Lore: An LWE-based Key Encapsulation Mechanism with Variable Modulus and CRT Compression

Abstract. We propose Lore, an LWE-based key encapsulation mechanism that supports variable modulus selection and Chinese Remainder Theorem (CRT) compression for improved bandwidth efficiency. Unlike existing LWE-based KEMs that fix the modulus a priori, Lore allows the modulus to be selected adaptively, enabling a trade-off between security and performance. The CRT compression technique reduces the ciphertext size by encoding components modulo different primes and reconstructing via CRT, without affecting security. We present complete parameter sets for multiple security levels and provide a comprehensive security analysis against known attacks. Our results show that Lore achieves smaller ciphertext sizes compared to FrodoKEM and Scloud+ at equivalent security levels, demonstrating the benefits of the variable modulus and CRT compression approach.