sizeof(bigint_word_t));
+		memcpy(&q, r->wordv, r->length_B*sizeof(bigint_word_t));
+		p %= q;
+		memcpy(a->wordv, &p, a->length_B*sizeof(bigint_word_t));
+		bigint_adjust(a);
+//		cli_putstr("\r\nDBG: (0) = "); bigint_print_hex(a);
+		return;
 	}
-	while((GET_FBS(a) > rfbs+1) && (a->length_B == r->length_B)){
-		bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
+	uint16_t shift;
+	while(a->length_B > r->length_B){
+		shift = (a->length_B - r->length_B) * 8 * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1;
+		/*
+		if((a->wordv[a->length_B-1] & ((1LL<<GET_FBS(a)) - 1)) > r->wordv[r->length_B-1]){
+			// cli_putc('~');
+			cli_putstr("\r\n ~ [a] = ");
+			cli_hexdump_rev(&a->wordv[a->length_B-1], 4);
+			cli_putstr("  [r] = ");
+			cli_hexdump_rev(&r->wordv[r->length_B-1], 4);
+			shift += 1;
+		}
+		*/
+//		cli_putstr("\r\nDBG: (p) shift = "); cli_hexdump_rev(&shift, 2);
+//		cli_putstr(" a_len = "); cli_hexdump_rev(&a->length_B, 2);
+//		cli_putstr(" r_len = "); cli_hexdump_rev(&r->length_B, 2);
+//		uart_flush(0);
+		bigint_sub_u_bitscale(a, r, shift);
+//		cli_putstr("\r\nDBG: (1) = "); bigint_print_hex(a);
+	}
+	while((GET_FBS(a) > rfbs) && (a->length_B == r->length_B)){
+		shift = GET_FBS(a)-rfbs-1;
+//		cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2);
+		bigint_sub_u_bitscale(a, r, shift);
+//		cli_putstr("\r\nDBG: (2) = "); bigint_print_hex(a);
 	}
 	while(bigint_cmp_u(a,r)>=0){
 		bigint_sub_u(a,a,r);
+//		cli_putstr("\r\nDBG: (3) = "); bigint_print_hex(a);
 	}
+	bigint_adjust(a);
+//	cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
+//	cli_putstr("\r\n");
 }
 
 /******************************************************************************/
@@ -623,71 +727,116 @@ void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, con
 	}
 
 	bigint_t res, base;
-	uint8_t base_b[MAX(a->length_B,r->length_B*2)], res_b[r->length_B*2];
+	bigint_word_t t, base_b[MAX(a->length_B,r->length_B)], res_b[r->length_B*2];
 	uint16_t i;
-	uint8_t j, t;
+	uint8_t j;
+//	uint16_t *xaddr = &i;
+//	cli_putstr("\r\npre-alloc (");
+//	cli_hexdump_rev(&xaddr, 4);
+//	cli_putstr(") ...");
 	res.wordv = res_b;
 	base.wordv = base_b;
 	bigint_copy(&base, a);
+//	cli_putstr("\r\npost-copy");
 	bigint_reduce(&base, r);
 	res.wordv[0]=1;
 	res.length_B=1;
 	res.info = 0;
 	bigint_adjust(&res);
-	for(i=0; i+1<exp->length_B; ++i){
-		t=exp->wordv[i];
-		for(j=0; j<8; ++j){
-			if(t&1){
-				bigint_mul_u(&res, &res, &base);
+	if(exp->length_B == 0){
+		bigint_copy(dest, &res);
+		return;
+	}
+	uint8_t flag = 0;
+	t=exp->wordv[exp->length_B - 1];
+	for(i=exp->length_B; i > 0; --i){
+		t = exp->wordv[i - 1];
+		for(j=BIGINT_WORD_SIZE; j > 0; --j){
+			if(!flag){
+				if(t & (1<<(BIGINT_WORD_SIZE-1))){
+					flag = 1;
+				}
+			}
+			if(flag){
+				bigint_square(&res, &res);
 				bigint_reduce(&res, r);
+				if(t & (1<<(BIGINT_WORD_SIZE-1))){
+					bigint_mul_u(&res, &res, &base);
+					bigint_reduce(&res, r);
+				}
 			}
-			bigint_square(&base, &base);
-			bigint_reduce(&base, r);
-			t>>=1;
-		}
-	}
-	t=exp->wordv[i];
-	while(t){
-		if(t&1){
-			bigint_mul_u(&res, &res, &base);
-			bigint_reduce(&res, r);
+			t<<=1;
 		}
-		bigint_square(&base, &base);
-		bigint_reduce(&base, r);
-		t>>=1;
 	}
+
+//	cli_putc('+');
 	SET_POS(&res);
 	bigint_copy(dest, &res);
 }
 
 /******************************************************************************/
+
+#define cli_putstr(a)
+#define bigint_print_hex(a)
+#define cli_hexdump_rev(a,b)
+#define uart_flush(a)
+
 /* gcd <-- gcd(x,y) a*x+b*y=gcd */
 void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, const bigint_t* y){
 	 bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
-	 volatile uint16_t i=0;
+	 uint16_t i=0;
 	 if(x->length_B==0 || y->length_B==0){
 		 return;
 	 }
+	 if(x->length_B==1 && x->wordv[0]==1){
+		 gcd->length_B = 1;
+		 gcd->wordv[0] = 1;
+		 if(a){
+			 a->length_B = 1;
+			 a->wordv[0] = 1;
+			 SET_POS(a);
+			 bigint_adjust(a);
+		 }
+		 if(b){
+			 bigint_set_zero(b);
+		 }
+		 return;
+	 }
+	 if(y->length_B==1 && y->wordv[0]==1){
+		 gcd->length_B = 1;
+		 gcd->wordv[0] = 1;
+		 if(b){
+			 b->length_B = 1;
+			 b->wordv[0] = 1;
+			 SET_POS(b);
+			 bigint_adjust(b);
+		 }
+		 if(a){
+			 bigint_set_zero(a);
+		 }
+		 return;
+	 }
+
 	 while(x->wordv[i]==0 && y->wordv[i]==0){
 		 ++i;
 	 }
-	 uint8_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
-	 uint8_t u_b[x->length_B-i], v_b[y->length_B-i];
-	 uint8_t a_b[y->length_B+2], c_b[y->length_B+2];
-	 uint8_t b_b[x->length_B+2], d_b[x->length_B+2];
+	 bigint_word_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
+	 bigint_word_t u_b[x->length_B-i], v_b[y->length_B-i];
+	 bigint_word_t a_b[y->length_B+2], c_b[y->length_B+2];
+	 bigint_word_t b_b[x->length_B+2], d_b[x->length_B+2];
 
 	 g.wordv = g_b;
 	 x_.wordv = x_b;
 	 y_.wordv = y_b;
-	 memset(g_b, 0, i);
+	 memset(g_b, 0, i*sizeof(bigint_word_t));
 	 g_b[i]=1;
 	 g.length_B = i+1;
 	 g.info=0;
 	 x_.info = y_.info = 0;
 	 x_.length_B = x->length_B-i;
 	 y_.length_B = y->length_B-i;
-	 memcpy(x_.wordv, x->wordv+i, x_.length_B);
-	 memcpy(y_.wordv, y->wordv+i, y_.length_B);
+	 memcpy(x_.wordv, x->wordv+i, x_.length_B*sizeof(bigint_word_t));
+	 memcpy(y_.wordv, y->wordv+i, y_.length_B*sizeof(bigint_word_t));
 	 for(i=0; (x_.wordv[0]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
 	 }
 
@@ -699,6 +848,7 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c
 		 bigint_shiftright(&x_, i);
 		 bigint_shiftright(&y_, i);
 	 }
+
 	 u.wordv = u_b;
 	 v.wordv = v_b;
 	 a_.wordv = a_b;
@@ -717,7 +867,9 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c
 	 bigint_set_zero(&b_);
 	 bigint_set_zero(&c_);
 	 do{
+		 cli_putstr("\r\nDBG (gcdext) 0");
 		 while((u.wordv[0]&1)==0){
+			 cli_putstr("\r\nDBG (gcdext) 0.1");
 			 bigint_shiftright(&u, 1);
 			 if((a_.wordv[0]&1) || (b_.wordv[0]&1)){
 				 bigint_add_s(&a_, &a_, &y_);
@@ -727,6 +879,7 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c
 			 bigint_shiftright(&b_, 1);
 		 }
 		 while((v.wordv[0]&1)==0){
+			 cli_putstr("\r\nDBG (gcdext) 0.2");
 			 bigint_shiftright(&v, 1);
 			 if((c_.wordv[0]&1) || (d_.wordv[0]&1)){
 				 bigint_add_s(&c_, &c_, &y_);
@@ -770,8 +923,8 @@ void bigint_inverse(bigint_t* dest, const bigint_t* a, const bigint_t* m){
 
 void bigint_changeendianess(bigint_t* a){
 	uint8_t t, *p, *q;
-	p = a->wordv;
-	q = p+a->length_B-1;
+	p = (uint8_t*)(a->wordv);
+	q = ((uint8_t*)p)+a->length_B*sizeof(bigint_word_t)-1;
 	while(p<q){
 		t = *p;
 		*p = *q;