Calculating K

To calculate our live session token, we need to use modulus division to receive a K value for a HMAC hash.

Begin by pulling the base value, B, which will be our dh_response value from our /live_session_token response, using a leading 0 as a sign bit for the hex string.

We will then need to retrieve a BigInteger value of the dh_response value.

Our exponent value would be equivalent to the same dh_random value used for our /live_session_token request.

Our modulus, p, would be the same as our dh_modulus or dh_prime value from our Diffie-Hellman file.

We would finally calculate K using the formula B^a modulo p.

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# K will be used to hash the prepend bytestring (the decrypted access token) to produce the LST.
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B = int(dh_response, 16)
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a = dh_random
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p = dh_prime
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K = pow(B, a, p)

Once K is receive, convert the integer to its hex string representation before converting it to a byte array. In some cases, the resultant K value will have an odd number of leading characters that should be prepended by an additional 0.

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# Generate hex string representation of integer K.
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hex_str_K = hex(K)[2:]
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# If hex string K has odd number of chars, add a leading 0, because all Python hex bytes must contain two hex digits  (0x01 not 0x1).
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if len(hex_str_K) % 2:
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    print("adding leading 0 for even number of chars")
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    hex_str_K = "0" + hex_str_K
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# Generate hex bytestring from hex string K.
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hex_bytes_K = bytes.fromhex(hex_str_K)
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# Prepend a null byte to hex bytestring K if lacking sign bit.
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if len(bin(K)[2:]) % 8 == 0:
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    hex_bytes_K = bytes(1) + hex_bytes_K