Applying the Simple Partial Discard Method to Crystals-Kyber

Abstract

In certain cryptographic applications random numbers are required (e.g., when generating cryptographic keys and generating digital signatures). To obtain these random numbers, the typical approach involves obtaining random bits first and then converting them into random numbers. Several methods to convert a sequence of random bits into a sequence of random numbers are known and some of them are standardized. Recently, ISO/IEC JTC 1/SC 27/WG 2 decided to add two more methods, the simple partial discard method and the complex partial discard method, to the existing four standard methods. Meanwhile, CRYSTALS-Kyber is the only public-key encryption and key-establishment algorithm selected for the post-quantum cryptography standardization project by NIST (National Institute of Standards and Technology). It uses an algorithm called Parse that takes a byte stream as input and outputs a polynomial of degree $d$ with coefficients in $\mathbb {Z}_{q}$ (for some positive integer $d$ and prime $q$ ) using the simple discard method to generate key pairs. In this paper, we apply the simple partial discard method to Parse. We show that using the simple partial discard method instead of the simple discard method can reduce the number of bits required by up to 12%. Furthermore, we show that, in some cases, using the simple partial discard method instead of the simple discard method can experimentally generate a polynomial up to 8% faster.

Keywords

• Conversion methods for random number generation
• CRYSTALS-Kyber
• simple discard method
• simple partial discard method