C语言实现基于rsa的盲签名算法，不使用库

以下是一个简单的C语言实现基于RSA的盲签名算法的示例代码，不使用库：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

#define RSA_KEY_SIZE 1024        // RSA密钥长度
#define RSA_BLOCK_SIZE (RSA_KEY_SIZE / 8)   // RSA块长度
#define RSA_E 65537              // RSA公钥指数

// 定义大数结构体
typedef struct {
    int len;        // 数字长度
    int *data;      // 数字数组
} bignum;

// 随机生成一个指定长度的大数
void rand_bignum(bignum *num, int len) {
    int i;
    num->len = len;
    num->data = (int*)malloc(sizeof(int) * len);
    for (i = 0; i < len; i++) {
        num->data[i] = rand() % 10;
    }
}

// 复制大数
void copy_bignum(bignum *dest, bignum *src) {
    int i;
    dest->len = src->len;
    dest->data = (int*)malloc(sizeof(int) * dest->len);
    for (i = 0; i < dest->len; i++) {
        dest->data[i] = src->data[i];
    }
}

// 比较两个大数的大小
int cmp_bignum(bignum *a, bignum *b) {
    int i;
    if (a->len > b->len) {
        return 1;
    } else if (a->len < b->len) {
        return -1;
    } else {
        for (i = a->len - 1; i >= 0; i--) {
            if (a->data[i] > b->data[i]) {
                return 1;
            } else if (a->data[i] < b->data[i]) {
                return -1;
            }
        }
        return 0;
    }
}

// 大数减法
void sub_bignum(bignum *a, bignum *b, bignum *c) {
    int i, borrow = 0;
    c->len = a->len;
    c->data = (int*)malloc(sizeof(int) * c->len);
    for (i = 0; i < c->len; i++) {
        c->data[i] = a->data[i] - borrow;
        if (i < b->len) {
            c->data[i] -= b->data[i];
        }
        if (c->data[i] < 0) {
            c->data[i] += 10;
            borrow = 1;
        } else {
            borrow = 0;
        }
    }
    while (c->len > 1 && c->data[c->len - 1] == 0) {
        c->len--;
    }
}

// 大数乘法
void mul_bignum(bignum *a, bignum *b, bignum *c) {
    int i, j, carry;
    c->len = a->len + b->len;
    c->data = (int*)malloc(sizeof(int) * c->len);
    memset(c->data, 0, sizeof(int) * c->len);
    for (i = 0; i < a->len; i++) {
        carry = 0;
        for (j = 0; j < b->len; j++) {
            c->data[i + j] += a->data[i] * b->data[j] + carry;
            carry = c->data[i + j] / 10;
            c->data[i + j] %= 10;
        }
        if (carry > 0) {
            c->data[i + j] += carry;
        }
    }
    while (c->len > 1 && c->data[c->len - 1] == 0) {
        c->len--;
    }
}

// 大数除法
void div_bignum(bignum *a, bignum *b, bignum *c) {
    int i, j, k;
    bignum r, tmp1, tmp2;
    c->len = a->len - b->len + 1;
    c->data = (int*)malloc(sizeof(int) * c->len);
    memset(c->data, 0, sizeof(int) * c->len);
    r.len = b->len;
    r.data = (int*)malloc(sizeof(int) * r.len);
    for (i = a->len - 1; i >= 0; i--) {
        for (j = r.len - 1; j > 0; j--) {
            r.data[j] = r.data[j - 1];
        }
        r.data[0] = a->data[i];
        while (r.len > 1 && r.data[r.len - 1] == 0) {
            r.len--;
        }
        if (cmp_bignum(&r, b) < 0) {
            continue;
        }
        k = r.len - b->len;
        tmp1.len = b->len + k;
        tmp1.data = (int*)malloc(sizeof(int) * tmp1.len);
        memset(tmp1.data, 0, sizeof(int) * tmp1.len);
        for (j = 0; j < k; j++) {
            tmp1.data[j] = 0;
        }
        for (j = k; j < tmp1.len; j++) {
            tmp1.data[j] = b->data[j - k];
        }
        while (cmp_bignum(&r, &tmp1) >= 0) {
            c->data[i - k]++;
            sub_bignum(&r, &tmp1, &tmp2);
            copy_bignum(&r, &tmp2);
        }
    }
    while (c->len > 1 && c->data[c->len - 1] == 0) {
        c->len--;
    }
}

// 大数取模
void mod_bignum(bignum *a, bignum *b, bignum *c) {
    int i, j, k;
    bignum r, tmp1, tmp2;
    r.len = a->len;
    r.data = (int*)malloc(sizeof(int) * r.len);
    for (i = 0; i < r.len; i++) {
        r.data[i] = a->data[i];
    }
    while (r.len > 1 && r.data[r.len - 1] == 0) {
        r.len--;
    }
    if (cmp_bignum(&r, b) < 0) {
        copy_bignum(c, &r);
        return;
    }
    c->len = b->len;
    c->data = (int*)malloc(sizeof(int) * c->len);
    for (i = 0; i < c->len; i++) {
        c->data[i] = r.data[r.len - i - 1];
    }
    for (i = r.len - b->len; i >= 0; i--) {
        k = c->len - 1;
        tmp1.len = c->len + 1;
        tmp1.data = (int*)malloc(sizeof(int) * tmp1.len);
        memset(tmp1.data, 0, sizeof(int) * tmp1.len);
        for (j = 0; j < c->len; j++) {
            tmp1.data[j] = c->data[j];
        }
        tmp1.data[c->len] = r.data[i];
        while (tmp1.len > 1 && tmp1.data[tmp1.len - 1] == 0) {
            tmp1.len--;
        }
        while (cmp_bignum(&tmp1, b) >= 0) {
            sub_bignum(&tmp1, b, &tmp2);
            copy_bignum(&tmp1, &tmp2);
        }
        c->data[k--] = tmp1.data[0];
        while (c->len > 1 && c->data[c->len - 1] == 0) {
            c->len--;
        }
    }
}

// 大数幂模运算
void powmod_bignum(bignum *a, bignum *b, bignum *n, bignum *c) {
    int i;
    bignum tmp1, tmp2;
    tmp1.len = 1;
    tmp1.data = (int*)malloc(sizeof(int));
    tmp1.data[0] = 1;
    copy_bignum(c, &tmp1);
    for (i = b->len - 1; i >= 0; i--) {
        mul_bignum(c, c, &tmp1);
        mod_bignum(&tmp1, n, &tmp2);
        copy_bignum(c, &tmp2);
        if (b->data[i] == 1) {
            mul_bignum(c, a, &tmp1);
            mod_bignum(&tmp1, n, &tmp2);
            copy_bignum(c, &tmp2);
        }
    }
}

// 生成RSA公钥和私钥
void gen_rsa_key(bignum *p, bignum *q, bignum *n, bignum *e, bignum *d) {
    bignum phi, tmp1, tmp2;
    bignum p_minus1, q_minus1;
    p_minus1.len = p->len;
    p_minus1.data = (int*)malloc(sizeof(int) * p_minus1.len);
    sub_bignum(p, &tmp1, &p_minus1);
    q_minus1.len = q->len;
    q_minus1.data = (int*)malloc(sizeof(int) * q_minus1.len);
    sub_bignum(q, &tmp1, &q_minus1);
    mul_bignum(&p_minus1, &q_minus1, &phi);
    mul_bignum(p, q, n);
    copy_bignum(e, &tmp1);
    while (1) {
        powmod_bignum(e, &phi, n, d);
        if (cmp_bignum(d, &tmp1) == 0) {
            break;
        }
        add_bignum(e, &tmp2, e);
    }
}

// 盲化处理
void blind_bignum(bignum *a, bignum *r, bignum *n, bignum *b) {
    powmod_bignum(r, b, n, a);
}

// 解盲处理
void unblind_bignum(bignum *a, bignum *r, bignum *n, bignum *b) {
    powmod_bignum(b, &tmp1, n, &tmp2);
    inv_bignum(&tmp2, r, n, &tmp1);
    mul_bignum(a, &tmp1, &tmp2);
    mod_bignum(&tmp2, n, a);
}

// RSA盲签名
void rsa_blind_sign(bignum *m, bignum *n, bignum *d, bignum *s) {
    bignum r, tmp1, tmp2;
    srand(time(NULL));
    rand_bignum(&r, RSA_BLOCK_SIZE);
    powmod_bignum(&r, n, n, &tmp1);
    mul_bignum(&tmp1, m, &tmp2);
    mod_bignum(&tmp2, n, s);
    powmod_bignum(&r, d, n, &tmp1);
    inv_bignum(&tmp1, n, &tmp2);
    mul_bignum(&tmp2, s, &tmp1);
    mod_bignum(&tmp1, n, s);
}

// RSA盲验签
int rsa_blind_verify(bignum *m, bignum *n, bignum *e, bignum *s) {
    bignum r, tmp1, tmp2, tmp3;
    int flag;
    srand(time(NULL));
    rand_bignum(&r, RSA_BLOCK_SIZE);
    powmod_bignum(&r, n, n, &tmp1);
    inv_bignum(&r, n, &tmp2);
    mul_bignum(s, &tmp2, &tmp1);
    mod_bignum(&tmp1, n, &tmp2);
    powmod_bignum(&tmp2, e, n, &tmp1);
    mul_bignum(&tmp1, &tmp1, &tmp2);
    mod_bignum(&tmp2, n, &tmp1);
    flag = cmp_bignum(m, &tmp1);
    if (flag == 0) {
        printf("Verify success!\n");
    } else {
        printf("Verify failed!\n");
    }
    return flag;
}

int main() {
    bignum p, q, n, e, d, m, s;
    p.len = RSA_BLOCK_SIZE / 2;
    p.data = (int*)malloc(sizeof(int) * p.len);
    q.len = RSA_BLOCK_SIZE / 2;
    q.data = (int*)malloc(sizeof(int) * q.len);
    e.len = 1;
    e.data = (int*)malloc(sizeof(int));
    m.len = RSA_BLOCK_SIZE / 2;
    m.data = (int*)malloc(sizeof(int) * m.len);
    s.len = RSA_BLOCK_SIZE / 2;
    s.data = (int*)malloc(sizeof(int) * s.len);
    gen_rsa_key(&p, &q, &n, &e, &d);
    rand_bignum(&m, RSA_BLOCK_SIZE / 2);
    rsa_blind_sign(&m, &n, &d, &s);
    rsa_blind_verify(&m, &n, &e, &s);
    return 0;
}

需要注意的是，以上代码仅作为示例，实现比较简单，没有做任何优化。在实际使用时应该考虑到算法的安全性和效率。