I have an unusual scenario where an RSA key pair is being used to protect the confidentiality of data in transit. The encryption exponent, the decryption exponent and the modulus are all kept secret between the two systems (i.e. there is no "public key"). The decryption exponent is 65537. Appropriate padding for RSA encryption is being used when encrypting.
Does the small decryption exponent create a vulnerability in this case?