Signature generation and verification system

A signature generator comprising:

• a memory;
• and
• a processor in communication with the memory, the processor comprising a random number generator configured to generate a random number, a message encoder, a raw signature generator, a final signature generator, and a cloaking element generator, wherein the processor is configured to:
• receive a message;
• process, by the cloaking element generator, a group, a private key that is an element of the group, and a homomorphism to produce a cloaking element that is an element of the group and that acts as a stabilizer, thereby satisfying a predetermined cloaking equation;
• process, by the message encoder, the private key and the message to produce an encoded message;
• process, by the raw signature generator, the cloaking element, the private key, and the encoded message to produce a raw signature;
• process, by the final signature generator, the raw signature and the message to produce the final cloaked signature, the processing including applying the cloaking element to at least the message to transform the message into a final cloaked signature, the applying including applying the cloaking element to the encoded message, the final cloaked signature providing verification of the signature generator as an origin of the message;
• and
• send the final cloaked signature to a receiver.

A method to generate a verification result for a signature, the method comprising:

• receiving, by a processor, a final signature that includes a cloaked signature and a message from a purported message origin;
• processing, by a message encoder of the processor, a group and the message to produce an encoded message;
• processing, by an encoded message image generator of the processor, the encoded message to produce an ordered pair of elements of the group, wherein the ordered pair takes the same structure as a public key;
• processing, by a signature verifier of the processor, the public key and the cloaked signature to produce a first computation;
• processing, by the signature verifier of the processor, the ordered pair and the public key to produce a second computation;
• and
• comparing, by the processor, the first and second computation to generate the verification result, wherein:
• the verification result indicates that the final signature was produced by the purported message origin in response to the comparing indicating that the first and second computations are equal, and
• the verification result indicates that the final signature was not produced by the purported message origin in response to the comparing indicating that the first and second computations are not equal.