A Post-Quantum Computing Cryptographic communication protocol including a lattice based RSA algorithm, the protocol may include: generating a public key and a private key pair; encrypting a message using a public key pair; transmitting the encrypted message over a communication channel; and decrypting the encrypted message using a private key pair, wherein the generating the public key and the private key pair includes; selecting a first random vector from lattices using a Klein's Algorithm; selecting a second random vector from lattices using the Klein's Algorithm; generating a shortest random vector using a Gauss Sieve algorithm; taking a first vector product of the first random vector and the second random vector; calculating a Totient function of the first vector product; converting the Totient function to the first vector product; generating the public key pair; and generating the private key pair.