Recursive cryptography protocol

A cryptographic method to enable encrypted communications between a first communication node (“first node”) and a second communication node (“second node”), the method including:

• establishing an initial version of the first symmetric key matrix between the first node and the second node, wherein the first symmetric key matrix comprises an array of symmetric keys containing a number of symmetric keys equal to a first maximum security level equal to an integer greater than or equal to zero, zero corresponding to one level of security using a single symmetric key, and wherein the first maximum security level is chosen by whichever of the first node or the second node initiates communications between the first node and the second node (“the initiating node”), wherein establishing the first symmetric key matrix includes:
• transmitting by the initiating node to whichever of the first node or the second node is not the initiating node (“the non-initiating node”), the first maximum security level, key encapsulation mechanism information indicating a key encapsulation mechanism chosen by the initiating node, and a public key array obtained by the initiating node using the key encapsulation mechanism;
• receiving from the non-initiating node an encrypted version of an entropy bank array, encrypted using the first symmetric key matrix, concatenated with a ciphertext array obtained using the key encapsulation mechanism, wherein the first symmetric key matrix is obtained by the non-initiating node by using the first maximum security level, the key encapsulation mechanism, and the public key array to obtain an initial matrix, by applying an initial key derivation algorithm to the initial matrix to obtain an intermediate matrix, and by concatenating the intermediate matrix with the entropy bank array,
• wherein the entropy bank array contains a number of entropy banks equal to the first maximum security level plus one, which is also equal to a dimension of the intermediate matrix, resulting in the first symmetric key matrix containing a number of symmetric keys equal to the first maximum security level plus one;
• obtaining the first symmetric key matrix, by the initiating node, by applying the key encapsulation mechanism to the received ciphertext and by decrypting the received encrypted version of the entropy bank;
• and
• communicating information to the non-initiating node using the first symmetric key matrix, wherein the initiating node sequentially applies all of the symmetric keys of the first symmetric key matrix to obtain ciphertext messages that are encrypted to a degree equal to the first maximum security level plus one.