Two common notions of security for public key encryption schemes are shown to be equivalent: we prove that indistinguishability against chosen-ciphertext attacks (IND-CCA) is in fact polynomially equivalent to (yet “slightly” weaker than) securely realizing the ideal functionality FPKE in the general modeling of cryptographic protocols of [Can01a]. This disproves in particular the claim that security in the sense of IND-CCA strictly implies security in the sense of realizing FPKE (see [Can01a]). Moreover, we give concrete reductions among such security notions and show that these relations hold for both uniform and non-uniform adversarial entities.
Two common notions of security for public key encryption schemes are shown to be equivalent: we prove that indistinguishability against chosen-ciphertext attacks (IND-CCA) is in fact polynomially equivalent to (yet “slightly” weaker than) securely realizing the ideal functionality FPKE in the general modeling of cryptographic protocols of [Can01a]. This disproves in particular the claim that security in the sense of IND-CCA strictly implies security in the sense of realizing FPKE (see [Can01a]). Moreover, we give concrete reductions among such security notions and show that these relations hold for both uniform and non-uniform adversarial entities.
Abstract. We construct a public-key encryption (PKE) scheme whose security is polynomial-time equivalent to the hardness of the Subset Sum problem. Our scheme achieves the standard notion of indistinguishabil-ity against chosen-ciphertext attacks (IND-CCA) and can be used to encrypt messages of arbitrary polynomial length, improving upon a pre-vious construction by Lyubashevsky, Palacio, and Segev (TCC 2010) which achieved only the weaker notion of semantic security (IND-CPA) and whose concrete security decreases with the length of the message being encrypted. At the core of our construction is a trapdoor technique which originates in the work of Micciancio and Peikert (Eurocrypt 2012).
Abstract. Security against adaptive chosen ciphertext attacks (or, CCA security) has been accepted as the standard requirement from encryption schemes that need to withstand active attacks. In particular, it is regarded as the appropriate security notion for encryption schemes used as components within general protocols and applications. Indeed, CCA security was shown to suffice in a large variety of contexts. However, CCA security often appears to be somewhat too strong: there exist encryption schemes (some of which come up naturally in practice) that are not CCA secure, but seem sufficiently secure “for most practical purposes.” We propose a relaxed variant of CCA security, called Replayable CCA (RCCA) security. RCCA security accepts as secure the non-CCA (yet arguably secure) schemes mentioned above; furthermore, it suffices for most existing applications of CCA security. We provide three formulations of RCCA security. The first one follows the spirit of semantic security and is formulated via an ideal functionality in the universally composable security framework. The other two are formulated following the indistinguishability and non-malleability approaches, respectively. We show that the three formulations are equivalent in most interesting cases. 1
Abstract In the era of cloud computing, public key encryption with keyword search (PEKS) is an extremely useful cryptographic tool for searching on encryption data, whose strongest security notion is indistinguishability encryption against chosen ciphertext attack (ind-cca). Adballa et al. presented a transformation from identity based encryption (IBE) to PEKS in the Theory of Cryptography Conference 2010. This paper proposes a new framework of ind-cca secure PEKS in the standard model. Our main technical tool is a newly introduced notion of smooth projective hash function with key mapping, in which the hash key hk is mapped into another mapping projection key mhp besides the classical projection key hp. Finally, we provide an instantiation of our framework based on symmetric eXternal Diffie–Hellman assumption.
Functional encryption (FE) can implement fine-grained control to encrypted plaintext via permitting users to compute only some specified functions on the encrypted plaintext using private keys with respect to those functions. Recently, many FEs were put forward; nonetheless, most of them cannot resist chosen-ciphertext attacks (CCAs), especially for those in the secret-key settings. This changed with the work, i.e., a generic transformation of public-key functional encryption (PK-FE) from chosen-plaintext (CPA) to chosen-ciphertext (CCA), where the underlying schemes are required to have some special properties such as restricted delegation or verifiability features. However, examples for such underlying schemes with these features have not been found so far. Later, a CCA-secure functional encryption from projective hash functions was proposed, but their scheme only applies to inner product functions. To construct such a scheme, some nontrivial techniques will be needed. Our key contribution in this work is to propose CCA-secure functional encryptions in the PKE and SK environment, respectively. In the existing generic transformation from (adaptively) simulation-based CPA- (SIM-CPA-) secure ones for deterministic functions to (adaptively) simulation-based CCA- (SIM-CCA-) secure ones for randomized functions, whether the schemes were directly applied to CCA settings for deterministic functions is not implied. We give an affirmative answer and derive a SIM-CCA-secure scheme for deterministic functions by making some modifications on it. Again, based on this derived scheme, we also propose an (adaptively) indistinguishable CCA- (IND-CCA-) secure SK-FE for deterministic functions. The final results show that our scheme can be instantiated under both nonstandard assumptions (e.g., hard problems on multilinear maps and indistinguishability obfuscation (IO)) and under standard assumptions (e.g., DDH, RSA, LWE, and LPN).
In 2013, Boneh and Zhandry introduced the notion of indistinguishability (IND) in chosen plaintext (CPA) and chosen ciphertext (CCA) attacks by a quantum adversary which is given superposition access to an oracle for encryption and decryption queries but is restricted to classical queries in the challenge phase. In this paper we define IND-CPA and IND-CCA notions for symmetric encryption schemes where the adversary has full quantum superposition access to the oracle, and give constructions that achieve these security notions. Our results are formulated in the concrete security framework.