About three decades ago it was realized that implementing private channels between parties which can be adaptively corrupted requires an encryption scheme that is secure against selective opening attacks. Whether standard (IND-CPA) security implies security against selective opening attacks has been a major open question since. The only known reduction from selective opening to IND-CPA security loses an exponential factor. A polynomial reduction is only known for the very special case where the distribution considered in the selective opening security experiment is a product distribution, i.e., the messages are sampled independently from each other. In this paper we give a reduction whose loss is quantified via the dependence graph (where message dependencies correspond to edges) of the underlying message distribution. In particular, for some concrete distributions including Markov distributions, our reduction is polynomial.
About three decades ago it was realized that implementing private channels between parties which can be adaptively corrupted requires an encryption scheme that is secure against selective opening attacks. Whether standard (IND-CPA) security implies security against selective opening attacks has been a major open question since. The only known reduction from selective opening to IND-CPA security loses an exponential factor. A polynomial reduction is only known for the very special case where the distribution considered in the selective opening security experiment is a product distribution, i.e., the messages are sampled independently from each other. In this paper we give a reduction whose loss is quantified via the dependence graph (where message dependencies correspond to edges) of the underlying message distribution. In particular, for some concrete distributions including Markov distributions, our reduction is polynomial.
We show that no commitment scheme that is hiding andbindingaccordingtothestandarddefinition is semantically-secure under selective opening attack (SOA), resolving a long-standing and fundamental open question about the power of SOAs. We also obtain the first examples of IND-CPA encryption schemesthatarenotsecureunderSOA, bothforsendercorruptionswhereencryptioncoinsare revealed and receiver corruptions where decryption keys are revealed. These results assume only the existence of collision-resistant hash functions.
Functional encryption (FE) has more fine-grained control to encrypted data than traditional encryption schemes. The well-accepted security of FE is indistinguishability-based security (IND-FE) and simulation-based security (SIMFE), but the security is not sufficient.For example, if an adversary has the ability to access a vector of ciphertexts and can ask to open some information of the messages, such as coins used in the encryption or secret key in multikey setting, whether the privacy of the unopened messages is guaranteed.This is called selective opening attack (SOA).In this paper, we propose a stronger security of FE which is secure against SOA (we call SO-FE) and propose a concrete construction of SO-FE scheme in the standard model.Our scheme is a non-adaptive IND-FE which satisfies selective opening secure in the simulation sense.In addition, the scheme can encrypt messages of any bit length other than bitwise and it is secure against SOA-C and SOAK simultaneously while the two attacks were appeared in different model before.According to the different functionality f, our scheme can specialize as IBE, ABE and even PE schemes secure against SOA.
In a selective-opening, chosen-ciphertext attack (SO-CCA) against a public key encryption scheme (PKE scheme), a probabilistic polynomial time (PPT) adversary obtains a vector of challenge ciphertexts, has access to a decryption oracle, adaptively selects to open some of the challenge ciphertexts and sees the corresponding messages together with the random coins. The simulation-based, selective-opening security against chosen-ciphertext attacks (SIM-SO-CCA security) protects the security of the unopened messages in a semantic way, i.e. it requires that the output of the adversary can be simulated by a simulator who sees only the opened messages. In particular, all information that the adversary can get from the unopened messages can also be simulated from the opened messages alone by the simulator. All security proofs of the available PKEs achieving SIM-SO-CCA security are not tight, and the security loss depends either on the number of challenge ciphertexts or on the number of decryption queries. In this work, we present the first PKE scheme which achieves SIM-SO-CCA security with a tight reduction to standard assumptions. This partially solves the open problem proposed by Hofheinz in EuroCrypt 2012.
In the first part of this work, Chapter 3 we present new and general constructions of lossy encryption schemes.
The Selective Opening problem is as follows: suppose an adversary receives n commitments (or encryptions) of (possibly) correlated messages, and now the adversary can choose n/2 of the messages, and receive de-commitments (or decryptions and the randomness used to encrypt them). Do the unopened commitments (encryptions) remain secure? A protocol achieving this type of security is called secure against a selective opening adversary (SOA). This question arises naturally in the context of Byzantine Agreement and Secure Multiparty Computation, where an active adversary is able to eavesdrop on all the wires, and then choose a subset of players to corrupt. Unfortunately, the traditional definitions of security (IND-CPA, IND-CCA) do not guarantee security in this setting. In this paper: · We formally define re-randomizable encryption and show that every re-randomizable encryption scheme gives rise to efficient encryptions secure against a selective opening adversary. (Very informally, an encryption is re-randomizable, if given any ciphertext, there is an efficient way to map it to an almost uniform re-encryption of the same underlying message). · We show that statistically-hiding 2-round Oblivious Transfer (OT) implies Lossy Encryption and so do smooth hash proof systems, as defined by Cramer-Shoup. Combining this with known results immediately shows that Private Information Retrieval and homomorphic encryption both imply Lossy Encryption, and thus Selective Opening Secure Public Key Encryption.
In the second part of this work, Chapter 4, we focus on constructing lossy trapdoor functions.
Lossy trapdoor functions (LTDFs) were introduced by Peikert and Waters in STOC '08. Since their introduction, lossy trapdoor functions have found many uses in cryptography. In the work of Peikert and Waters, lossy trapdoor functions were used to give an efficient construction of a chosen-ciphertext secure (IND-CCA2) cryptosystem. Lossy trapdoor functions were then shown to imply deterministic encryption by Boldyreva, Fehr and O'Neill in CRYPTO '08. In TCC '09, Rosen and Segev showed that lossy trapdoor functions are correlated product secure, meaning that they remain one-way even when evaluated on correlated inputs.
In this section we extend the notion of smooth hash proof systems as defined by Cramer and Shoup in Eurocrypt '02, to include an additional homomorphic property. We call this primitive smooth homomorphic hash proof systems . We show that smooth homomorphic projective hash proof systems include all Diverse Group Systems, as defined by Cramer and Shoup. Using this definition, we show that · Smooth homomorphic hash proof systems imply LTDFs. · Diverse group systems as defined in [CS02] imply LTDFs. These are the first known generic constructions of LTDFs. · Applying our generic construction the specific constructions of smooth hash proof systems given by Cramer and Shoup, we obtain the first construction of fully lossy trapdoor functions from the quadratic residuosity (QR) assumption. We also obtain a novel construction of LTDFs from Paillier's decisional composite residuosity (DCR) assumption. · Applying the black-box separation results of Rosen and Segev, we show that there is a black-box separation between smooth homomorphic hash proof systems and one-way trapdoor permutations.
In the third part of this work, Chapter 5, we examine in what situations we can construct lossy trapdoor functions from the seemingly weaker primitive lossy encryption.
Injective one-way trapdoor functions are one of the most fundamental cryptographic primitives. In this section we give a novel construction of injective trapdoor functions based on oblivious transfer for long strings. Our main result is to show that any 2-message statistically sender-private semi-honest oblivious transfer (OT) for strings longer than the sender randomness implies the existence of injective one-way trapdoor functions. This is perhaps surprising given the black box separation of injective one-way trapdoor functions from many common cryptographic protocols, e.g. IND-CCA encryption. As a tool for creating injective one-way trapdoor functions, we define a new notion of security for a public key encryption scheme called Randomness Dependent Message (RDM) security, and use it as a stepping stone for creating injective one-way trapdoor functions. (Abstract shortened by UMI.)
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).