Methods and systems for digital message encoding and signing

A non-transitory computer-readable medium storing computer-readable instructions which, when read and executed by at least one processing unit associated with a computing device, cause the processing unit to carry out a method of cryptographic data communication over a network with a remote device, the method comprising that comprises:

• obtaining a set of base data elements;
• generating a first key from (i) the set of base data elements and (ii) a set of first entanglement data elements, the first key comprised of a first public component and a first private component;
• generating a second key from (i) the set of base data elements and (ii) a set of second entanglement data elements, the second key comprised of a second public component and a second private component;
• making the first public component and the second public component accessible to the remote device;
• receiving, from the remote device, a first cipher and a second cipher, the first cipher comprising a result of encoding a digital message using the first public component, the second cipher comprising a result of encoding the digital message using the second public component;
• extracting the digital message based on the first and second ciphers, the first and second private component, and the sets of first and second entanglement data elements;
• and
• storing the digital message in computer memory associated with the computing device such that the computing device and the remote device securely communicate over the network.

A data communication system, comprising:

• a first apparatus associated with a public component and a private component;
• and
• a second apparatus coupled to the first apparatus over a network;
• the first apparatus configured for:
• obtaining a set of base data elements;
• generating a first key from (i) the set of base data elements and (ii) a set of first entanglement data elements, the first key comprised of a first public component and a first private component;
• generating a second key from (i) the set of base data elements and (ii) a set of second entanglement data elements, the second key comprised of a second public component and a second private component;
• and
• releasing the first and second public components, such that the first and second public components are accessible to the second apparatus;
• wherein:
• the second apparatus is configured for:
• obtaining the first and second public components;
• generating a first cipher by encoding a digital message using the first public component;
• generating a second cipher by encoding said digital message using the second public component;
• and
• sending the first and second ciphers over the network towards the first apparatus;
• the first apparatus is further configured for:
• receiving the first cipher and the second cipher from the second apparatus;
• and
• extracting the digital message based on the first and second ciphers, the first and second private component, and the sets of first and second entanglement data elements such that the first and second apparatus perform cryptographic communication over the network.