Saving SecKeyRef device generated public/private key pair on disk

You can use the latest crypto API of iOS, You can save the key as NSData and retrieve the key from NSData

SecKeyRef key = <# a key #>;
CFErrorRef error = NULL;
NSData* keyData = (NSData*)CFBridgingRelease(  // ARC takes ownership
                       SecKeyCopyExternalRepresentation(key, &error)
                   );
if (!keyData) {
    NSError *err = CFBridgingRelease(error);  // ARC takes ownership
    // Handle the error. . .
}

https://developer.apple.com/documentation/security/certificate_key_and_trust_services/keys/storing_keys_as_data?language=objc

Ah, found the answer myself; you can get the bytes for a public key using SecItemCopyMatching().

- (NSData *)getPublicKeyBits {
    OSStatus sanityCheck = noErr;
    NSData * publicKeyBits = nil;

    NSMutableDictionary * queryPublicKey = [[NSMutableDictionary alloc] init];

    // Set the public key query dictionary.
    [queryPublicKey setObject:(id)kSecClassKey forKey:(id)kSecClass];
    [queryPublicKey setObject:publicTag forKey:(id)kSecAttrApplicationTag];
    [queryPublicKey setObject:(id)kSecAttrKeyTypeRSA forKey:(id)kSecAttrKeyType];
    [queryPublicKey setObject:[NSNumber numberWithBool:YES] forKey:(id)kSecReturnData];

    // Get the key bits.
    sanityCheck = SecItemCopyMatching((CFDictionaryRef)queryPublicKey, (CFTypeRef *)&publicKeyBits);

    if (sanityCheck != noErr)
    {
        publicKeyBits = nil;
    }

    [queryPublicKey release];

    return publicKeyBits;
}

The above is from Apple's CryptoExercise. Not sure if it works for private keys though.