Method for multiplying polynomials for a cryptographic operation

A data processing system comprising instructions embodied in a non-transitory computer readable medium, the instructions for multiplying a first and a second polynomial in the ring [X]/(XN−1) and performing a cryptographic operation using a hardware processor, the instructions executed by the hardware processor, comprising:

• instructions for receiving the first polynomial and the second polynomial by the processor;
• instructions for mapping the first polynomial into a third polynomial in a first ring and a fourth polynomial in a second ring using a map;
• instructions for mapping the second polynomial into a fifth polynomial in the first ring and a sixth polynomial in the second ring using the map;
• instructions for multiplying the third polynomial in the first ring with the fifth polynomial in the first ring to produce a first multiplication result;
• instructions for multiplying the fourth polynomial in the second ring with the sixth polynomial in the second ring to produce a second multiplication result using Renes multiplication;
• instructions for combining the first multiplication result and the second multiplication result using the map,
• wherein the first ring is [X]/(XN/2−1), and
• wherein the second ring is [X]/(XN/2+1),
• instructions for performing a post-quantum cryptography operation using the hardware processor including executing a verification, encryption, or decryption operation using the multiplication of the first polynomial and the second polynomial with integer coefficients.