問題描述

P 和 Q 的值與 .Net RSAParameters 的模量值不匹配.根據 RSA 算法和 MSDN 文檔，它應該是:P * Q = Modulus

The values of P and Q do not match value of the Modulus of the .Net RSAParameters. According to RSA algorithm and MSDN documentation it should be: P * Q = Modulus

我生成了一個 512 位 RSA 密鑰對并通過調用將其導出為 XML:

I generated a 512bit RSA keypair and exported it to XML by invoking:

RSACryptoServiceProvider rsa = new RSACryptoServiceProvider(512);
rsa.ToXmlString(true);

這給了我以下 XML:

This gave me the following XML:

<RSAKeyValue>
  <Modulus>rcLI1XTfmXtX05zq67d1wujnUvevBu8dZ5Q5uBUi2mKndH1FZLYCKrjFaDTB/mXW1l5C74YycVLS6msY2NNJYw==</Modulus>
  <Exponent>AQAB</Exponent>
  <P>1dwGkK5POlcGCjQ96Se5NSPu/hCm8F5EYwyqRpLVzgk=</P>
  <Q>0AAEMHBj7CP2XHfCG/RzGldw1GdsW13rTo3uEE9Dtws=</Q>
  <DP>PO4jMLV4/TYuElowCW235twGC3zTE0jIUzAYk2LiZ4E=</DP>
  <DQ>ELJ/o5fSHanBZCjk9zOHbezpDNQEmc0PT64LF1oVmIM=</DQ>
  <InverseQ>NyCDwTra3LiUin05ZCGkdKLwReFC9L8Zf01ZfYabSfQ=</InverseQ>
  <D>EWwFTPmx7aajULFcEJRNd2R4xSXWY8CX1ynSe7WK0BCH42wf/REOS9l8Oiyjf587BhGa3y8jGKhUD7fXANDxcQ==</D>
</RSAKeyValue>

現在我成功編寫了一個小測試程序來加密、解密、簽名和驗證數據.

Now I successfully wrote a litte test programm to encrypt, decrypt, sign and verify data.

最后我加了一點測試代碼:

At the end I added a little test code:

RSACryptoServiceProvider rsa = new RSACryptoServiceProvider(512);
rsa.FromXmlString(key); // key = string with XML above

RSAParameters param = rsa.ExportParameters(true);
BigInteger p = new BigInteger(param.P);
BigInteger q = new BigInteger(param.Q);
BigInteger n = new BigInteger(param.Modulus);
BigInteger myN = BigInteger.Multiply(p, q);
Console.WriteLine("n   = " + n.ToString());
Console.WriteLine("myN = " + myN.ToString());

這給了我們以下輸出:

<代碼> N = 5200154866521200075264779234483365112866265806746380532891861717388028374942014660490111623133775661411009378522295439774347383363048751390839618325234349MYN = 23508802329434377088477386089844302414021121047189424894399694701810500376591071843028984420422297770783276119852460021668188142735325512873796040092944

為什么 P 和 Q 相乘不等于模數?

Why does multiplying P and Q not equal the Modulus?

我已經檢查了很多東西，比如字節序、編碼、BigInteger 類，使用上述 XML 密鑰成功加密、解密、簽名、驗證，但找不到任何解釋為什么 P 和 Q 相乘不等于模數...

I already checked a lot of things like endian, encoding, BigInteger class, successfully encrypted, decrypted, signed, verified with the above XML keys but cannot find any explanation why P and Q multiplied is not equaling the Modulus...

誰能幫我解釋一下為什么 P*Q 不是模數?

Can anybody help me explain why P*Q is not the Modulus ?

可讀格式的所有值:

<代碼>模量= 5200154866521200075264779234483365112866265806746380532891861717388028374942014660490111623133775661411009378522295439774347383363048751390839618325234349指數 = 65537P = 4436260148159638728185416185189716006279182659244174640493183003717504785621Q = 5299238895894527538601438806093945941831432623367272568173893997325464109264DP = -57260184070162652127728137041376572684067529466727954512100856352006444159428DQ = -56270397953566513533764063103154348713259844205844432469862161942601135050224逆Q = -5297700950752995201824767053303055736360972826004414985336436365496709603273d = 5967761894604968266284398550464653556930604493620355473531132912985865955601309375321441883258487907574824598936524238049397825498463180877735939967118353

更新:

根據答案，我為 .Net BigInteger 類編寫了一個小擴展方法，以便與 RSAParameters 一起正常工作:

According to the answer I wrote a little extension method for the .Net BigInteger class to work correctly with the RSAParameters:

public static class BigIntegerExtension
{
    public static BigInteger FromBase64(this BigInteger i, string base64)
    {
        byte[] p = Convert.FromBase64String(base64).Reverse().ToArray();
        if (p[p.Length - 1] > 127)
        {
            Array.Resize(ref p, p.Length + 1);
            p[p.Length - 1] = 0;
        }
       return new BigInteger(p);
    }

    public static BigInteger FromBigEndian(this BigInteger i, byte[] p)
    {
        p = p.Reverse().ToArray();
        if (p[p.Length - 1] > 127)
        {
            Array.Resize(ref p, p.Length + 1);
            p[p.Length - 1] = 0;
        }
        return new BigInteger(p);
    }
}

使用示例:

BigInteger modulus1 = new BigInteger().FromBase64("rcLI1XTfmXtX05zq67d1wujnUvevBu8dZ5Q5uBUi2mKndH1FZLYCKrjFaDTB/mXW1l5C74YycVLS6msY2NNJYw==");

BigInteger modulus2 = new BigInteger().FromBigEndian(param.Modulus);

希望這可以幫助其他有同樣問題的人:-)

Hope this helps others with the same problem :-)

推薦答案

這是我對你提供的 XML 參數的解析:

Here is my parsing of the XML parameters you provided:

<代碼> N = 9100595563660672087698322262735024483609782000266155222822537546670463733453350686171384417480667378838400923087358115007100900745853538273602044437940579P = 96731388413554317303099785843734797692955743043844132225634400270674214374921Q = 94081101418218318334927154927633016498744568046568114230258529096538660255499

如您所見，N 確實等于 P * Q.

As you can verify, N does indeed equal P * Q.

您不能像現在這樣使用 BigInteger(byte []) 構造函數，因為它期望字節數組采用小端序，并且因為 Microsoft 已經做了一些事情來表示贊同.相反，顛倒字節的順序.最后，因為字節數組應該是二進制補碼并且您的數字保證為正數，您必須在數組的高位字節中添加一個零字節 if 否則高位字節將大于或等于 128.

You cannot use the BigInteger(byte []) constructor the way you are because it expects the byte array to be in little-endian, and because Microsoft has done things bass ackwards. Instead, reverse the order of the bytes. And finally, because the bytes arrays are supposed to be twos complement and your numbers are guaranteed to be positive you must add a zero byte to the high order byte of the array if the high-order byte would otherwise be greater than or equal to 128.

這篇關于為什么RSAParameters Modulus不等于P和Q的乘積?的文章就介紹到這了，希望我們推薦的答案對大家有所幫助，也希望大家多多支持html5模板網！