Ring-LWR-based quantum-resistant signature method and system thereof

A non-transitory computer-readable medium storing a computer program including instructions that, when executed by a processor, causes a computer to execute the instructions comprising:

• receiving a security parameter, and outputting a signature key and a verification key, via an operation on a ring defined by a cyclotomic equation comprising three terms;
• outputting a signature value based on the output signature key;
• and
• calculating an operation value based on the output verification key and signature value, and verifying a signature based on a result of comparing the output signature value with the calculated operation value,
• wherein a degree n of a leading term of the cyclotomic equation is a product of a power of 2 and a power of 3.

A ring-learning with rounding (LWR)-based quantum-resistant signature method comprising:

• a key generation step of receiving a security parameter, and outputting a signature key and a verification key, via an operation on a ring defined by a cyclotomic equation comprising three terms;
• a signature value output step of outputting a signature value based on the output signature key;
• and
• a signature verification step of calculating an operation value based on the output verification key and signature value, and verifying a signature based on a result of comparing the output signature value with the calculated operation value,
• wherein the signature value output step comprises outputting the signature value, by applying a truncate function of selectively extracting only coefficients of terms selected under a preset condition.

A ring-learning with rounding (LWR)-based quantum-resistant signature method comprising:

• a key generation step of receiving a security parameter, and outputting a signature key and a verification key, via an operation on a ring defined by a cyclotomic equation comprising three terms;
• a signature value output step of outputting a signature value based on the output signature key;
• and
• a signature verification step of calculating an operation value based on the output verification key and signature value, and verifying a signature based on a result of comparing the output signature value with the calculated operation value,
• wherein the signature verification step comprises calculating the operation value, by applying a truncate function of selectively extracting only coefficients of terms selected under a preset condition.