如何处理C中的大整数

我想实现加密算法。 所以我需要一个合适的数据类型来处理具有大量数字的整数。

许多最新的语言,如Java,Python和Ruby提供了本机方法。 但是,我正在用C编程,我想知道在那里实现基本操作的最佳方式和最简单的方法是什么。

我想写它没有任何外部库。 我想到了两个选择:

  1. 使用char数组(如字符串,这对加密/解密密钥有用)
  2. 使用位数组(我不知道怎么做,但我认为这将取决于编译器)

你会怎么做?

如果您对密码学感兴趣,那么一切都必须正确。 您要么花费数月时间编写和测试,测试和测试……您自己的大量算术函数,或者您使用现有的库。

当你知道你使用的方法是正确的时,让加密正常工作是很困难的。 如果您使用的方法有微妙的错误几乎是不可能的。

对于加密使用GMP,并专注于加密。

如果你想编写自己的大量算术包,那么一定要这样做。 我自己做了同样的事情,这是一个有趣而有用的经历。 但是,不要将自己的工作用于任何关键的事情。

(对我而言)明显的选择是GMP,其主要开发者TorbjörnGranlund是2000年赢得Simon Singh“Cipher Challenge”的瑞典五人团队的成员。

根据该网站,该代码可用于在AMD Phenom II @ 3.2 GHz上计算1957秒内的100亿个pi数字。

该代码自1991年开发。

我首先强烈建议使用现有的库。

但是,我之前做过这个实验。 我选择选项2.代表像“10000000002000000000”这样的值

int array[2] = { 1000000000, 2000000000 } 

并且一次一个地执行操作和携带值。 效率不高,但function合理。

处理一组字符会更容易。 最好设计自己的类(/ datatype),定义处理所有算术运算的函数以备将来使用。 您可以使用ACRush设计的这个参考。

main函数中的变量可以在c ++中存储100个阶乘

 #include  #include  #include  #include  #include  #include  #include  #include  #include  #include  #include  #include  #include  #include  #include  #include  #include  using namespace std; //template for BIGINIT // base and base_digits must be consistent const int base = 10; const int base_digits = 1; struct bigint { vector a; int sign; bigint() : sign(1) { } bigint(long long v) { *this = v; } bigint(const string &s) { read(s); } void operator=(const bigint &v) { sign = v.sign; a = va; } void operator=(long long v) { sign = 1; if (v < 0) sign = -1, v = -v; for (; v > 0; v = v / base) a.push_back(v % base); } bigint operator+(const bigint &v) const { if (sign == v.sign) { bigint res = v; for (int i = 0, carry = 0; i < (int) max(a.size(), vasize()) || carry; ++i) { if (i == (int) res.a.size()) res.a.push_back(0); res.a[i] += carry + (i < (int) a.size() ? a[i] : 0); carry = res.a[i] >= base; if (carry) res.a[i] -= base; } return res; } return *this - (-v); } bigint operator-(const bigint &v) const { if (sign == v.sign) { if (abs() >= v.abs()) { bigint res = *this; for (int i = 0, carry = 0; i < (int) vasize() || carry; ++i) { res.a[i] -= carry + (i < (int) vasize() ? va[i] : 0); carry = res.a[i] < 0; if (carry) res.a[i] += base; } res.trim(); return res; } return -(v - *this); } return *this + (-v); } void operator*=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) { if (i == (int) a.size()) a.push_back(0); long long cur = a[i] * (long long) v + carry; carry = (int) (cur / base); a[i] = (int) (cur % base); //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base)); } trim(); } bigint operator*(int v) const { bigint res = *this; res *= v; return res; } friend pair divmod(const bigint &a1, const bigint &b1) { int norm = base / (b1.a.back() + 1); bigint a = a1.abs() * norm; bigint b = b1.abs() * norm; bigint q, r; qaresize(aasize()); for (int i = aasize() - 1; i >= 0; i--) { r *= base; r += aa[i]; int s1 = rasize() <= basize() ? 0 : ra[basize()]; int s2 = rasize() <= basize() - 1 ? 0 : ra[basize() - 1]; int d = ((long long) base * s1 + s2) / baback(); r -= b * d; while (r < 0) r += b, --d; qa[i] = d; } q.sign = a1.sign * b1.sign; r.sign = a1.sign; q.trim(); r.trim(); return make_pair(q, r / norm); } bigint operator/(const bigint &v) const { return divmod(*this, v).first; } bigint operator%(const bigint &v) const { return divmod(*this, v).second; } void operator/=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) { long long cur = a[i] + rem * (long long) base; a[i] = (int) (cur / v); rem = (int) (cur % v); } trim(); } bigint operator/(int v) const { bigint res = *this; res /= v; return res; } int operator%(int v) const { if (v < 0) v = -v; int m = 0; for (int i = a.size() - 1; i >= 0; --i) m = (a[i] + m * (long long) base) % v; return m * sign; } void operator+=(const bigint &v) { *this = *this + v; } void operator-=(const bigint &v) { *this = *this - v; } void operator*=(const bigint &v) { *this = *this * v; } void operator/=(const bigint &v) { *this = *this / v; } bool operator<(const bigint &v) const { if (sign != v.sign) return sign < v.sign; if (a.size() != vasize()) return a.size() * sign < vasize() * v.sign; for (int i = a.size() - 1; i >= 0; i--) if (a[i] != va[i]) return a[i] * sign < va[i] * sign; return false; } bool operator>(const bigint &v) const { return v < *this; } bool operator<=(const bigint &v) const { return !(v < *this); } bool operator>=(const bigint &v) const { return !(*this < v); } bool operator==(const bigint &v) const { return !(*this < v) && !(v < *this); } bool operator!=(const bigint &v) const { return *this < v || v < *this; } void trim() { while (!a.empty() && !a.back()) a.pop_back(); if (a.empty()) sign = 1; } bool isZero() const { return a.empty() || (a.size() == 1 && !a[0]); } bigint operator-() const { bigint res = *this; res.sign = -sign; return res; } bigint abs() const { bigint res = *this; res.sign *= res.sign; return res; } long long longValue() const { long long res = 0; for (int i = a.size() - 1; i >= 0; i--) res = res * base + a[i]; return res * sign; } friend bigint gcd(const bigint &a, const bigint &b) { return b.isZero() ? a : gcd(b, a % b); } friend bigint lcm(const bigint &a, const bigint &b) { return a / gcd(a, b) * b; } void read(const string &s) { sign = 1; a.clear(); int pos = 0; while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) { if (s[pos] == '-') sign = -sign; ++pos; } for (int i = s.size() - 1; i >= pos; i -= base_digits) { int x = 0; for (int j = max(pos, i - base_digits + 1); j <= i; j++) x = x * 10 + s[j] - '0'; a.push_back(x); } trim(); } friend istream& operator>>(istream &stream, bigint &v) { string s; stream >> s; v.read(s); return stream; } friend ostream& operator<<(ostream &stream, const bigint &v) { if (v.sign == -1) stream << '-'; stream << (vaempty() ? 0 : vaback()); for (int i = (int) vasize() - 2; i >= 0; --i) stream << setw(base_digits) << setfill('0') << va[i]; return stream; } static vector convert_base(const vector &a, int old_digits, int new_digits) { vector p(max(old_digits, new_digits) + 1); p[0] = 1; for (int i = 1; i < (int) p.size(); i++) p[i] = p[i - 1] * 10; vector res; long long cur = 0; int cur_digits = 0; for (int i = 0; i < (int) a.size(); i++) { cur += a[i] * p[cur_digits]; cur_digits += old_digits; while (cur_digits >= new_digits) { res.push_back(int(cur % p[new_digits])); cur /= p[new_digits]; cur_digits -= new_digits; } } res.push_back((int) cur); while (!res.empty() && !res.back()) res.pop_back(); return res; } typedef vector vll; static vll karatsubaMultiply(const vll &a, const vll &b) { int n = a.size(); vll res(n + n); if (n <= 32) { for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) res[i + j] += a[i] * b[j]; return res; } int k = n >> 1; vll a1(a.begin(), a.begin() + k); vll a2(a.begin() + k, a.end()); vll b1(b.begin(), b.begin() + k); vll b2(b.begin() + k, b.end()); vll a1b1 = karatsubaMultiply(a1, b1); vll a2b2 = karatsubaMultiply(a2, b2); for (int i = 0; i < k; i++) a2[i] += a1[i]; for (int i = 0; i < k; i++) b2[i] += b1[i]; vll r = karatsubaMultiply(a2, b2); for (int i = 0; i < (int) a1b1.size(); i++) r[i] -= a1b1[i]; for (int i = 0; i < (int) a2b2.size(); i++) r[i] -= a2b2[i]; for (int i = 0; i < (int) r.size(); i++) res[i + k] += r[i]; for (int i = 0; i < (int) a1b1.size(); i++) res[i] += a1b1[i]; for (int i = 0; i < (int) a2b2.size(); i++) res[i + n] += a2b2[i]; return res; } bigint operator*(const bigint &v) const { vector a6 = convert_base(this->a, base_digits, 6); vector b6 = convert_base(va, base_digits, 6); vll a(a6.begin(), a6.end()); vll b(b6.begin(), b6.end()); while (a.size() < b.size()) a.push_back(0); while (b.size() < a.size()) b.push_back(0); while (a.size() & (a.size() - 1)) a.push_back(0), b.push_back(0); vll c = karatsubaMultiply(a, b); bigint res; res.sign = sign * v.sign; for (int i = 0, carry = 0; i < (int) c.size(); i++) { long long cur = c[i] + carry; res.a.push_back((int) (cur % 1000000)); carry = (int) (cur / 1000000); } res.a = convert_base(res.a, 6, base_digits); res.trim(); return res; } }; //use : bigint var; //template for biginit over int main() { bigint var=10909000890789; cout<