Ciphertext expansion

Abstract: We present a Hierarchical Identity Based Encryption (HIBE) system where the ciphertext consists of just three group elements and decryption requires only two bilinear map computations, regardless of the hierarchy depth. Encryption is as ecient as in other HIBE systems. We prove that the scheme is selective-ID secure in the standard model and fully secure in the random oracle model. Our system has a number of applications: it gives very ecient forward secure public key and identity based cryptosystems (with short ciphertexts), it converts the NNL broadcast encryption system into an ecient public key broadcast system, and it provides an ecient mechanism for encrypting to the future. The system also supports limited delegation where users can be given restricted private keys that only allow delegation to bounded depth. The HIBE system can be modified to support sublinear size private keys at the cost of some ciphertext expansion.

Abstract: This work describes a fast fully homomorphic encryption scheme over the torus (TFHE) that revisits, generalizes and improves the fully homomorphic encryption (FHE) based on GSW and its ring variants. The simplest FHE schemes consist in bootstrapped binary gates. In this gate bootstrapping mode, we show that the scheme FHEW of Ducas and Micciancio (Eurocrypt, 2015) can be expressed only in terms of external product between a GSW and an LWE ciphertext. As a consequence of this result and of other optimizations, we decrease the running time of their bootstrapping from 690 to 13 ms single core, using 16 MB bootstrapping key instead of 1 GB, and preserving the security parameter. In leveled homomorphic mode, we propose two methods to manipulate packed data, in order to decrease the ciphertext expansion and to optimize the evaluation of lookup tables and arbitrary functions in $${\mathrm {RingGSW}}$$-based homomorphic schemes. We also extend the automata logic, introduced in Gama et al. (Eurocrypt, 2016), to the efficient leveled evaluation of weighted automata, and present a new homomorphic counter called $$\mathrm {TBSR}$$, that supports all the elementary operations that occur in a multiplication. These improvements speed up the evaluation of most arithmetic functions in a packed leveled mode, with a noise overhead that remains additive. We finally present a new circuit bootstrapping that converts $$\mathsf {LWE}$$ ciphertexts into low-noise $${\mathrm {RingGSW}}$$ ciphertexts in just 137 ms, which makes the leveled mode of TFHE composable and which is fast enough to speed up arithmetic functions, compared to the gate bootstrapping approach. Finally, we provide an alternative practical analysis of LWE based schemes, which directly relates the security parameter to the error rate of LWE and the entropy of the LWE secret key, and we propose concrete parameter sets and timing comparison for all our constructions.

Abstract: We propose a simple and general framework for constructing oblivious transfer (OT) protocols that are efficient, universally composable, and generally realizableunder any one of a variety of standard number-theoretic assumptions, including the decisional Diffie-Hellman assumption, the quadratic residuosity and decisional composite residuosity assumptions, and worst-caselattice assumptions. Our OT protocols are round-optimal (one message each way), quite efficient in computation and communication, and can use a single common string for an unbounded number of executions between the same sender and receiver. Furthermore, the protocols can provide statisticalsecurity to either the sender or the receiver, simply by changing the distribution of the common string. For certain instantiations of the protocol, even a common uniformly randomstring suffices. Our key technical contribution is a simple abstraction that we call a dual-modecryptosystem. We implement dual-mode cryptosystems by taking a unified view of several cryptosystems that have what we call "messy" public keys, whose defining property is that a ciphertext encrypted under such a key carries no information(statistically) about the encrypted message. As a contribution of independent interest, we also provide a multi-bit amortizedversion of Regev's lattice-based cryptosystem (STOC 2005) whose time and space complexity are improved by a linear factor in the security parameter n. The resulting amortized encryption and decryption times are only $\tilde{O}(n)$ bit operations per message bit, and the ciphertext expansion can be made as small as a constant; the public key size and underlying lattice assumption remain essentially the same.

Abstract: We present a Hierarchical Identity Based Encryption (HIBE) system where the ciphertext consists of just three group elements and decryption requires only two bilinear map computations, regardless of the hierarchy depth. Encryption is as efficient as in other HIBE systems. We prove that the scheme is selective-ID secure in the standard model and fully secure in the random oracle model. Our system has a number of applications: it gives very efficient forward secure public key and identity based cryptosystems (with short ciphertexts), it converts the NNL broadcast encryption system into an efficient public key broadcast system, and it provides an efficient mechanism for encrypting to the future. The system also supports limited delegation where users can be given restricted private keys that only allow delegation to bounded depth. The HIBE system can be modified to support sublinear size private keys at the cost of some ciphertext expansion.