adding modulo-reduction to bigint
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parent
eb09a2a6f4
commit
4bd4efef59
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@ -344,19 +344,18 @@ void bigint_shiftleft(bigint_t* a, uint16_t shift){
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t >>= 8;
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}
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a->wordv[i] = (uint8_t)t;
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byteshift++;
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}else{ /* shift to the right */
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bitshift = 8 - bitshift;
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for(i=a->length_B+byteshift-1; i>byteshift; --i){
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t |= (a->wordv[i])<<(8-bitshift);
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for(i=a->length_B+byteshift-1; i>byteshift-1; --i){
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t |= (a->wordv[i])<<(bitshift);
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a->wordv[i] = (uint8_t)(t>>8);
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t <<= 8;
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}
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t |= (a->wordv[i])<<(8-bitshift);
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t |= (a->wordv[i])<<(bitshift);
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a->wordv[i] = (uint8_t)(t>>8);
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}
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}
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a->length_B += byteshift+1;
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a->length_B += byteshift;
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bigint_adjust(a);
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}
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@ -422,7 +421,6 @@ void bigint_set_zero(bigint_t* a){
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void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
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if(a->length_B==0 || b->length_B==0){
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bigint_set_zero(dest);
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depth -= 1;
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return;
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}
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if(a->length_B==1 || b->length_B==1){
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@ -488,7 +486,6 @@ void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
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/* now we have split up a and b */
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uint8_t tmp_b[2*n+2], m_b[2*(n+1)];
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bigint_t tmp, tmp2, m;
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/* calculate h=xh*yh; l=xl*yl; sx=xh+xl; sy=yh+yl */
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tmp.wordv = tmp_b;
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tmp2.wordv = tmp_b+n+1;
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m.wordv = m_b;
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@ -562,12 +559,70 @@ void bigint_square(bigint_t* dest, const bigint_t* a){
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bigint_mul_u(&tmp, &xl, &xh);
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bigint_shiftleft(&tmp, 1);
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bigint_add_scale_u(dest, &tmp, n);
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}
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/******************************************************************************/
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void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
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bigint_t tmp;
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uint8_t tmp_b[b->length_B+1];
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uint16_t i,j,byteshift=bitscale/8;
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uint8_t borrow=0;
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int16_t t;
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if(a->length_B < b->length_B+byteshift){
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cli_putstr_P(PSTR("\r\nERROR: bigint_sub_u_bitscale result negative"));
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bigint_set_zero(a);
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return;
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}
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tmp.wordv = tmp_b;
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bigint_copy(&tmp, b);
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bigint_shiftleft(&tmp, bitscale&7);
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for(j=0,i=byteshift; i<tmp.length_B+byteshift; ++i, ++j){
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t = a->wordv[i] - tmp.wordv[j] - borrow;
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a->wordv[i] = (uint8_t)t;
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if(t<0){
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borrow = 1;
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}else{
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borrow = 0;
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}
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}
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while(borrow){
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if(i+1 > a->length_B){
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cli_putstr_P(PSTR("\r\nERROR: bigint_sub_u_bitscale result negative (2) shift="));
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cli_hexdump_rev(&bitscale, 2);
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bigint_set_zero(a);
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return;
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}
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a->wordv[i] -= borrow;
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if(a->wordv[i]!=0xff){
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borrow=0;
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}
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++i;
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}
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bigint_adjust(a);
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}
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/******************************************************************************/
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void bigint_reduce(bigint_t* a, const bigint_t* r){
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uint8_t rfbs = GET_FBS(r);
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if(r->length_B==0){
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return;
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}
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while(a->length_B > r->length_B){
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bigint_sub_u_bitscale(a, r, (a->length_B-r->length_B)*8+GET_FBS(a)-rfbs-1);
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}
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while(GET_FBS(a) > rfbs+1){
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bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
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}
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while(bigint_cmp_u(a,r)>=0){
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bigint_sub_u(a,a,r);
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}
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bigint_adjust(a);
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}
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@ -42,7 +42,7 @@ typedef struct{
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/******************************************************************************/
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void bigint_adjust(bigint_t* a);
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void bigint_copy(bigint_t* dest, const bigint_t* src);
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void bigint_copy(bigint_t* dest, const bigint_t* src);
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void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b);
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void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale);
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void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b);
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@ -57,7 +57,8 @@ void bigint_set_zero(bigint_t* a);
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void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b);
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void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b);
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void bigint_square(bigint_t* dest, const bigint_t* a);
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void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale);
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void bigint_reduce(bigint_t* a, const bigint_t* r);
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/******************************************************************************/
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#endif /*BIGINT_H_*/
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@ -234,6 +234,55 @@ def square_test(a)
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return false
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end
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################################################################################
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# reduce_test #
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################################################################################
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def reduce_test(a,b)
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begin
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line = $sp.gets()
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line = "" if line==nil
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puts("DBG got: "+line) if $debug
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if /^Error:.*/.match(line)
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puts line
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return false
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end
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end while not /[\s]*enter a:[\s]*/.match(line)
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$sp.print(a.to_s(16)+" ")
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begin
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line = $sp.gets()
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line = "" if line==nil
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puts("DBG got: "+line) if $debug
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if /^Error:.*/.match(line)
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puts line
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return false
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end
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end while not /[\s]*enter b:[\s]*/.match(line)
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$sp.print(b.to_s(16)+" ")
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begin
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line = $sp.gets()
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line = "" if line==nil
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puts("DBG got: "+line) if $debug
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if /^Error:.*/.match(line)
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puts line
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return false
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end
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end while not m=/[\s]*([+-]?[0-9a-fA-F]*)[\s]+%[\s]+([+-]?[0-9a-fA-F]*)[\s]*=[\s]*([+-]?[0-9a-fA-F]*)/.match(line)
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a_ = m[1].to_i(16)
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b_ = m[2].to_i(16)
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c_ = m[3].to_i(16)
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line.chomp!
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if(a_== a && b_ == b && c_ == (a%b))
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$logfile.printf("[pass]: %s\n", line)
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return true
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else
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$logfile.printf("[fail (%s%s%s)]: %s", (a==a_)?"":"a", (b==b_)?"":"b", (c_==a+b)?"":"c",line)
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$logfile.printf(" ; should %s %% %s = %s\n", a.to_s(16), b.to_s(16), (a%b).to_s(16))
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return false
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end
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return false
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end
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################################################################################
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# run_test_add #
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################################################################################
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@ -322,6 +371,33 @@ def run_test_square(skip=0)
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end while length_a_B<4096/8
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end
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################################################################################
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# run_test_reduce #
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################################################################################
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def run_test_reduce(skip=0)
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length_a_B = skip+1
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length_b_B = skip+1
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begin
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$size = length_a_B
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(0..16).each do |i|
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a = rand(256**length_a_B)
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b = rand(256**length_a_B)+1
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v = reduce_test(a, b)
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screen_progress(v)
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end
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(0..16).each do |i|
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b_size = rand(length_b_B+1)
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a = rand(256**length_a_B)
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b = rand(256**b_size)+1
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v = reduce_test(a, b)
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screen_progress(v)
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end
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length_a_B += 1
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length_b_B += 1
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end while length_a_B<4096/8
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end
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################################################################################
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# MAIN #
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################################################################################
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@ -395,10 +471,12 @@ tests = Hash.new
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tests['a'] = proc {|x| run_test_add(x) }
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tests['m'] = proc {|x| run_test_mul(x) }
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tests['s'] = proc {|x| run_test_square(x) }
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tests['r'] = proc {|x| run_test_reduce(x) }
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init_str = Hash.new
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init_str['a'] = 'add-test'
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init_str['m'] = 'mul-test'
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init_str['s'] = 'square-test'
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init_str['r'] = 'reduce-test'
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srand(0xdeadbeef)
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@ -413,7 +491,7 @@ if opts['a']
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end
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end
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else
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'ams'.each_char do |x|
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'amsr'.each_char do |x|
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if tests[x]
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puts init_str[x]
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init_system(init_str[x])
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@ -163,6 +163,34 @@ void test_square_bigint(void){
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}
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}
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void test_reduce_bigint(void){
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bigint_t a, b, c;
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cli_putstr_P(PSTR("\r\nreduce test\r\n"));
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for(;;){
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cli_putstr_P(PSTR("\r\nenter a:"));
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if(bigint_read_hex_echo(&a)){
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cli_putstr_P(PSTR("\r\n end reduce test"));
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return;
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}
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cli_putstr_P(PSTR("\r\nenter b:"));
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if(bigint_read_hex_echo(&b)){
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free(a.wordv);
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cli_putstr_P(PSTR("\r\n end reduce test"));
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return;
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}
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cli_putstr_P(PSTR("\r\n "));
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bigint_print_hex(&a);
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cli_putstr_P(PSTR(" % "));
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bigint_print_hex(&b);
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cli_putstr_P(PSTR(" = "));
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bigint_reduce(&a, &b);
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bigint_print_hex(&a);
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cli_putstr_P(PSTR("\r\n"));
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free(a.wordv);
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free(b.wordv);
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}
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}
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void test_simple(void){
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bigint_t a, b, c;
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uint8_t a_b[1], b_b[1], c_b[2];
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@ -226,6 +254,26 @@ void test_mul_simple(void){
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}
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// f4 b86a 2220 0774 437d 70e6 **2 = e9f00f29ca1c876a7a682bd1e04f6925caffd6660ea4
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/*
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uint8_t square_test_data[] PROGMEM = {
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0xA0, 0x3C, 0x23, 0x9F, 0x7A, 0xFC, 0x60, 0xEB, 0x96, 0xC2, 0xA8, 0xAC, 0xC3, 0xC9, 0x9E, 0xEC,
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0x4A, 0xF0, 0x1C, 0xB2, 0x36, 0x68, 0xD6, 0x4D, 0x3E, 0x4F, 0x8E, 0x55, 0xEA, 0x52, 0x46, 0x68,
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0x6E, 0x18, 0x88, 0x37, 0x03, 0x70, 0xBD, 0x01, 0x60, 0xE2, 0xD6, 0x12, 0xA0, 0x0E, 0xD2, 0x72,
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0x0D, 0x9D, 0x9F, 0x03, 0xC5, 0x81, 0xCA, 0x6E, 0x88, 0x1E, 0xF5, 0xD8, 0x14, 0x15, 0x30, 0xEB,
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0x28, 0x7C, 0x80, 0x07, 0x34, 0x05, 0x5D, 0xAA, 0xDC, 0xA8, 0xAA, 0x88, 0xC5, 0xE5, 0xC9, 0xFE,
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0x9C, 0xA1, 0xCE, 0xC2, 0x09, 0x0D, 0xC4, 0xC8, 0xD3, 0xE7, 0x3A, 0xF3, 0xEF, 0xDF, 0xAE, 0x07,
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0xEC, 0xC7, 0x83, 0x50, 0x9F, 0x6D, 0xB9, 0x28, 0x77, 0xC0, 0xFE, 0x69, 0xB2, 0x2E, 0x55, 0x90,
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0x50, 0xED, 0xE0, 0xA1, 0x4D, 0x3D, 0x38, 0xC9, 0x0E, 0xCD, 0x04, 0x3B, 0x64, 0x3F, 0x56, 0xC5,
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0xC3, 0x9E, 0x89, 0x81, 0x44, 0x60, 0xBA, 0x8E, 0x88, 0xA4, 0xA3, 0x42, 0x7B, 0x06, 0x93, 0x1C,
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0x6B, 0x04, 0x29, 0xF9, 0xDD, 0xFF, 0xB0, 0x48, 0x2F, 0x6D, 0xD1, 0x0F, 0x7D, 0xA6, 0x26, 0xD8,
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0xEF, 0x5E, 0x04, 0x18, 0xD1, 0x61, 0x46, 0x37, 0x87, 0xE2, 0x97, 0xDF, 0x10, 0xB4, 0x9A, 0x39,
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0xB1, 0xD0, 0xCA, 0x91, 0x48, 0x1E, 0x5D, 0xA1, 0x38, 0x89, 0x02, 0xC1, 0x49, 0x86, 0xB7, 0xAE,
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0x69, 0x20, 0xFA, 0x0E, 0x39, 0xDA, 0xA5, 0xEF, 0x7F, 0xB2, 0x81, 0xB8, 0xC0, 0x3A, 0xF8, 0xDB,
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0xBC, 0x45, 0xF6, 0xDA, 0xCD, 0xBE, 0x27, 0xBE, 0xF6, 0x20, 0x79, 0xF3, 0xC3, 0xC8, 0xFF, 0x85,
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0x43, 0x9F, 0xB1, 0x9B, 0x72, 0x88, 0xDD, 0xA4, 0x0D, 0xFC, 0xC6, 0xB5, 0x74, 0x67, 0x29, 0xF5
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};
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*/
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void test_square_simple(void){
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bigint_t a, c;
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@ -243,6 +291,32 @@ void test_square_simple(void){
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bigint_print_hex(&c);
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}
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// [fail (c)]: A862 % 2752 = 0D1A ; should a862 % 2752 = b1a
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void test_reduce_simple(void){
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bigint_t a, b, c;
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uint8_t a_b[2] = {0x62, 0xA8};
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uint8_t b_b[2] = {0x52, 0x27};
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uint8_t c_b[2];
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a.wordv=a_b;
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a.length_B = 2;
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a.info=0x00;
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bigint_adjust(&a);
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b.wordv=b_b;
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b.length_B = 2;
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b.info=0x00;
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bigint_adjust(&b);
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c.wordv = c_b;
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bigint_copy(&c, &a);
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bigint_reduce(&c, &b);
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cli_putstr_P(PSTR("\r\n test: "));
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bigint_print_hex(&a);
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cli_putstr_P(PSTR(" % "));
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bigint_print_hex(&b);
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cli_putstr_P(PSTR(" = "));
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bigint_print_hex(&c);
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}
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void testrun_performance_bigint(void){
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@ -255,6 +329,7 @@ const char echo_test_str[] PROGMEM = "echo-test";
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const char add_test_str[] PROGMEM = "add-test";
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const char mul_test_str[] PROGMEM = "mul-test";
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const char square_test_str[] PROGMEM = "square-test";
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const char reduce_test_str[] PROGMEM = "reduce-test";
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const char quick_test_str[] PROGMEM = "quick-test";
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const char performance_str[] PROGMEM = "performance";
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const char echo_str[] PROGMEM = "echo";
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@ -263,7 +338,8 @@ cmdlist_entry_t cmdlist[] PROGMEM = {
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{ add_test_str, NULL, test_add_bigint },
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{ mul_test_str, NULL, test_mul_bigint },
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{ square_test_str, NULL, test_square_bigint },
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{ quick_test_str, NULL, test_mul_simple },
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{ reduce_test_str, NULL, test_reduce_bigint },
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{ quick_test_str, NULL, test_reduce_simple },
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{ echo_test_str, NULL, test_echo_bigint },
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{ performance_str, NULL, testrun_performance_bigint },
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{ echo_str, (void*)1, (void_fpt)echo_ctrl },
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