Zvika Brakerski presents a new tensoring technique for LWE-based fully homomorphic encryption, which reduces the noise growth from quadratic to linear. This technique allows the construction of a *scale-invariant* fully homomorphic encryption scheme, where the properties only depend on the ratio between the modulus \( q \) and the initial noise level \( B \), not their absolute values. The scheme has several advantages over previous candidates, including no need for modulus switching, flexibility in choosing the modulus, and classical reduction from the worst-case hardness of the GapSVP problem. The paper also discusses the implications and optimizations of the scheme, including its application to fully homomorphic encryption using bootstrapping and without bootstrapping, as well as potential improvements in implementation.Zvika Brakerski presents a new tensoring technique for LWE-based fully homomorphic encryption, which reduces the noise growth from quadratic to linear. This technique allows the construction of a *scale-invariant* fully homomorphic encryption scheme, where the properties only depend on the ratio between the modulus \( q \) and the initial noise level \( B \), not their absolute values. The scheme has several advantages over previous candidates, including no need for modulus switching, flexibility in choosing the modulus, and classical reduction from the worst-case hardness of the GapSVP problem. The paper also discusses the implications and optimizations of the scheme, including its application to fully homomorphic encryption using bootstrapping and without bootstrapping, as well as potential improvements in implementation.