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/*
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/*
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* the code assumes mpdigit to be at least an int
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7 |
* the code assumes mpdigit to be at least an int
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* mpdigit must be an atomic type. mpdigit is defined
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* mpdigit must be an atomic type. mpdigit is defined
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* in the architecture specific u.h
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* in the architecture specific u.h
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*/
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*/
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typedef struct mpint mpint;
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typedef struct mpint mpint;
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struct mpint
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struct mpint
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{
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{
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int sign; /* +1 or -1 */
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int sign; /* +1 or -1 */
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Line 19... |
| 20 |
char flags;
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char flags;
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};
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};
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enum
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enum
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{
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{
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MPstatic= 0x01,
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MPstatic= 0x01, /* static constant */
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MPnorm= 0x02, /* normalization status */
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MPtimesafe= 0x04, /* request time invariant computation */
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27 |
MPfield= 0x08, /* this mpint is a field modulus */
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Dbytes= sizeof(mpdigit), /* bytes per digit */
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Dbytes= sizeof(mpdigit), /* bytes per digit */
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Dbits= Dbytes*8 /* bits per digit */
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Dbits= Dbytes*8 /* bits per digit */
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};
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};
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/* allocation */
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/* allocation */
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void mpsetminbits(int n); /* newly created mpint's get at least n bits */
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void mpsetminbits(int n); /* newly created mpint's get at least n bits */
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mpint* mpnew(int n); /* create a new mpint with at least n bits */
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35 |
mpint* mpnew(int n); /* create a new mpint with at least n bits */
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void mpfree(mpint *b);
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36 |
void mpfree(mpint *b);
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void mpbits(mpint *b, int n); /* ensure that b has at least n bits */
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37 |
void mpbits(mpint *b, int n); /* ensure that b has at least n bits */
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void mpnorm(mpint *b); /* dump leading zeros */
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mpint* mpnorm(mpint *b); /* dump leading zeros */
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mpint* mpcopy(mpint *b);
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39 |
mpint* mpcopy(mpint *b);
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void mpassign(mpint *old, mpint *new);
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40 |
void mpassign(mpint *old, mpint *new);
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41 |
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/* random bits */
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/* random bits */
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mpint* mprand(int bits, void (*gen)(uchar*, int), mpint *b);
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mpint* mprand(int bits, void (*gen)(uchar*, int), mpint *b);
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/* return uniform random [0..n-1] */
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mpint* mpnrand(mpint *n, void (*gen)(uchar*, int), mpint *b);
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46 |
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/* conversion */
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/* conversion */
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mpint* strtomp(char*, char**, int, mpint*); /* ascii */
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mpint* strtomp(char*, char**, int, mpint*); /* ascii */
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int mpfmt(Fmt*);
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int mpfmt(Fmt*);
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char* mptoa(mpint*, int, char*, int);
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char* mptoa(mpint*, int, char*, int);
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mpint* letomp(uchar*, uint, mpint*); /* byte array, little-endian */
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mpint* letomp(uchar*, uint, mpint*); /* byte array, little-endian */
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int mptole(mpint*, uchar*, uint, uchar**);
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int mptole(mpint*, uchar*, uint, uchar**);
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void mptolel(mpint *b, uchar *p, int n);
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mpint* betomp(uchar*, uint, mpint*); /* byte array, little-endian */
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mpint* betomp(uchar*, uint, mpint*); /* byte array, big-endian */
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int mptobe(mpint*, uchar*, uint, uchar**);
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int mptobe(mpint*, uchar*, uint, uchar**);
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void mptober(mpint *b, uchar *p, int n);
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uint mptoui(mpint*); /* unsigned int */
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uint mptoui(mpint*); /* unsigned int */
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mpint* uitomp(uint, mpint*);
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mpint* uitomp(uint, mpint*);
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int mptoi(mpint*); /* int */
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int mptoi(mpint*); /* int */
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mpint* itomp(int, mpint*);
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60 |
mpint* itomp(int, mpint*);
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uvlong mptouv(mpint*); /* unsigned vlong */
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61 |
uvlong mptouv(mpint*); /* unsigned vlong */
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mpint* uvtomp(uvlong, mpint*);
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62 |
mpint* uvtomp(uvlong, mpint*);
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vlong mptov(mpint*); /* vlong */
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vlong mptov(mpint*); /* vlong */
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mpint* vtomp(vlong, mpint*);
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mpint* vtomp(vlong, mpint*);
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65 |
double mptod(mpint*); /* double */
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mpint* dtomp(double, mpint*);
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/* divide 2 digits by one */
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/* divide 2 digits by one */
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void mpdigdiv(mpdigit *dividend, mpdigit divisor, mpdigit *quotient);
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void mpdigdiv(mpdigit *dividend, mpdigit divisor, mpdigit *quotient);
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/* in the following, the result mpint may be */
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/* in the following, the result mpint may be */
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/* the same as one of the inputs. */
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/* the same as one of the inputs. */
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void mpadd(mpint *b1, mpint *b2, mpint *sum); /* sum = b1+b2 */
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void mpadd(mpint *b1, mpint *b2, mpint *sum); /* sum = b1+b2 */
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void mpsub(mpint *b1, mpint *b2, mpint *diff); /* diff = b1-b2 */
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74 |
void mpsub(mpint *b1, mpint *b2, mpint *diff); /* diff = b1-b2 */
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void mpleft(mpint *b, int shift, mpint *res); /* res = b<<shift */
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75 |
void mpleft(mpint *b, int shift, mpint *res); /* res = b<<shift */
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void mpright(mpint *b, int shift, mpint *res); /* res = b>>shift */
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76 |
void mpright(mpint *b, int shift, mpint *res); /* res = b>>shift */
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void mpmul(mpint *b1, mpint *b2, mpint *prod); /* prod = b1*b2 */
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77 |
void mpmul(mpint *b1, mpint *b2, mpint *prod); /* prod = b1*b2 */
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void mpexp(mpint *b, mpint *e, mpint *m, mpint *res); /* res = b**e mod m */
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78 |
void mpexp(mpint *b, mpint *e, mpint *m, mpint *res); /* res = b**e mod m */
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void mpmod(mpint *b, mpint *m, mpint *remainder); /* remainder = b mod m */
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79 |
void mpmod(mpint *b, mpint *m, mpint *remainder); /* remainder = b mod m */
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80 |
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81 |
/* logical operations */
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82 |
void mpand(mpint *b1, mpint *b2, mpint *res);
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83 |
void mpbic(mpint *b1, mpint *b2, mpint *res);
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84 |
void mpor(mpint *b1, mpint *b2, mpint *res);
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85 |
void mpnot(mpint *b, mpint *res);
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86 |
void mpxor(mpint *b1, mpint *b2, mpint *res);
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87 |
void mptrunc(mpint *b, int n, mpint *res);
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88 |
void mpxtend(mpint *b, int n, mpint *res);
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89 |
void mpasr(mpint *b, int shift, mpint *res);
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90 |
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91 |
/* modular arithmetic, time invariant when 0≤b1≤m-1 and 0≤b2≤m-1 */
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92 |
void mpmodadd(mpint *b1, mpint *b2, mpint *m, mpint *sum); /* sum = b1+b2 % m */
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93 |
void mpmodsub(mpint *b1, mpint *b2, mpint *m, mpint *diff); /* diff = b1-b2 % m */
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94 |
void mpmodmul(mpint *b1, mpint *b2, mpint *m, mpint *prod); /* prod = b1*b2 % m */
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95 |
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/* quotient = dividend/divisor, remainder = dividend % divisor */
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96 |
/* quotient = dividend/divisor, remainder = dividend % divisor */
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void mpdiv(mpint *dividend, mpint *divisor, mpint *quotient, mpint *remainder);
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97 |
void mpdiv(mpint *dividend, mpint *divisor, mpint *quotient, mpint *remainder);
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98 |
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| 75 |
/* return neg, 0, pos as b1-b2 is neg, 0, pos */
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99 |
/* return neg, 0, pos as b1-b2 is neg, 0, pos */
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| 76 |
int mpcmp(mpint *b1, mpint *b2);
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100 |
int mpcmp(mpint *b1, mpint *b2);
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101 |
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102 |
/* res = s != 0 ? b1 : b2 */
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103 |
void mpsel(int s, mpint *b1, mpint *b2, mpint *res);
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104 |
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105 |
/* return n! */
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106 |
mpint* mpfactorial(ulong n);
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107 |
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| 78 |
/* extended gcd return d, x, and y, s.t. d = gcd(a,b) and ax+by = d */
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108 |
/* extended gcd return d, x, and y, s.t. d = gcd(a,b) and ax+by = d */
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| 79 |
void mpextendedgcd(mpint *a, mpint *b, mpint *d, mpint *x, mpint *y);
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109 |
void mpextendedgcd(mpint *a, mpint *b, mpint *d, mpint *x, mpint *y);
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110 |
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| 81 |
/* res = b**-1 mod m */
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111 |
/* res = b**-1 mod m */
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Line 132... |
| 102 |
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132 |
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| 103 |
/* p[0:n] -= m * b[0:n-1] */
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133 |
/* p[0:n] -= m * b[0:n-1] */
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| 104 |
/* prereq: p has room for n+1 digits */
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134 |
/* prereq: p has room for n+1 digits */
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| 105 |
int mpvecdigmulsub(mpdigit *b, int n, mpdigit m, mpdigit *p);
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135 |
int mpvecdigmulsub(mpdigit *b, int n, mpdigit m, mpdigit *p);
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| 106 |
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136 |
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| 107 |
/* p[0:alen*blen-1] = a[0:alen-1] * b[0:blen-1] */
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137 |
/* p[0:alen+blen-1] = a[0:alen-1] * b[0:blen-1] */
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/* prereq: alen >= blen, p has room for m*n digits */
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138 |
/* prereq: alen >= blen, p has room for m*n digits */
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| 109 |
void mpvecmul(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *p);
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139 |
void mpvecmul(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *p);
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| - |
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140 |
void mpvectsmul(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *p);
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| 110 |
|
141 |
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| 111 |
/* sign of a - b or zero if the same */
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142 |
/* sign of a - b or zero if the same */
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| 112 |
int mpveccmp(mpdigit *a, int alen, mpdigit *b, int blen);
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143 |
int mpveccmp(mpdigit *a, int alen, mpdigit *b, int blen);
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| - |
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144 |
int mpvectscmp(mpdigit *a, int alen, mpdigit *b, int blen);
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| 113 |
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145 |
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| 114 |
/* divide the 2 digit dividend by the one digit divisor and stick in quotient */
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146 |
/* divide the 2 digit dividend by the one digit divisor and stick in quotient */
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| 115 |
/* we assume that the result is one digit - overflow is all 1's */
|
147 |
/* we assume that the result is one digit - overflow is all 1's */
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| 116 |
void mpdigdiv(mpdigit *dividend, mpdigit divisor, mpdigit *quotient);
|
148 |
void mpdigdiv(mpdigit *dividend, mpdigit divisor, mpdigit *quotient);
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| 117 |
|
149 |
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Line 169... |
| 137 |
CRTres* crtin(CRTpre*, mpint*); /* convert mpint to residues */
|
169 |
CRTres* crtin(CRTpre*, mpint*); /* convert mpint to residues */
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| 138 |
void crtout(CRTpre*, CRTres*, mpint*); /* convert residues to mpint */
|
170 |
void crtout(CRTpre*, CRTres*, mpint*); /* convert residues to mpint */
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| 139 |
void crtprefree(CRTpre*);
|
171 |
void crtprefree(CRTpre*);
|
| 140 |
void crtresfree(CRTres*);
|
172 |
void crtresfree(CRTres*);
|
| 141 |
|
173 |
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| - |
|
174 |
/* fast field arithmetic */
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| - |
|
175 |
typedef struct Mfield Mfield;
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| - |
|
176 |
|
| - |
|
177 |
struct Mfield
|
| - |
|
178 |
{
|
| - |
|
179 |
mpint;
|
| - |
|
180 |
int (*reduce)(Mfield*, mpint*, mpint*);
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| - |
|
181 |
};
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| - |
|
182 |
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| - |
|
183 |
mpint *mpfield(mpint*);
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| - |
|
184 |
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| - |
|
185 |
Mfield *gmfield(mpint*);
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| - |
|
186 |
Mfield *cnfield(mpint*);
|
| 142 |
|
187 |
|
| 143 |
#pragma varargck type "B" mpint*
|
188 |
#pragma varargck type "B" mpint*
|