使用RSA的Visa测试卡解密错误

Question

I am working on developing an application for a smart card reader, using the Visa test kit in the C language. On reading card number 2, am getting the following Issuer Public Key Certificate after reading the card:

uint8_t ISSUER_PK_CERTIFICATE[] = {41 03 b1 61 f7 dd 14 34 85 79 1b f6 01 04 ea 10 08 06 9d 16 b6 c3 b3 5b 4e 37 ed 20 25 66 d8 77 6f 48 02 28 32 0a 90 31 ae 28 28 75 fa 1b 3a bf c7 6d 15 6f f4 b5 08 4a fd 9c b0 ef b0 8a 8e 5b 41 fa be 99 3b 04 fe 1b 76 8d ef b6 eb ae d1 77 4d d0 5e 7f f7 0c 45 86 42 85 e6 d0 06 2d 86 65 4e 7a 88 5f 49 f9 f3 11 9f 24 35 18 4c 28 1c 14 93 d2 ac 69 ec c7 88 da c0 75 9a 73 ec d5 f0 28 b3 27 a1 e5 1d c5 cb 43 53 7b 1d 2a a7 04 62 cd a3 c8 74 a5 7c 45 8e 52 15 09 ff 98 73 71 d6 da 8d 7a 4f f5 6f 10 87 89 68 86 33 17 1e f1 d6 9d},

...(ignoring the specifics of formatting in C arrays) where the modulus is 176 and from Visa, I have the following CA Public Key Modulus. The cards are test cards, thus I have no problem sharing the output publicly:

uint8_t VISA_PK_MODULUS[] = {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},

also ignoring the formatting (I have written it like that here for simplicity), where the modulus is also 176. The CA Public Key index is 5 and the exponent is 3, that's how I retrieved the above key. Now, I have written the following function to implement the RSA decryption algorithm to be able to verify the signature of the certificate:

uint32_t buffer[ISSUER_PK_CERTIFICATE_LENGTH]; //this holds the "decrypted" data

void decryptCertificate(uint8_t exponent)
{
    uint32_t buffer[ISSUER_PK_CERTIFICATE_LENGTH]; //the length is in hex

    for(int i = 0; i < hexToDecimal(ISSUER_PK_CERTIFICATE_LENGTH); i++) //conversion to integer for my convenience
    {
        uint32_t powered = pow(ISSUER_PK_CERTIFICATE[i], exponent);
        uint32_t remainder = powered / VISA_PK_MODULUS[i];
        uint32_t multiplied = remainder * VISA_PK_MODULUS[i];
        uint32_t original = powered - multiplied;

        buffer[i] = original;
    }
}

but the final "decrypted" array does not fit the requirements of the Validation test specified by VISA. Anyone see where I could have gone wrong in the implementation of the above algorithm or can someone point me in the right direction if I have gone wrong? the output of the decryption is as shown:

8f  1b  94  1f  2d  3d  23  00  8b  40  be  00  01  40  06  d0  24  0c  2e  2e  5c  03  35  16  82  7d  5c  08  7b  94  67  4b  0b  84  02  00  8a  14  01  c9  20  9e  98  5d  1c  63  8c  08  43  35  27  14  0c  3d  86  94  61  81  4c  27  3a  48  d0  31  05  01  20  3f  b3  40  a1  77  1b  4b  ef  5b  ab  60  36  38  31  1c  18  01  3d  01  45  e0  43  13  6e  43  d8  4e  6e  29  7a  08  70  41  48  27  37  11  28  00  32  5a  0a  10  34  3e  00  00  0d  49  b0  c7  36  08  30  4d  00  1b  08  99  00  11  b3  27  3d  19  01  35  0c  03  07  2a  5e  ed  2f  40  20  8d  02  39  2f  45  13  bd  0d  10  2d  09  41  08  25  08  58  00  01  2c  51  05  06  07  13  a1  cc  0a  1b  88  00  01  04  97

NB: The Visa Specification states the Recovery function as: X = Recover(P _K )[S] = S ^e mod n, given a digital Signature S and public key P _K

Answer 1

It appears that you're trying to perform RSA decryption on each byte individually. This is incorrect — the certificate and modulus arrays each represent a single big integer. You will need to use a big-integer math library (or a special-purpose crypto library) to perform this decryption.

Answer 2

As a general comment OpenSSL may be a good fit for you. If its overhead or library size is too large for the card reader, there are other libraries specifically designed for embedded device environments. Check out the crypto library modules on the wiki ( Crypto Libraries ) and among them CyaSSL, MatrixSSL, PolarSSL, and SharkSSL are known to be for embedded devices.