Public key encryption secure against related-key attacks and key-leakage attacks from extractable hash proofs

Public-key encryption (PKE) can be used in cloud system to protect data in data sharing, identity authentication, etc. However, the security model of traditional PKE does not capture the "key-leakage attacks" which can leak partial information about the secret key. Also, the adversary can inject fault to tamper with the secret key and observe the output of the public key encryption scheme under this modified key which is called "related-key attack". In this paper, we present a method to construct public key encryption schemes secure against both weak key-leakage attacks and affine related-key attacks directly from extractable hash proof systems. Specifically, we first add Key Homomorphism and Fingerprinting properties to all-but-one (ABO) extractable hash proofs and construct a key encapsulation mechanism scheme secure against related-key attacks via it and thus public key encryption scheme secure against related-key attacks. Also, we prove that if the based ABO-extractable hash proof with Key Homomorphism and Fingerprinting properties is weak leakage-resilient, then the key encapsulation mechanism scheme constructed from it is weak leakage-resilient and related-key attack secure. Moreover, we propose a public key encryption scheme secure against affine related-key attacks based on lattice.