Chosen-Ciphertext Secure Multi-Identity and Multi-Attribute Pure FHE

A multi-identity pure fully homomorphic encryption (MIFHE) enables a server to perform arbitrary computation on the ciphertexts that are encrypted under different identities. In case of multi-attribute pure FHE (MAFHE), the ciphertexts are associated with different attributes. Clear and McGoldrick (CANS 2014) gave the first chosen-plaintext attack secure MIFHE and MAFHE based on indistinguishability obfuscation. In this study, we focus on building MIFHE and MAFHE which are se- cure under type 1 of chosen-ciphertext attack (CCA1) security model. In particular, using witness pseudorandom functions (Zhandry, TCC 2016) and multi-key pure FHE or MFHE (Mukherjee and Wichs, EUROCRYPT 2016) we propose the following constructions: – CCA secure identity-based encryption (IBE) that enjoys an optimal size ciphertexts, which we extend to a CCA1 secure MIFHE scheme. – CCA secure attribute-based encryption (ABE) having an optimal size ciphertexts, which we transform into a CCA1 secure MAFHE scheme. By optimal size, we mean that the bit-length of a ciphertext is the bit-length of the message plus a security parameter multiplied with a constant. Known constructions of multi-identity(attribute) FHEs are either leveled, that is, support only bounded depth circuit evaluations or secure in a weaker CPA security model. With our new approach, we achieve both CCA1 security and evaluation on arbitrary depth circuits for multi-identity(attribute) FHE schemes

Constant-size ciphertexts in threshold attribute-based encryption without dummy attributes

Attribute-based encryption (ABE) is an augmentation of public key encryption that allows users to encrypt and decrypt messages based on users’ attributes. In a ( t, s ) threshold ABE, users who can decrypt a ciphertext must hold at least t attributes among the s attributes specified by the encryptor. At PKC 2010, Herranz, Laguillaumie and Ràfols proposed the first threshold ABE with constant-size ciphertexts. In order to ensure the encryptor can flexibly select the attribute set and a threshold value, they use dummy attributes to satisfy the decryption requirement. The advantage of their scheme is that any addition or removal of the attributes will not require any change to users’ private keys or public parameters. Unfortunately, the need for dummy attributes makes their scheme inefficient, since the computational cost of encryption is linear to the size of selected attribute set and dummy attribute set. In this work, we improve Herranz et al.’s work, and propose a new threshold ABE scheme which does not use any dummy attribute . Our scheme not only retains the nice feature of Herranz et al.’s scheme, but also offers two improvements in comparison to the previous work. Firstly, the computational costs of encryption and decryption are only linear in the size of the selected attribute set. Secondly, without any dummy attribute, most of the computations can be conducted without the knowledge of the threshold t . Hence, threshold change in the encryption phase does not require complete recomputation of the ciphertext

Efficient Construction for Full Black-Box Accountable Authority Identity-Based Encryption

Accountable authority identity-based encryption (A-IBE), as an attractive way to guarantee the user privacy security, enables a malicious private key generator (PKG) to be traced if it generates and re-distributes a user private key. Particularly, an A-IBE scheme achieves full black-box security if it can further trace a decoder box and is secure against a malicious PKG who can access the user decryption results. In PKC\u2711, Sahai and Seyalioglu presented a generic construction for full black-box A-IBE from a primitive called dummy identity-based encryption, which is a hybrid between IBE and attribute-based encryption (ABE). However, as the complexity of ABE, their construction is inefficient and the size of private keys and ciphertexts in their instantiation is linear in the length of user identity. In this paper, we present a new efficient generic construction for full black-box A-IBE from a new primitive called token-based identity-based encryption (TB-IBE), without using ABE. We first formalize the definition and security model for TB-IBE. Subsequently, we show that a TB-IBE scheme satisfying some properties can be converted to a full black-box A-IBE scheme, which is as efficient as the underlying TB-IBE scheme in terms of computational complexity and parameter sizes. Finally, we give an instantiation with the computational complexity as O(1) and the constant size master key pair, private keys, and ciphertexts

ABE for Circuits with Constant-Size Secret Keys and Adaptive Security

An important theme in research on attribute-based encryption (ABE) is minimizing the sizes of the secret keys and ciphertexts. In this work, we present two new ABE schemes with *constant-size* secret keys, that is, the key size is independent of the sizes of policies or attributes, and dependent only on the security parameter lambda. * We construct the first key-policy ABE scheme for circuits with constant-size secret keys, |sk_f|=poly(lambda), which concretely consist of only three group elements. The previous state-of-the-art construction by [Boneh et al., Eurocrypt \u2714] has key size polynomial in the maximum depth d of the policy circuits, |sk_f|=poly(d,lambda). Our new scheme removes this dependency of key size on d while keeping the ciphertext size the same, which grows linearly in the attribute length and polynomially in the maximal depth, |ct|=|x|poly(d,lambda). * We present the first ciphertext-policy ABE scheme for Boolean formulae that simultaneously has constant-size keys and succinct ciphertexts of size independent of the policy formulae, in particular, |sk_f|=poly(lambda) and |ct_x|=poly(|x|,lambda). Concretely, each secret key consists of only two group elements. Previous ciphertext-policy ABE schemes either have succinct ciphertexts but non constant-size keys [Agrawal--Yamada, Eurocrypt \u2720; Agrawal--Wichs--Yamada, TCC \u2720], or constant-size keys but large ciphertexts that grow with the policy size, as well as the attribute length. Our second construction is the first ABE scheme achieving *double succinctness*, where both keys and ciphertexts are smaller than the corresponding attributes and policies tied to them. Our constructions feature new ways of combining lattices with pairing groups for building ABE and are proven selectively secure based on LWE and in the generic (pairing) group model. We further show that when replacing the LWE assumption with its adaptive variant introduced in [Quach--Wee--Wichs FOCS \u2718] the constructions become adaptively secure