Empirical Profiling of Noise Growth in the BGV Scheme using Lattigo v6

This paper presents an empirical study on how noise grows in the Brakerski-Gentry- Vaikuntanathan (BGV) homomorphic encryption scheme using the Go-based Lattigo v6 library. To bridge the gap between worst-case theoretical bounds and practical behavior in a Residue Number System (RNS) implementation, noise evolution is studied across ring degrees ranging from N=4096 to N=32768. The results indicate that ciphertext multiplication combined with relinearization is the largest contributor to noise amplification, consuming approximately 29.5 bits of the available noise budget per operation, whereas addition consumes exactly one bit. Furthermore, this study supports the critical role of modulus switching in maintaining a sufficient noise margin. Based on these observations, a library-specific design heuristic is proposed: allocating approximately 30 bits of modulus capacity per multiplicative level. This provides a concrete reference point for engineering decisions.