Simulation-Secure Threshold PKE from LWE with Polynomial Modulus

Simulation-Secure Threshold PKE from LWE with Polynomial Modulus

2024-08-29 | Daniele Micciancio and Adam Suhl
This paper presents the first construction of simulation-secure lattice-based threshold PKE (public key encryption) with a polynomially bounded modulus. The construction is based on the hardness of the Learning With Errors (LWE) problem and uses an improved analysis that allows for very small flooding noise, which is crucial for efficiency. The key contributions include: 1. **Simulation Security**: The scheme achieves a strong notion of simulation security, which is relevant for threshold cryptography in MPC ( Multi-Party Computation) applications. 2. **Polynomial Modulus**: The modulus used in the scheme is polynomially bounded, which is more efficient than previous schemes that required superpolynomially large moduli. 3. **Efficiency**: The parameters of the scheme are comparable to those of highly optimized non-threshold schemes like FrodoKEM, making it practical for real-world applications. The paper also provides a detailed analysis of the security of the scheme, showing that it remains secure even when some types of leakage are present. This is achieved by proving that the LWE problem remains hard in the presence of certain types of leakage, such as Gaussian noise. The techniques used in the analysis are applicable to a broad range of lattice-based encryption schemes and may have broader implications in the field of cryptography.This paper presents the first construction of simulation-secure lattice-based threshold PKE (public key encryption) with a polynomially bounded modulus. The construction is based on the hardness of the Learning With Errors (LWE) problem and uses an improved analysis that allows for very small flooding noise, which is crucial for efficiency. The key contributions include: 1. **Simulation Security**: The scheme achieves a strong notion of simulation security, which is relevant for threshold cryptography in MPC ( Multi-Party Computation) applications. 2. **Polynomial Modulus**: The modulus used in the scheme is polynomially bounded, which is more efficient than previous schemes that required superpolynomially large moduli. 3. **Efficiency**: The parameters of the scheme are comparable to those of highly optimized non-threshold schemes like FrodoKEM, making it practical for real-world applications. The paper also provides a detailed analysis of the security of the scheme, showing that it remains secure even when some types of leakage are present. This is achieved by proving that the LWE problem remains hard in the presence of certain types of leakage, such as Gaussian noise. The techniques used in the analysis are applicable to a broad range of lattice-based encryption schemes and may have broader implications in the field of cryptography.
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