Nostalgia Cipher: Can Filtered LFSRs Be Secure Again? An Application to Hybrid Homomorphic Encryption with Sub-50 ms Latency

Linear Feedback Shift Registers (LFSRs) combined with non linear filtering functions have long been a fundamental design for stream ciphers, offering a wellunderstood structure that remains easy to analyze. However, the introduction of algebraic attacks in 2003 shifted the focus toward more complex designs, as filtered LFSRs required larger registers to maintain security. While this was seen as a drawback at the time, it is no longer a limiting factor, and emerging cryptographic applications benefit from specialized designs—challenges that filtered LFSRs can effectively address. In this work, we propose a new filtered LFSR design, called Nostalgia, tailored for Hybrid Homomorphic Encryption (HHE). We use a weightwise quadratic function as filtering function, leveraging its efficiency in the HHE setting while ensuring security against classical attacks. We also discuss the parameter selection of our design and demonstrate its efficiency in this setting by providing a proof-of-concept implementation. In terms of latency, our HHE solution outperforms current state-of-the-art for TFHE-based HHE (Baudrin et al., Crypto 2025) by a factor of 6.1 times. By revisiting filtered LFSRs in light of modern security requirements, we aim to renew interest in their potential applications and stimulate further cryptanalysis efforts.