Method for forming virtual private network providing virtual private network through sealed key exchange based on post quantum cryptography and system for operating virtual private network performing same

1. A method for forming a virtual private network performed by a server comprising a processor, the method comprising the steps of:

generating, by the processor, a public key and a private key;

transmitting, by the processor, the public key;

receiving, by the processor, a key capsule corresponding to the public key;

generating, by the processor, a verification capsule from the key capsule utilizing the private key;

generating, by the processor, a symmetric key by verifying the verification capsule; and

performing, by the processor, communication over the virtual private network utilizing the symmetric key,

wherein generating the symmetric key by verifying the verification capsule comprises the steps of:

determining, by the processor, whether the verification capsule is the same as the key capsule;

generating, by the processor, a prekey via a key message and a hash of the public key when the verification capsule is the same as the key capsule; and

generating, by the processor, the symmetric key via the key capsule and a hash of the prekey,

wherein generating, by the processor, the public key and the private key comprises the steps of:

defining, by the processor, a key matrix corresponding to a random polynomial ring; and

sampling, by the processor, a first key vector generated by a lattice-based algorithm and a second key vector having a first distance from the first key vector.

2. The method for forming a virtual private network of claim 1 , wherein the key capsule is generated by capsuling a randomly generated key message and a capsule random value generated by hashing the key message using the public key.

3. The method for forming a virtual private network claim 1 , wherein the generating of the verification capsule from the key capsule using the private key comprises the steps of:

extracting, by the processor, a key message by opening the key capsule using the private key;

generating, by the processor, a release random value by hashing the key message; and

generating, by the processor, the verification capsule by sealing the key message and the release random value with the public key.

4. A method for forming a virtual private network performed by a client including a processor, the method comprising the steps of:

receiving, by the processor, a public key;

generating, by the processor, a key message using a random number generator;

generating, by the processor, a key capsule using the key message;

transmitting, by the processor, the key capsule;

generating, by the processor, a symmetric key using the key capsule; and

performing, by the processor, communication over the virtual private network using the symmetric key,

wherein the generating of the symmetric key using the key capsule comprises the steps of:

generating, by the processor, a prekey by hashing the key message and the public key;

generating, by the processor, a key hash value by hashing the prekey and the key capsule; and

generating, by the processor, the key hash value as the symmetric key,

wherein the public key is generated using a key matrix corresponding to a random polynomial ring, a first key vector sampled corresponding to a lattice, and a second key vector having a first distance from the first key vector on the lattice.

5. The method for forming a virtual private network of claim 4 , wherein the generating of the key capsule using the key message comprises the steps of:

generating, by the processor, a sealing random value by hashing the key message; and

generating, by the processor, the key capsule by capsuling the key message and the capsule random value using the public key.