A Practical Adaptive Key Recovery Attack on the LGM (GSW-like) Cryptosystem
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Original versionIn: Cheon, J.H., Tillich, JP. (eds) Post-Quantum Cryptography. PQCrypto 2021 2021. Lecture Notes in Computer Science(), vol 12841, 483-498.. https://doi.org/10.1007/978-3-030-81293-5_25
We present an adaptive key recovery attack on the leveled homomorphic encryption scheme suggested by Li, Galbraith and Ma (Provsec 2016), which itself is a modification of the GSW cryptosystem designed to resist key recovery attacks by using a different linear combination of secret keys for each decryption. We were able to efficiently recover the secret key for a realistic choice of parameters using a statistical attack. In particular, this means that the Li, Galbraith and Ma strategy does not prevent adaptive key recovery attacks.