How to find out the modulus and exponent of RSA Public Key on iPhone/Objective C

Question

Is there a possible way to find out the modulus and exponent of the Public Key, created with SecKeyGeneratePair (the Security Framework in general)?

Answer 1

Busted my head on this, but here's a solution I've found (without using any external packages).

First, go to Apple's CryptoExercise example. Download the "SecKeyWrapper" class from there. The interesting function in that class is getPublicKeyBits.

Link to the example: http://developer.apple.com/library/ios/#samplecode/CryptoExercise/Introduction/Intro.html

The bits you will receive is a DER encoded (wiki it) public key containing both the modulus and exp. Here's a code that will decode it for you, pretty easy:

- (NSData *)getPublicKeyExp
{
    NSData* pk = [self getPublicKeyBits];
    if (pk == NULL) return NULL;

    int iterator = 0;

    iterator++; // TYPE - bit stream - mod + exp
    [self derEncodingGetSizeFrom:pk at:&iterator]; // Total size

    iterator++; // TYPE - bit stream mod
    int mod_size = [self derEncodingGetSizeFrom:pk at:&iterator];
    iterator += mod_size;

    iterator++; // TYPE - bit stream exp
    int exp_size = [self derEncodingGetSizeFrom:pk at:&iterator];

    return [pk subdataWithRange:NSMakeRange(iterator, exp_size)];
}

- (NSData *)getPublicKeyMod
{
    NSData* pk = [self getPublicKeyBits];
    if (pk == NULL) return NULL;

    int iterator = 0;

    iterator++; // TYPE - bit stream - mod + exp
    [self derEncodingGetSizeFrom:pk at:&iterator]; // Total size

    iterator++; // TYPE - bit stream mod
    int mod_size = [self derEncodingGetSizeFrom:pk at:&iterator];

    return [pk subdataWithRange:NSMakeRange(iterator, mod_size)];
}

- (int)derEncodingGetSizeFrom:(NSData*)buf at:(int*)iterator
{
    const uint8_t* data = [buf bytes];
    int itr = *iterator;
    int num_bytes = 1;
    int ret = 0;

    if (data[itr] > 0x80) {
        num_bytes = data[itr] - 0x80;
        itr++;
    }

    for (int i = 0 ; i < num_bytes; i++) ret = (ret * 0x100) + data[itr + i];

    *iterator = itr + num_bytes;
    return ret;
}

Answer 2

I tried this approach and it works fine for extracting the exponent. It is 3 bytes in size as expected but the extracted modulus is not the correct size. The size of the modulus is 129 bytes instead of 128 bytes.

The code is as follows:

- (NSData *)getPublicKeyBits: (NSString*) publicKeyIdentifier {

    OSStatus sanityCheck = noErr;
    NSData * publicKeyBits = nil;
    CFTypeRef pk;
    NSMutableDictionary * queryPublicKey = [[NSMutableDictionary alloc] init];

    NSData* publicTag = [publicKeyIdentifier dataUsingEncoding:NSUTF8StringEncoding];

    // Set the public key query dictionary.
    [queryPublicKey setObject:(__bridge_transfer id)kSecClassKey forKey:(__bridge_transfer id)kSecClass];

    [queryPublicKey setObject:publicTag forKey:(__bridge_transfer id)kSecAttrApplicationTag];
    [queryPublicKey setObject:(__bridge_transfer id)kSecAttrKeyTypeRSA forKey:(__bridge_transfer id)kSecAttrKeyType];
    [queryPublicKey setObject:[NSNumber numberWithBool:YES] forKey:(__bridge_transfer id)kSecReturnData];

    // Get the key bits.
    sanityCheck = SecItemCopyMatching((__bridge_retained CFDictionaryRef)queryPublicKey, &pk);
    if (sanityCheck != noErr)
    {
        publicKeyBits = nil;
    }
    publicKeyBits = (__bridge_transfer NSData*)pk;
    //NSLog(@"public bits %@",publicKeyBits);

    return publicKeyBits;
}


- (NSData *)getPublicKeyExp
{
    NSData* pk = [self getPublicKeyBits:@"RSA Public Key"];
    if (pk == NULL) return NULL;

    int iterator = 0;

    iterator++; // TYPE - bit stream - mod + exp
    [self derEncodingGetSizeFrom:pk at:&iterator]; // Total size

    iterator++; // TYPE - bit stream mod
    int mod_size = [self derEncodingGetSizeFrom:pk at:&iterator];
    iterator += mod_size;

    iterator++; // TYPE - bit stream exp
    int exp_size = [self derEncodingGetSizeFrom:pk at:&iterator];

    return [pk subdataWithRange:NSMakeRange(iterator, exp_size)];
    return pk;
}


- (NSData *)getPublicKeyMod
{
    NSData* pk = [self getPublicKeyBits:@"RSA Public Key"];
    if (pk == NULL) return NULL;

    int iterator = 0;

    iterator++; // TYPE - bit stream - mod + exp
    [self derEncodingGetSizeFrom:pk at:&iterator]; // Total size

    iterator++; // TYPE - bit stream mod
    int mod_size = [self derEncodingGetSizeFrom:pk at:&iterator];

    return [pk subdataWithRange:NSMakeRange(iterator, mod_size)];
    return pk;
    NSLog(@"public size: %d",pk.length);
}

- (int)derEncodingGetSizeFrom:(NSData*)buf at:(int*)iterator
{
    const uint8_t* data = [buf bytes];
    int itr = *iterator;
    int num_bytes = 1;
    int ret = 0;

    if (data[itr] > 0x80) {
        num_bytes = data[itr] - 0x80;
        itr++;
    }

    for (int i = 0 ; i < num_bytes; i++) 
        ret = (ret * 0x100) + data[itr + i];

    *iterator = itr + num_bytes;
    return ret;
}

Answer 3

Something like the following is much more reliable:

+ (NSInteger)keyModulusSize:(NSData *)keyData
{
    NSString *randomTag = [NSString ptk_randomStringOfLength:32];
    SecKeyRef key = [self addPublicKeyRef:keyData withTag:randomTag];

    NSInteger size = 0;
    if (key) {
        size = SecKeyGetBlockSize(key);
        [self removePublicKeyRef:randomTag];
    }

    return size;
}

Answer 4

I removed that extra byte at the beginning, now it works fine. In my case it was always extracting 129 bytes modulus.

- (NSData *)getPublicKeyModFromKeyData:(NSData*)pk
{
if (pk == NULL) return NULL;

int iterator = 0;

iterator++; // TYPE - bit stream - mod + exp
[self derEncodingGetSizeFrom:pk at:&iterator]; // Total size

iterator++; // TYPE - bit stream mod
int mod_size = [self derEncodingGetSizeFrom:pk at:&iterator];

// return [pk subdataWithRange:NSMakeRange(iterator, mod_size)];
NSData* subData=[pk subdataWithRange:NSMakeRange(iterator, mod_size)];
return  [subData subdataWithRange:NSMakeRange(1, subData.length-1)];

}