The existing LWE-based dual-mode scheme could not fit the framework of dual-mode cryptosystem very well. In this paper, we give two solutions of constructing "full-fledged" dual-mode cryptosystems based on LWE. In our first construction, we give a modified "dual version" of Peikert et al.'s (Crypto'08) construction, in which the simulated public keys can be uniformly and randomly chosen just like the real ones, thus it can fit the framework of dual-mode cryptosystem very well. Then, our second construction gets rid of the lattice trapdoor, which is known as lacking of efficiency and is used in our first construction as well as Peikert et al.'s construction.

Based on the learning with errors (LWE) problem, we construct an identity-based encryption (IBE) scheme in the standard-model which is secure against the key dependent message (KDM) attacks and the selective opening (SO) attacks. KDM security, which requires that the scheme can still obtain secrecy even if the messages depend on the secret key, is necessary for IBE when updating the identity secret keys with the old ones. SO security, which requires that when the adversary corrupts some fraction of senders, the uncorrupted senders' messages still maintain privacy, is useful for IBE since that one user receives messages from many senders is a natural scenario. Although there is a KDM secure IBE scheme based on LWE constructed by Alperin-Sheriff and Peikert (PKC'12), and a SO secure IBE scheme based on LWE constructed by He et al. (IWSEC'15), those two schemes cannot achieve both of the security requirements at the same time. In this paper, first, we propose a new transformation which is a new variant of LWE assumption. Then, we prove that a dual-style public key encryption (PKE) scheme of the LWE based PKE of Gentry et al. (STOC'08) is KDM secure with the help of our transformation. At last, based on the PKE scheme, we construct an IBE scheme in the standard model that is both KDM and SO secure.

Leakage-resilient cryptography requires that a crypto-system remain provably secure even if the attacker gets additional information about the internal states, which is usually the secret key in the scenario of public key encryption.

We introduce the notion of approximate-deterministic public key encryption (A-DPKE), which extends the notion of deterministic public key encryption (DPKE) by allowing the encryption algorithm to be “slightly” randomized. However, a ciphertext convergence property is required for A-DPKE such that the ciphertexts of a message are gathering in a small metric space, while ciphertexts of different messages can be distinguished easily. Thus, A-DPKE maintains the convenience of DPKE in fast search and de-duplication on encrypted data, and encompasses new constructions. We present two simple constructions of A-DPKE, respectively from the learning parity with noise and the learning with errors assumptions.

In this paper, we define a new security property called "instance-non-malleability" for the Instance-dependent commitment (IDC). Our definition can be consistent with the definition of non-malleability for zero-knowledge proofs, which was not the case for previous definitions of non-malleability for commitments. Our definition of instance-non-malleable instance-dependent commitment requires the non-malleability of the instances as well as the committed messages. We also present a DDH-based IDC scheme, which satisfies previous definitions of non-malleability but not our definition of instance-non-malleable IDC, to show that instance-non-malleability is a stronger notion. Finally, we modify our DDH-based construction to satisfy our definition of instance-non-malleable IDC. The security of our construction is proved in the random oracle model.

An instance-dependent commitment (IDC) scheme takes an instance in a promise problem as public input at each time of committing and separately achieves statistical hiding and statistical binding when the instance is from different subsets of the promise. In this paper, we define a new security property called “instance-non-malleability ” for the IDC. It requires the non-malleability of the instances as well as the committed messages. Instance-non-malleability is not only stronger than previous definitions of non-malleability for commitments, but can be achieved in the standard model as well. We also present a general construction of the non-interactive instance-non-malleable IDC.

The idea of Zero-Knowledge Sets (ZKS) was firstly proposed by Micali, Rabin and Kilian. It allows the prover to commit to a secret set and then prove either " x ∈ S" or "x ∉ S " without revealing any more knowledge of the set S. Afterwards, R.Gennaro defined the concept of independence for ZKS and gave two tree-based constructions. In this paper, we define the independence property for ZKS in a more flexible way than the definition of Gennaro's and prove that for ZKS, our independence implies non-malleability and vice versa. Then an independent ZKS scheme is constructed in an algebraic way by mapping values to unique primes, accumulating the set members and hiding the set. Comparing with the tree-based constructions: our scheme is more efficient while proving a value belongs (resp. not belongs) to the committed set; furthermore, the committed set is easier to update.