Dingding Jia

Chosen ciphertext secure encryption under factoring assumption revisited

In Eurocrypt 2009, Hofheinz and Kiltz proposed a practical chosen ciphertext (CCA) secure public key encryption under factoring assumption based on Rabin trapdoor one-way permutation. We show that when the modulus is special such that ZN* has semi-smooth order, the instantiation of Hofheinz-Kiltz 09 scheme (HK09) over a much smaller subgroup of quadratic residue group (Semi-smooth Subgroup) is CCA secure as long as this type of modulus is hard to be factored. Since the exponent domain of this instantiation is much smaller than the original one, the efficiency is substantially improved. In addition, we show how to construct a practical CCA secure encryption scheme from ElGamal trapdoor one-way function under factoring assumption.When instantiated over Semi-smooth Subgroup, this scheme has even better decryption efficiency than HK09 instantiation.

Efficient Lossy Trapdoor Functions Based on Subgroup Membership Assumptions

We propose a generic construction of lossy trapdoor function from the subgroup membership assumption. We present three concrete constructions based on the k-DCR assumption over

RKA Secure PKE Based on the DDH and HR Assumptions

\mathbb{Z}^*_{N^2}

KDM-CCA Security from RKA Secure Authenticated Encryption

, the extended p-subgroup assumption over

Related-Key Security for Hybrid Encryption

\mathbb{Z}^*_{N^2}

Related Key Secure PKE from Hash Proof Systems

, and the decisional RSA subgroup membership assumption over

Constructions Secure Against Receiver Selective Opening and Chosen Ciphertext Attacks

\mathbb{Z}^*_{N}

Efficient CCA-secure CDH based KEM balanced between ciphertext and key

. Our constructions are more efficient than the previous construction from the DCR assumption over

Receiver Selective Opening Security from Indistinguishability Obfuscation

\mathbb{Z}^*_{N^{s}}

(Deterministic) Hierarchical Identity-based Encryption from Learning with Rounding over Small Modulus

(s ≤ 3).