如何使用模数和指数生成公钥？

Question

Hi I am new for developing the ios application. I have a modulus and an exponent and i need to generate SecKey and then use this to encrypt some data (RSA encryption). Please any one help in swift.

Answer 1

You should not implement crypto algorithms or key generation by yourself (not being an expert in cryptography). Where security matters, use mature and well-known libraries and tools.

On iOS it's worth checking out SecKey API ( SecKeyEncrypt(_:_:_:_:_:_:) and so on). It was mentioned at WWDC 2016 Session 706 starting at 16:10 .

You may find useful investigating the CryptoCompatibility example project which "shows common cryptographic operations using Apple APIs."

As a cross-platform solution you can use OpenSSL which also provides RSA API .

Answer 2

A few similar questions have been asked/answered already, here's one where you can take a modulus and exponent and get a .PEM format out of it: Generate RSA Public Key from Modulus and Exponent

Here's another, although this one uses OpenSSL: https://stackoverflow.com/a/31010530/209855

Additionally, you've probably run into some people recommending https://github.com/StCredZero/SCZ-BasicEncodingRules-iOS like here https://stackoverflow.com/a/10643894/209855

But if you're like me, nothing actually worked or gave you exactly what you wanted.

If you read through the issues on that github repo, you'll find something broke around iOS 8 and it no longer generates the correct data.

However, someone posted a fix for this: https://github.com/Meniny/Meniny.github.io/blob/5895a2d51502881a7d6cda418beafa546874dfa7/_posts/2017-08-12-RSA_public_key_with_modulus_and_exponent.md I'll reproduce the code here, in case it disappears in the future.

+ (NSData * __nullable)generateRSAPublicKeyWithModulus:(NSData * __nonnull)modulus exponent:(NSData * __nonnull)exponent {
    const uint8_t DEFAULT_EXPONENT[] = {0x01, 0x00, 0x01,}; //default: 65537
    const uint8_t UNSIGNED_FLAG_FOR_BYTE = 0x81;
    const uint8_t UNSIGNED_FLAG_FOR_BYTE2 = 0x82;
    const uint8_t UNSIGNED_FLAG_FOR_BIGNUM = 0x00;
    const uint8_t SEQUENCE_TAG = 0x30;
    const uint8_t INTEGER_TAG = 0x02;

    uint8_t* modulusBytes = (uint8_t*)[modulus bytes];
    uint8_t* exponentBytes = (uint8_t*)(exponent == nil ? DEFAULT_EXPONENT : [exponent bytes]);

    //(1) calculate lengths
    //- length of modulus
    int lenMod = (int)[modulus length];
    if (modulusBytes[0] >= 0x80)
        lenMod ++;  //place for UNSIGNED_FLAG_FOR_BIGNUM
    int lenModHeader = 2 + (lenMod >= 0x80 ? 1 : 0) + (lenMod >= 0x0100 ? 1 : 0);
    //- length of exponent
    int lenExp = exponent == nil ? sizeof(DEFAULT_EXPONENT) : (int)[exponent length];
    int lenExpHeader = 2;
    //- length of body
    int lenBody = lenModHeader + lenMod + lenExpHeader + lenExp;
    //- length of total
    int lenTotal = 2 + (lenBody >= 0x80 ? 1 : 0) + (lenBody >= 0x0100 ? 1 : 0) + lenBody;

    int index = 0;
    uint8_t* byteBuffer = malloc(sizeof(uint8_t) * lenTotal);
    memset(byteBuffer, 0x00, sizeof(uint8_t) * lenTotal);

    //(2) fill up byte buffer
    //- sequence tag
    byteBuffer[index ++] = SEQUENCE_TAG;
    //- total length
    if(lenBody >= 0x80)
        byteBuffer[index ++] = (lenBody >= 0x0100 ? UNSIGNED_FLAG_FOR_BYTE2 : UNSIGNED_FLAG_FOR_BYTE);
    if(lenBody >= 0x0100) {
        byteBuffer[index ++] = (uint8_t)(lenBody / 0x0100);
        byteBuffer[index ++] = lenBody % 0x0100;
    }
    else
        byteBuffer[index ++] = lenBody;
    //- integer tag
    byteBuffer[index ++] = INTEGER_TAG;
    //- modulus length
    if (lenMod >= 0x80)
        byteBuffer[index ++] = (lenMod >= 0x0100 ? UNSIGNED_FLAG_FOR_BYTE2 : UNSIGNED_FLAG_FOR_BYTE);
    if (lenMod >= 0x0100) {
        byteBuffer[index ++] = (int)(lenMod / 0x0100);
        byteBuffer[index ++] = lenMod % 0x0100;
    }
    else
        byteBuffer[index ++] = lenMod;
    //- modulus value
    if (modulusBytes[0] >= 0x80)
        byteBuffer[index ++] = UNSIGNED_FLAG_FOR_BIGNUM;
    memcpy(byteBuffer + index, modulusBytes, sizeof(uint8_t) * [modulus length]);
    index += [modulus length];
    //- exponent length
    byteBuffer[index ++] = INTEGER_TAG;
    byteBuffer[index ++] = lenExp;
    //- exponent value
    memcpy(byteBuffer + index, exponentBytes, sizeof(uint8_t) * lenExp);
    index += lenExp;

    if (index != lenTotal)
        NSLog(@"lengths mismatch: index = %d, lenTotal = %d", index, lenTotal);

    NSMutableData* buffer = [NSMutableData dataWithBytes:byteBuffer length:lenTotal];
    free(byteBuffer);

    return buffer;
}

And last but not least, to generate the RSA Public Key from a Modulus and Exponent in Swift 3:

public func encrypt(_ string: String, modulus: String, exponent: String) -> String? {
  if let modData = Data(base64Encoded: modulus),
    let expData = Data(base64Encoded: exponent),
    let keyData = PublicKeyRSA.generatePublicKey(withModulus: modData, exponent: expData) {
      /// encrypt...
  }
}

Answer 3

PublicKeyRSA.generatePublicKey is returning the data in bytes, not returning the public key. We have to use the public keys to encrypt our data.