void newhope_sharedb(unsigned char *sharedkey, unsigned char *send, const unsigned char *received)
{
poly sp, ep, v, a, pka, c, epp, bp;
unsigned char seed[NEWHOPE_SEEDBYTES];
unsigned char noiseseed[32];
randombytes(noiseseed, 32);
decode_a(&pka, seed, received);
gen_a(&a, seed);
poly_getnoise(&sp,noiseseed,0);
poly_ntt(&sp);
poly_getnoise(&ep,noiseseed,1);
poly_ntt(&ep);
poly_pointwise(&bp, &a, &sp);
poly_add(&bp, &bp, &ep);
poly_pointwise(&v, &pka, &sp);
poly_bitrev(&v);
poly_invntt(&v);
poly_getnoise(&epp,noiseseed,2);
poly_add(&v, &v, &epp);
helprec(&c, &v, noiseseed, 3);
encode_b(send, &bp, &c);
rec(sharedkey, &v, &c);
sha3256(sharedkey, sharedkey, 32);
}
void poly_multiple(int startA,int endA,int startB,int endB,int *avail,int *avail_end) //多項式乘法
{
int i, j, n;
for(i=0;startA+i <= endA;i++){ //算出乘法項
for(j=0;startB+j <= endB;j++,(*avail)++){
p[*avail].coef = p[startA+i].coef * p[startB+j].coef;
p[*avail].expon = p[startA+i].expon + p[startB+j].expon;
}
if(i==1){ //相加前兩項乘法項
poly_add(*avail-j*2,*avail-j-1,*avail-j,*avail-1,avail,avail_end);
n = *avail_end - *avail;
*avail = *avail_end;
}
if(i>1){ //相加前一項乘法項與後一項相加後乘法項
poly_add(*avail-j-n,*avail-j-1,*avail-j,*avail-1,avail,avail_end);
n = *avail_end - *avail;
*avail = *avail_end;
}
}
*avail-=n;
for(i=0;(*avail)+i < *avail_end;i++){ //印出結果
if(i!=0)printf(" + ");
printf("%g",p[*avail_end-n+i].coef);
if(p[*avail_end-n+i].expon != 0)
printf("X^%u\n",p[*avail_end-n+i].expon);
}
}
static void berlekamp_massey(const uint8_t *s, int N,
const struct galois_field *gf,
uint8_t *sigma)
{
uint8_t C[MAX_POLY];
uint8_t B[MAX_POLY];
int L = 0;
int m = 1;
uint8_t b = 1;
int n;
memset(B, 0, sizeof(B));
memset(C, 0, sizeof(C));
B[0] = 1;
C[0] = 1;
for (n = 0; n < N; n++) {
uint8_t d = s[n];
uint8_t mult;
int i;
for (i = 1; i <= L; i++) {
if (!(C[i] && s[n - i]))
continue;
d ^= gf->exp[(gf->log[C[i]] +
gf->log[s[n - i]]) %
gf->p];
}
mult = gf->exp[(gf->p - gf->log[b] + gf->log[d]) % gf->p];
if (!d) {
m++;
} else if (L * 2 <= n) {
uint8_t T[MAX_POLY];
memcpy(T, C, sizeof(T));
poly_add(C, B, mult, m, gf);
memcpy(B, T, sizeof(B));
L = n + 1 - L;
b = d;
m = 1;
} else {
poly_add(C, B, mult, m, gf);
m++;
}
}
memcpy(sigma, C, MAX_POLY);
}
void poly_mul(node **Hpoly1,node **Hpoly2,node **Hpoly3)
{
node *temp1,*temp2,*temp31,*temp32;
if(*Hpoly1==NULL)
*Hpoly3=*Hpoly2;
else if(*Hpoly2==NULL)
*Hpoly3=*Hpoly1;
temp31=(node*)malloc(sizeof(node));
temp31->next=NULL;
for(temp1=*Hpoly1;temp1!=NULL;temp1=temp1->next)
{
for(temp2=*Hpoly2;temp2!=NULL;temp2=temp2->next)
{
temp31->coeff=temp1->coeff*temp2->coeff;
temp31->expn=temp1->expn+temp2->expn;
temp32=*Hpoly3;
*Hpoly3=NULL;
poly_add(&temp32,&temp31,&*Hpoly3);
poly_reverse(&*Hpoly3);
}
}
}
void main()
{
char opt;
clrscr();
printf("\nCreate the first list\n");
do
{
creat(&x1);
printf("\nPress 'y' to continue");
flushall();
scanf("%c",&opt);
}while(opt=='y');
printf("\nCreate the second list\n");
do
{
creat(&x2);
printf("\nPress 'y' to continue");
flushall();
scanf("%c",&opt);
}while(opt=='y');
getch();
clrscr();
printf("\n\nElements in list1\n\n");
traverse(&x1);
printf("\n\nElements in list2\n\n");
traverse(&x2);
printf("\n\n\n After addition\n\n");
x3=poly_add(x1,x2);
traverse(&x3);
printf("\n\n\n After multiplication\n\n");
x4=poly_mul(x1,x2);
traverse(&x4);
getch();
}
GFn_el_t & GFn_el_t::operator += (const GFn_el_t &_h) {
assert( &GFn == &_h.GFn );
poly_add(prime, degree, comp, degree, comp, degree, _h.comp);
return *this;
}
int main(void)
{
FILE *fp;
int i;
int startA = 0, endA, startB, endB, startD, avail, avail_end;
memset(p,0,MAX_TERM);//把 p[MAX_TERM]全陣列初始化為0
fp = fopen("poly_a.txt","r");//讀取poly_a.txt並印出-------------------------------
if(fp==NULL)printf("開檔失敗");
printf("A(x) = ");
for(i=0;!feof(fp);i++){
if(i!=0)printf(" + ");
fscanf(fp,"%f\t%u\n",&p[startA+i].coef,&p[startA+i].expon);
printf("%g",p[startA+i].coef);
if(p[startA+i].expon != 0)
printf("X^%u",p[startA+i].expon);
}
printf("\n");
fclose(fp);//關閉poly_a.txt-------------------------------------------------------
endA = startA+i-1;
startB = endA+1;
printf("\nB(x) = ");
fp = fopen("poly_b.txt","r");//讀取poly_b.txt並印出-------------------------------
if(fp==NULL)printf("開檔失敗");
for(i=0;!feof(fp);i++){
if(i!=0)printf(" + ");
fscanf(fp,"%f\t%u\n",&p[startB+i].coef,&p[startB+i].expon);
printf("%g",p[startB+i].coef);
if(p[startB+i].expon != 0)
printf("X^%u",p[startB+i].expon);
}
printf("\n");
fclose(fp);//關閉poly_b.txt-------------------------------------------------------
endB = startB+i-1;
startD = endB+1;
poly_add(startA,endA,startB,endB,&startD,&avail);
printf("\nA(x) + B(x) = ");
for(i=0;p[startD+i].coef!=0;i++){
if(i!=0)printf(" + ");
printf("%g",p[startD+i].coef);
if(p[startD+i].expon != 0)
printf("X^%u",p[startD+i].expon);
}
printf("\n");
printf("\n[A(x) + B(x)] * B(x) = \n");
poly_multiple(startD,avail-1,startB,endB,&avail,&avail_end);
printf("\nX = 3.14 : %f\n",substitute(avail,avail_end));
system("pause");
return 0;
}
Poly *poly_multi(Poly *poly1, Poly *poly2)
{
Poly *retPoly, *tmpM, *tmpA;
// to ensure that no memory leaking during the operation, we use two temporary pointers for memory management purposes
// tmpM is used to track the poly object during multiplication
// tmpA is used to track the poly object during addition
Term *iter;
retPoly = poly_new();
for (iter = poly2->head; iter != NULL; iter = iter->next)
{
tmpM = poly_term_multi(poly1, iter);
tmpA = retPoly;
retPoly = poly_add(retPoly, tmpM);
poly_destroy(tmpM);
poly_destroy(tmpA);
}
return retPoly;
}
void newhope_keygen(unsigned char *send, poly *sk)
{
poly a, e, r, pk;
unsigned char seed[NEWHOPE_SEEDBYTES];
unsigned char noiseseed[32];
randombytes(seed, NEWHOPE_SEEDBYTES);
randombytes(noiseseed, 32);
gen_a(&a, seed); //unsigned
poly_getnoise(sk,noiseseed,0);
poly_ntt(sk); //unsigned
poly_getnoise(&e,noiseseed,1);
poly_ntt(&e); //unsigned
poly_pointwise(&r,sk,&a); //unsigned
poly_add(&pk,&e,&r); //unsigned
encode_a(send, &pk, seed);
}
void main()
{
NODE head1,head2,head3;
MALLOC(head1,1,struct node);
MALLOC(head2,1,struct node);
MALLOC(head3,1,struct node);
head1->link=head1;
head2->link=head2;
head3->link=head3;
printf("enter the first polynomial\n");
head1=read_polynomial(head1);
printf("enter the second polynomial\n");
head2=read_polynomial(head2);
head3=poly_add(head1,head2,head3);
printf("polynomial 1:");
display(head1);
printf("\npolynomial 2:");
display(head2);
printf("\npolynomial 3:");
display(head3);
getch();
}
main()
{
ListHeader list1, list2, list3;
init(&list1);
init(&list2);
init(&list3);
// 다항식 1을 생성
insert_node_last(&list1, 3,12);
insert_node_last(&list1, 2,8);
insert_node_last(&list1, 1,0);
// 다항식 2를 생성
insert_node_last(&list2, 8,12);
insert_node_last(&list2, -3,10);
insert_node_last(&list2, 10,6);
// 다항식 3 = 다항식 1 + 다항식 2
poly_add(&list1, &list2, &list3);
poly_print(&list3);
}
main( )
{
struct node *p1_start,*p2_start,*p3_start;
p1_start=NULL;
p2_start=NULL;
p3_start=NULL;
printf("Polynomial 1 :\n");
p1_start=enter(p1_start);
printf("Polynomial 2 :\n");
p2_start=enter(p2_start);
p3_start=poly_add(p1_start,p2_start);
printf("Polynomial 1 is : ");
display(p1_start);
printf("Polynomial 2 is : ");
display(p2_start);
printf("Added polynomial is : ");
display(p3_start);
}/*End of main()*/
int main( )
{
struct polynode *first, *second, *total ;
int i = 0 ;
first = second = total = NULL ; /* empty linked lists */
poly_append ( &first, 1.4f, 5 ) ;
poly_append ( &first, 1.5f, 4 ) ;
poly_append ( &first, 1.7f, 2 ) ;
poly_append ( &first, 1.8f, 1 ) ;
poly_append ( &first, 1.9f, 0 ) ;
system ( "cls" ) ;
display_poly ( first ) ;
poly_append ( &second, 1.5f, 6 ) ;
poly_append ( &second, 2.5f, 5 ) ;
poly_append ( &second, -3.5f, 4 ) ;
poly_append ( &second, 4.5f, 3 ) ;
poly_append ( &second, 6.5f, 1 ) ;
printf ( "\n\n" ) ;
display_poly ( second ) ;
/* draws a dashed horizontal line */
printf ( "\n" ) ;
while ( i++ < 79 )
printf ( "-" ) ;
printf ( "\n\n" ) ;
poly_add ( first, second, &total ) ;
display_poly ( total ) ; /* displays the resultant polynomial */
return 0 ;
}
int poly_binary_parse(poly_data *cd, char *filename, float scale)
{
FILE *fp = fopen(filename, "rb");
if(fp == NULL) {
return 1;
}
float delta, val;
uint32_t nvals;
uint32_t n;
while(1){
fread(&delta, sizeof(float), 1, fp);
if(feof(fp)){
break;
}
#ifdef POLY_DEBUG
printf("reading delta value of %g\n", delta);
#endif
fread(&nvals, sizeof(uint32_t), 1, fp);
#ifdef POLY_DEBUG
printf("reading %d nvals\n", nvals);
#endif
poly_add(cd, (uint32_t) scale * delta, nvals);
for(n = 0; n < nvals; n++) {
fread(&val, sizeof(float), 1, fp);
#ifdef POLY_DEBUG
printf("---- reading %g\n", val);
#endif
poly_pset(cd, n, val);
}
}
fclose(fp);
return 0;
}
int main (void) {
poly *P0, *P1, *P2, *P3, *M1, *M2, *P4, *P5, *P6, *P7;
P0=poly_create(4,2,1,3,2,6,5,1,7); //4 terms: 1x^7 + 6x^5 + 3x^2 + 2x^1
P1=poly_create(3,3,2,1,4,6,5); //3 terms: 6x^5 + 1x^4 + 3x^2
P2=poly_create(1,16,2); //1 term: 16x^2
P3=poly_create(0); // no terms
printf("P0: "); poly_print(P0);
printf("P1: "); poly_print(P1);
printf("P2: "); poly_print(P2);
printf("P3: "); poly_print(P3);
M1=poly_scalar_mult(P1,2);
printf("M1 (P1*2): "); poly_print(M1);
M2=poly_scalar_mult(P3,4);
printf("M2 (P3*4): "); poly_print(M2);
P4=poly_duplicate(M1);
printf("P4 (dup M1): "); poly_print(P4);
P5=poly_add(P1,P0);
printf("P5 (P1+P0): "); poly_print(P5);
P6=poly_add(P3,P3);
printf("P6 (P3+P3): "); poly_print(P6);
P7=poly_add(P0,P3);
printf("P7 (P0+P3): "); poly_print(P7);
poly_free(&P1);
if (P1==NULL) printf("P1: was freed\n");
else printf("P1: is not null!!\n");
poly *test1=poly_create(4,2,1,3,2,6,5,1,7); //4 terms: 1x^7 + 6x^5 + 3x^2 + 2x^1
poly *test2=poly_duplicate(test1);
test2=poly_scalar_mult(test2, 5);
printf("test1: ");poly_print(test1);
printf("test2: ");poly_print(test2);
//printf("%p, %p\n", test1, test2);
poly_free(&test1);
poly *MM1 = poly_create(5,1,1,2,2,3,3,4,4,5,5);
poly *MM2 = poly_create(5,-1,1,-2,2,-3,3,-4,4,-5,5);
printf("MM1: ");poly_print(MM1);
printf("MM2: ");poly_print(MM2);
poly *MM1_Plus_MM2 = poly_add(MM1, MM2);
printf("(MM1+MM2): ");poly_print(MM1_Plus_MM2);
poly *MM1_Multiplied_By_5 = poly_scalar_mult(MM1, 5);
poly *MM2_Multiplied_By_10 = poly_scalar_mult(MM2, 10);
printf("MM1*5: ");poly_print(MM1_Multiplied_By_5);
printf("MM2*10: ");poly_print(MM2_Multiplied_By_10);
printf("MM1: ");poly_print(MM1);
printf("MM2: ");poly_print(MM2);
}
void gui_add_vertex (gui *g, int x, int y) {
poly_add (g->poly, vertex_new (x, y));
gui_draw_all (g);
}
int main(void)
{
DList listhdr1, listhdr2, listhdr3, listhdr4;
int coef, expon;
initList(&listhdr1);
initList(&listhdr2);
initList(&listhdr3);
initList(&listhdr4);
//다항식 p(x) 입력
printf("다항식 p(x)의 계수, 차수 쌍을 입력하세요. 끝이면 0 0을 입력하세요. \n");
while(1){
scanf("%d %d", &coef, &expon);
if(coef==0){
if(expon!=0)
printf("계수가 0인 값은 입력 할 필요가 없습니다! \n");
else
break;
}
else
insert_node(&listhdr1, coef, expon);
}
poly_sort(&listhdr1); //p(x) 내림차순 정렬
poly_dup(&listhdr1); //p(x) 중복 차수 제거
fflush(stdin); //입력 버퍼 비우기(입력값 오류 방지)
//다항식 q(x) 입력
printf("다항식 q(x)의 계수, 차수 쌍을 입력하세요. 끝이면 0 0을 입력하세요. \n");
while(1){
scanf("%d %d", &coef, &expon);
if(coef==0){
if(expon!=0)
printf("계수가 0인 값은 입력 할 필요가 없습니다! \n");
else
break;
}
else
insert_node(&listhdr2, coef, expon);
}
poly_sort(&listhdr2); //q(x) 내림차순 정렬
poly_dup(&listhdr2); //q(x) 중복 차수 제거
fflush(stdin); //입력 버퍼 비우기(입력값 오류 방지)
poly_add(&listhdr1, &listhdr2, &listhdr3);
poly_sub(&listhdr1, &listhdr2, &listhdr4);
printf("**************** Input value ****************\n");
printf("p(x)=");
poly_print(&listhdr1);
printf("\n");
printf("q(x)=");
poly_print(&listhdr2);
printf("\n");
printf("**************** Result ****************\n");
printf("p(x)+q(x)=");
poly_print(&listhdr3);
printf("\n");
printf("p(x)-q(x)=");
poly_print(&listhdr4);
printf("\n");
system("pause");
return 0;
}
