Generating Gaussian error in lattice cryptography with quantum random number generator

Abstract

The Gaussian Error, represented by random numbers with a Gaussian distribution, plays a critical role in the security of modern lattice-based cryptography. Lattice-based cryptography is the most important category of post-quantum cryptography capable of resisting attacks from both classical and quantum.While current schemes of generating Gaussian Error used in lattice cryptography face severe challenges. On the one hand, the current scheme produces an approximate Gaussian distribution rather than the rigorously proven Gaussian distribution required in lattice cryptography, posing a security risk. Meanwhile, the Gaussian Error of current schemes is obtained by using algorithms to compute uniformly distributed random numbers, which lack provable randomness and also pose security risks. On the other hand, the generation rate of Gaussian Error is not high enough for many applications of cryptographic systems in current schemes. To address these challenges, this paper proposes a novel scheme that uses a quantum random number generator(QRNG) to generate the Gaussian Error, which follows a theoretically proven Gaussian distribution and satisfies rigorous security justification in lattice cryptography. Furthermore, based on the quantum mechanical process of measuring vacuum fluctuations and the principle of minimum entropy under classical noise conditions, the Gaussian Error obtained by our scheme is theoretically unpredictable, further enhancing the security of lattice cryptography compared to the current schemes. Finally, an experiment for generating Gaussian Error was constructed, and our experimental results demonstrate that the Gaussian Error generation rate is 1 G/s, which achieves higher speed among existing works.