RSA公开指数默认为65537.该值应该是多少？我的选择有什么影响？

Question

我正在为可能遇到不同指数大小的软件创建单元测试。 （see section 3.3.1 of this RFC）

如何使用充气城堡，或任何其他C＃库生成RSA密钥对that doesn't have a key size of 65537.

如果答案是，我可以直接修改这个，只要我更新私钥那么，我应该为公钥和私钥做出什么样的具体变化（或重新计算）呢？

下面是我使用创建的65537指数的关键示例代码：

 // Create key 
     RsaKeyPairGenerator generator = new RsaKeyPairGenerator(); 
     var param = new KeyGenerationParameters(new SecureRandom(), 1024); 
     generator.Init(param); 
     AsymmetricCipherKeyPair keyPair= generator.GenerateKeyPair(); 

     // Save to export format 
     SubjectPublicKeyInfo info = SubjectPublicKeyInfoFactory.CreateSubjectPublicKeyInfo(keyPair.Public); 
     byte[] ret = info.GetEncoded(); 
     string ovalue1 = Convert.ToBase64String(ret); 

     // Read from export format 
     byte[] publicKeyBytes = Convert.FromBase64String(ovalue1); 
     AsymmetricKeyParameter asymmetricKeyParameter = PublicKeyFactory.CreateKey(publicKeyBytes); 

     RsaKeyParameters rsaKeyParameters = (RsaKeyParameters)asymmetricKeyParameter; 
     RSAParameters rsaParameters = new RSAParameters(); 
     rsaParameters.Modulus = rsaKeyParameters.Modulus.ToByteArray(); 
     rsaParameters.Exponent = rsaKeyParameters.Exponent.ToByteArray(); 
     RSACryptoServiceProvider rsa = new RSACryptoServiceProvider(); 
     rsa.ImportParameters(rsaParameters); 

Answer 1

感谢@BrettHale我能解决这个问题。

这是如何在充气城堡创建密钥对，涉及到他的建议使用RSAKeyGenerationParameters

 // Create key 
     RsaKeyPairGenerator generator = new RsaKeyPairGenerator(); 

     /* 
     * This value should be a Fermat number. 0x10001 (F4) is current recommended value. 3 (F1) is known to be safe also. 
     * 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 
     * 
     * Practically speaking, Windows does not tolerate public exponents which do not fit in a 32-bit unsigned integer. Using e=3 or e=65537 works "everywhere". 
     */ 
     BigInteger exponentBigInt = new BigInteger(exponent.ToString()); 

     var param = new RsaKeyGenerationParameters(
      exponentBigInt, // new BigInteger("10001", 16) publicExponent 
      new SecureRandom(), // SecureRandom.getInstance("SHA1PRNG"),//prng 
      keyStrength, //strength 
      certaninty);//certainty 
     generator.Init(param); 

其他环节：包括

• Why is exponent value 65537 used, what are the alternatives and impacts?

• What is certainty, and what is the correct value for this（提示：取决于密钥长度）