Base58编码

Base58编码简析与C++实现

参照：

https://en.wikipedia.org/wiki/Base58
https://en.wikipedia.org/wiki/Binary-to-text_encoding
https://en.bitcoin.it/wiki/Base58Check_encoding

Base58可以简单理解为将数据，以58进制的形式进行表示。
实现伪代码如下：

code_string = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"
   x = convert_bytes_to_big_integer(hash_result)

   output_string = ""

   while(x > 0) 
       {
           (x, remainder) = divide(x, 58)
           output_string.append(code_string[remainder])
       }

   repeat(number_of_leading_zero_bytes_in_hash)
       {
       output_string.append(code_string[0]);
       }

   output_string.reverse();

大值思路为：
1. 将数据转换为大整数x，
2. 依次将（x % 58）的值表示的编码添加到输出字符串末尾；
3. 令x = ( x / 58 );
4. 重复2-3，直到x等于0；
5. 将数据前所有0的编码（即“1”）添加到输出字符串末尾；
6. 将输出字符串反转，即为Base58编码字符串。

由于编码前数据可以视为256进制编码数据，所以转换为58进制编码数据后，数据长度为变长。
假设原长度为Len256，转换为长度为Len58，则：

Len58 = Len256 * ( log256 / log58 ) + 1

Bitcoin（0.16.0）中实现代码如下：

/** All alphanumeric characters except for "0", "I", "O", and "l" */
static const char* pszBase58 = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz";

bool DecodeBase58(const char* psz, std::vector<unsigned char>& vch)
{
    // Skip leading spaces.
    while (*psz && isspace(*psz))
        psz++;
    // Skip and count leading '1's.
    int zeroes = 0;
    int length = 0;
    while (*psz == '1') {
        zeroes++;
        psz++;
    }
    // Allocate enough space in big-endian base256 representation.
    int size = strlen(psz) * 733 /1000 + 1; // log(58) / log(256), rounded up.
    std::vector<unsigned char> b256(size);
    // Process the characters.
    while (*psz && !isspace(*psz)) {
        // Decode base58 character
        const char* ch = strchr(pszBase58, *psz);
        if (ch == nullptr)
            return false;
        // Apply "b256 = b256 * 58 + ch".
        int carry = ch - pszBase58;
        int i = 0;
        for (std::vector<unsigned char>::reverse_iterator it = b256.rbegin(); (carry != 0 || i < length) && (it != b256.rend()); ++it, ++i) {
            carry += 58 * (*it);
            *it = carry % 256;
            carry /= 256;
        }
        assert(carry == 0);
        length = i;
        psz++;
    }
    // Skip trailing spaces.
    while (isspace(*psz))
        psz++;
    if (*psz != 0)
        return false;
    // Skip leading zeroes in b256.
    std::vector<unsigned char>::iterator it = b256.begin() + (size - length);
    while (it != b256.end() && *it == 0)
        it++;
    // Copy result into output vector.
    vch.reserve(zeroes + (b256.end() - it));
    vch.assign(zeroes, 0x00);
    while (it != b256.end())
        vch.push_back(*(it++));
    return true;
}

std::string EncodeBase58(const unsigned char* pbegin, const unsigned char* pend)
{
    // Skip & count leading zeroes.
    int zeroes = 0;
    int length = 0;
    while (pbegin != pend && *pbegin == 0) {
        pbegin++;
        zeroes++;
    }
    // Allocate enough space in big-endian base58 representation.
    int size = (pend - pbegin) * 138 / 100 + 1; // log(256) / log(58), rounded up.
    std::vector<unsigned char> b58(size);
    // Process the bytes.
    while (pbegin != pend) {
        int carry = *pbegin;
        int i = 0;
        // Apply "b58 = b58 * 256 + ch".
        for (std::vector<unsigned char>::reverse_iterator it = b58.rbegin(); (carry != 0 || i < length) && (it != b58.rend()); it++, i++) {
            carry += 256 * (*it);
            *it = carry % 58;
            carry /= 58;
        }

        assert(carry == 0);
        length = i;
        pbegin++;
    }
    // Skip leading zeroes in base58 result.
    std::vector<unsigned char>::iterator it = b58.begin() + (size - length);
    while (it != b58.end() && *it == 0)
        it++;
    // Translate the result into a string.
    std::string str;
    str.reserve(zeroes + (b58.end() - it));
    str.assign(zeroes, '1');
    while (it != b58.end())
        str += pszBase58[*(it++)];
    return str;
}

std::string EncodeBase58(const std::vector<unsigned char>& vch)
{
    return EncodeBase58(vch.data(), vch.data() + vch.size());
}

bool DecodeBase58(const std::string& str, std::vector<unsigned char>& vchRet)
{
    return DecodeBase58(str.c_str(), vchRet);
}

编码与解码，即为256进制与58进制大数据间的相互转换。