LOL: a highly flexible framework for designing stream ciphers

In this paper, we propose LOL, a general framework for designing blockwise stream ciphers. The proposed framework achieves ultrafast software implementations for ubiquitous virtual networks in 5G/6G environments and high-security levels for post-quantum cryptography. The LOL framework is structurally strong; furthermore, this framework and all its components enjoy high flexibility with various extensions. On the basis of the LOL framework, we propose new stream-cipher designs called LOL-MINI and LOL-DOUBLE with the support of the AES-NI and single instruction multiple data instructions. The former applies the basic LOL single mode, while the latter uses the extended parallel-dual mode. LOL-MINI and LOL-DOUBLE support 256-bit key length. Our thorough evaluations revealed that these cipher designs have 256-bit security margins against all existing cryptanalysis methods, including differential, linear, and integral. The software performances of LOL-MINI and LOL-DOUBLE can reach 89 and 135 Gbps. In addition to pure encryptions, the LOL-MINI and LOL-DOUBLE stream ciphers can be applied in a stream-cipher-then-MAC strategy to make AEAD schemes.