C++ 处理非常大的整数

2022-01-14 00:00:00 integer biginteger rsa c++

我正在使用 RSA 算法进行加密/解密，为了解密文件，您必须处理一些相当大的值.更具体地说，像

I am using the RSA Algorithm for encryption/decryption, and in order to decrypt the files you have to deal with some pretty big values. More specifically, things like 

P = C^d % n
  = 62^65 % 133

现在这确实是唯一不合适的计算.我曾尝试使用 Matt McCutchen 的 BigInteger 库，但在链接过程中出现很多编译器错误，例如:

Now that is really the only calculations that ill be doing. I have tried using Matt McCutchen's BigInteger Library, but I am getting a lot of compiler errors during linking, such as:

encryption.o(.text+0x187):encryption.cpp: undefined reference to `BigInteger::BigInteger(int)'

encryption.o(.text+0x302):encryption.cpp: undefined reference to `operator<<(std::ostream&, BigInteger const&)'

encryption.o(.text$_ZNK10BigIntegermlERKS_[BigInteger::operator*(BigInteger const&) const]+0x63):encryption.cpp: undefined reference to `BigInteger::multiply(BigInteger const&, BigInteger const&)'

所以我想知道处理来自 RSA 算法的真正大整数的最佳方法是什么.

So I was wondering what would be the best way to go about handling the really big integers that come out of the RSA Algorithm.

我听说有可能将你的变量声明为双长，所以...

I heard that a possibility would be to declare your variables as a double long, so...

long long decryptedCharacter;

但我不确定可以存储多大的整数.

but I'm not sure exactly how big of an integer that can store.

例如，我尝试使用 dev C++ 编译并运行以下程序:

Well for example, I try to compile and run the following program using dev C++:

#include iostream

#include "bigintBigIntegerLibrary.hh"

using namespace std;

int main()
{
    BigInteger a = 65536;
    cout << (a * a * a * a * a * a * a * a);
    return 0;
}

然后我得到这些错误.

Derek，我认为通过包含 BigIntegerLibrary.hh 文件，编译器将遍历并编译它将使用的所有必要文件.

Derek, I thought that by including the BigIntegerLibrary.hh file, that the compiler would go through and compile all the necessary files that it will use.

我应该如何尝试编译上述程序以解决链接错误?

How should I try and compile the program above in order to resolve the linking errors?

推荐答案

Tomek，听起来您没有正确链接到 BigInteger 代码.我认为你应该解决这个问题而不是寻找一个新的图书馆.我查看了源代码，BigInteger::BigInteger(int) 是最明确定义的.简单的一瞥表明其他人也是如此.

Tomek, it sounds like you aren't linking to the BigInteger code correctly. I think you should resolve this problem rather than looking for a new library. I took a look at the source, and BigInteger::BigInteger(int) is most definitely defined. A brief glance indicates that the others are as well.

您遇到的链接错误表明您要么忽略了编译 BigInteger 源代码，要么在链接时忽略了包含生成的目标文件.请注意，BigInteger 源使用cc"扩展名而不是cpp"，因此请确保您也在编译这些文件.

The link errors you're getting imply that you are either neglecting to compile the BigInteger source, or neglecting to include the resulting object files when you link. Please note that the BigInteger source uses the "cc" extension rather than "cpp", so make sure you are compiling these files as well.

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