Scloud+: An Efficient LWE-Based KEM Without Ring/Module Structure

Abstract. We present Scloud+, an LWE-based key encapsulation mechanism (KEM). The key feature of Scloud+ is its use of the unstructured-LWE problem (i.e., without algebraic structures such as rings or modules) and its incorporation of ternary secrets and lattice coding to enhance performance. A notable advantage of the unstructured-LWE problem is its resistance to potential attacks exploiting algebraic structures, making it a conservative choice for constructing high-security schemes. However, a key disadvantage of such schemes is their limited computational and communication efficiency. Scloud+ utilizes ternary secrets and $\text{BW}_{32}$ lattice codes to enhance noise control and ensure robust error correction during decryption, enabling smaller parameters while maintaining low decryption failure probabilities. Equipped with these techniques, Scloud+ exhibits a significant improvement in efficiency. When compared with FrodoKEM for parameter sets targeting 128, 192, and 256 bits of security respectively, Scloud+ achieves practical performance with a public key size approximately $0.71 \sim 0.87$x and a ciphertext size approximately $0.56 \sim 0.78$x that of FrodoKEM. The encapsulation plus decapsulation time is approximately $0.74 \sim 0.84$x that of FrodoKEM.