Ring-LWR-based quantum-resistant signature method and system thereof
According to an embodiment of the present disclosure, a ring-learning with rounding (LWR)-based quantum-resistant signature method includes: 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 including 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.
1. 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 a degree n of a leading term of the cyclotomic equation is a product of a power of 2 and a power of 3.
2. The ring-LWR-based quantum-resistant signature method of claim 1 , 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.
3. The ring-LWR-based quantum-resistant signature method of claim 1 , 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.
4. 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.
5. 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.
6. The ring-LWR-based quantum-resistant signature method of claim 5 , 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.
7. 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.