Decisional Composite Residuosity Assumption Research Articles

A tighter proof for CCA secure inner product functional encryption: Genericity meets efficiency

Inner product functional encryption (IPFE) is a primitive which produces, from a master secret key, decryption keys skk associated to vectors k over some specified base ring. Decrypting an encryption of vector m with skk only reveals 〈k,m〉. Benhamouda et al. [7] provided a generic construction for CCA-secure IPFE from projective hash functions (PHFs), unfortunately their security reduction suffers an exponential loss. Their only instantiation capable of decrypting inner products of large sizes, which relies on the decisional composite residuosity (DCR) assumption, is impractical due to the large size of ciphertexts, decryption keys, and the prohibitive speed of the scheme. Our core contribution is a new approach to proving CCA security. Our constructions maintain the genericity of [7], while our security proof relaxes the requirements on the underlying PHFs and gains in reduction tightness. We instantiate these constructions from the DCR assumption, an assumption in class groups (HSMCL) and the decision Diffie Hellman (DDH) assumption. Our CCA-secure constructions from DCR and HSMCL are the first such schemes to efficiently decrypt inner products of large size, improving by multiple orders of magnitude upon the work of [7]. A single-core C implementation of these schemes shows that, for a 112 bit security, and 100-dimensional vectors, their DCR-based scheme takes 1 h 20 min to encrypt, and over 5 min to decrypt, whereas our slowest scheme takes 5.2 s to encrypt and 0.5 s to decrypt. Similarly a ciphertext for their scheme is of 283 MB; those of our HSMCL-based scheme are of 30 kB.

An efficient key authentication procedure for IND-CCA2 secure Paillier-based cryptosystem

Public key cryptosystems more recently developed have to be strong against newer and more advanced forms of attacks. The security protection of a public key cryptosystem relies heavily on the design of the public key. The key authentication procedure is one of the easiest and most advantageous authentication mechanisms used over insecure networks and widely applied for the remote login with various operation systems, computer networks, wireless networks, database management systems, and many others. In a typical key authentication procedure, however, there is at least one authority involved to authenticate the keys. In this paper, we shall propose a new key authentication procedure built on the basis of the decisional composite residuosity assumption. As with ordinary certificate-based procedures, the proposed procedure involves no authorities. With the certificate of the public key of a client being a blend of his/her private key and password, the proposed procedure is exceptionally secure, and the authentication process is very simple.

Public key encryption with equality test via hash proof system

Public key encryption with equality test (PKEET) allows a tester to know whether ciphertexts are the encryptions of a same message or not by using the trapdoors issued from their owners, which is a useful cryptographic primitive can be deployed in many applications, such as in the mechanism of searching over encrypted data. Based on Hash Proof System (HPS) introduced by Cramer and Shoup, this paper presents an oversimplified paradigm for constructing PKEET in the standard model. Compared with the previous works that use identity-based encryption, strongly unforgeable one-time signature or other strong cryptographic primitives, our paradigm requires only the universal2 property of HPS and provides an efficient way to obtain concrete PKEET schemes based on different assumptions in the standard model, since HPS has been shown can be easily realized from a board range of NP languages (e.g., DLIN-based, DCR-based, Lattice-based and so on). Moreover, to demonstrate the practicality of the proposed paradigm, we instantiate it based on two kinds of NP languages respectively, one is based on the decisional Diffie-Hellman (DDH) assumption, the other one is based on the decisional composite residuosity (DCR) assumption, which results in the first concrete PKEET schemes that in the standard model without using pairing operations, and the schemes' security are also based on the standard DDH assumption and the standard DCR assumption respectively.

A generic construction of tightly secure signatures in the multi-user setting

In this paper, we present a generic construction of tightly secure signature schemes in the multi-user setting, which is in turn used to construct tightly secure identity-based signature schemes. Both of the securities of the constructions are based on the hardness of some subset membership problems (SMP). By instantiating SMP with the Decisional Composite Residuosity (DCR) and Matrix Decisional Diffie–Hellman (MDDH) problems, we obtain tightly secure signature schemes and tightly secure identity-based signatures based on the DCR and MDDH assumptions, respectively.

Practical key‐dependent message chosen‐ciphertext security based on decisional composite residuosity and quadratic residuosity assumptions

AbstractAn encryption scheme is key‐dependent message chosen plaintext attack (KDM‐CPA) secure if it is secure even against an attacker who has access to encryptions of messages that depend on the secret key. Such situations naturally occur in some scenarios such as formal calculus, hard‐disk encryption, or multi‐party protocols. However, up to now, there are not many schemes that achieve KDM‐CPA security, let alone KDM chosen ciphertext attack (KDM‐CCA) security. The constructions proposed by Camenisch, Chandran, and Shoup (Eurocrypt 2009), and Hofheinz (Eurocrypt 2013) are the only two general constructions that can be proved to be KDM‐CCA secure in the standard model. Besides, Qin, Liu, and Huang (ACISP 2013) also presented another concrete implementation. In particular, they showed how to obtain KDM‐CCA security from the classic Cramer–Shoup cryptosystem (based on the decisional Diffie–Hellman assumption) w.r.t. a new ensemble of functions (we call QLH ensemble). Since the Cramer–Shoup scheme has short ciphertext size and higher computational efficiency, they obtain practical KDM‐CCA security w.r.t. a reasonably large ensemble.In this paper, we study the KDM‐CCA security of other cryptosystems proposed by Cramer and Shoup (Eurocrypt 2002). In particular, we prove that the schemes, based on decisional composite residuosity (DCR) and quadratic residuosity (QR) assumptions, respectively, also achieve KDM‐CCA security w.r.t. the QLH ensemble. On the one hand, because the DCR‐based and QR‐based schemes of Cramer et al. are fairly practical, we also obtain practical KDM‐CCA security based on DCR and QR assumptions, respectively. On the other hand, compared with the result of Qin et al., we need not tailor the original schemes of Cramer et al. because themselves have natural “compatibility” for the message space and the secret key space. Copyright © 2014 John Wiley & Sons, Ltd.

Primitive Power Roots of Unity and Its Application to Encryption

We first consider a variant of the Schmidt-Samoa-Takagi encryption scheme without losing additively homomorphic properties. We show that this variant is secure in the sense of IND-CPA under the decisional composite residuosity assumption, and of OW-CPA under the assumption on the hardness of factoring n = p2q. Second, we introduce new algebraic properties “affine” and “pre-image restriction, ” which are closely related to homomorphicity. Intuitively, “affine” is a tuple of functions which have a special homomorphic property, and “pre-image restriction” is a function which can restrict the receiver to having information on the encrypted message. Then, we propose an encryption scheme with primitive power roots of unity in (Z/ns+1)×. We show that our scheme has, in addition to the additively homomorphic property, the above algebraic properties. In addition to the properties, we also show that the encryption scheme is secure in the sense of OW-CPA and IND-CPA under new number theoretic assumptions.