## CryptoDB

### Papers from Journal of Cryptology 2019

**Year**

**Venue**

**Title**

2019

JOFC

Blockcipher-Based Authenticated Encryption: How Small Can We Go?
Abstract

This paper presents a lightweight blockcipher-based authenticated encryption mode mainly focusing on minimizing the implementation size, i.e., hardware gates or working memory on software. The mode is called $$\textsf {COFB}$$COFB, for COmbined FeedBack. $$\textsf {COFB}$$COFB uses an n-bit blockcipher as the underlying primitive and relies on the use of a nonce for security. In addition to the state required for executing the underlying blockcipher, $$\textsf {COFB}$$COFB needs only n / 2 bits state as a mask. Till date, for all existing constructions in which masks have been applied, at least n bit masks have been used. Thus, we have shown the possibility of reducing the size of a mask without degrading the security level much. Moreover, it requires one blockcipher call to process one input block. We show $$\textsf {COFB}$$COFB is provably secure up to $$O(2^{n/2}/n)$$O(2n/2/n) queries which is almost up to the standard birthday bound. We first present an idealized mode $$\textsf {iCOFB}$$iCOFB along with the details of its provable security analysis. Next, we extend the construction to the practical mode COFB. We instantiate COFB with two 128-bit blockciphers, AES-128 and GIFT-128, and present their implementation results on FPGAs. We present two implementations, with and without CAESAR hardware API. When instantiated with AES-128 and implemented without CAESAR hardware API, COFB achieves only a few more than 1000 Look-Up-Tables (LUTs) while maintaining almost the same level of provable security as standard AES-based AE, such as GCM. When instantiated with GIFT-128, COFB performs much better in hardware area. It consumes less than 1000 LUTs while maintaining the same security level. However, when implemented with CAESAR hardware API, there are significant overheads both in hardware area and in throughput. COFB with AES-128 achieves about 1475 LUTs. COFB with GIFT-128 achieves a few more than 1000 LUTs. Though there are overheads, still both these figures show competitive implementation results compared to other authenticated encryption constructions.

2019

JOFC

On Black-Box Complexity of Universally Composable Security in the CRS Model
Abstract

In this work, we study the intrinsic complexity of black-box Universally Composable (UC) secure computation based on general assumptions. We present a thorough study in various corruption modelings while focusing on achieving security in the common reference string (CRS) model. Our results involve the following:Static UC secure computation. Designing the first static UC oblivious transfer protocol based on public-key encryption and stand-alone semi-honest oblivious transfer. As a corollary, we obtain the first black-box constructions of UC secure computation assuming only two-round semi-honest oblivious transfer.One-sided UC secure computation. Designing adaptive UC two-party computation with single corruptions assuming public-key encryption with oblivious ciphertext generation.Adaptive UC secure computation. Designing adaptively secure UC commitment scheme assuming only public-key encryption with oblivious ciphertext generation. As a corollary, we obtain the first black-box constructions of adaptive UC secure computation assuming only (trapdoor) simulatable public-key encryption (as well as a variety of concrete assumptions).We remark that such a result was not known even under non-black-box constructions.

2019

JOFC

Efficient Constant-Round Multi-party Computation Combining BMR and SPDZ
Abstract

Recently, there has been huge progress in the field of concretely efficient secure computation, even while providing security in the presence of malicious adversaries. This is especially the case in the two-party setting, where constant-round protocols exist that remain fast even over slow networks. However, in the multi-party setting, all concretely efficient fully secure protocols, such as SPDZ, require many rounds of communication. In this paper, we present a constant-round multi-party secure computation protocol that is fully secure in the presence of malicious adversaries and for any number of corrupted parties. Our construction is based on the constant-round protocol of Beaver et al. (the BMR protocol) and is the first version of that protocol that is concretely efficient for the dishonest majority case. Our protocol includes an online phase that is extremely fast and mainly consists of each party locally evaluating a garbled circuit. For the offline phase, we present both a generic construction (using any underlying MPC protocol) and a highly efficient instantiation based on the SPDZ protocol. Our estimates show the protocol to be considerably more efficient than previous fully secure multi-party protocols.

2019

JOFC

Multi-theorem Preprocessing NIZKs from Lattices
Abstract

Non-interactive zero-knowledge (NIZK) proofs are fundamental to modern cryptography. Numerous NIZK constructions are known in both the random oracle and the common reference string (CRS) models. In the CRS model, there exist constructions from several classes of cryptographic assumptions such as trapdoor permutations, pairings, and indistinguishability obfuscation. However, at the time of the initial publication of this work, we did not have constructions of NIZKs from standard lattice assumptions. In this work, we take an initial step toward constructing multi-theorem NIZKs for general $$\mathsf {NP}$$NP languages from standard lattice assumptions by considering a relaxation to the preprocessing model and a new model we call the designated-prover model. In the preprocessing model, a setup algorithm generates secret proving and verification keys for the prover and the verifier, respectively. In the designated-prover model, the proving key is secret, but the verification key is public. In both settings, the proving key is used to construct proofs and the verification key is used to check proofs. Finally, in the multi-theorem setting, both the proving and verification keys should be reusable for an unbounded number of theorems without compromising soundness or zero-knowledge. Previous constructions of NIZKs in the preprocessing model that rely on weaker assumptions like one-way functions or oblivious transfer are only secure in a single-theorem setting. Thus, constructing multi-theorem NIZKs in these relaxed models does not seem to be inherently easier than constructing them in the CRS model. In this work, we first construct a multi-theorem preprocessing NIZK argument from context-hiding homomorphic signatures. In fact, the construction is a designated-prover NIZK. We also show that using homomorphic commitments, we can get statistically sound proofs in the preprocessing and designated-prover models. Together with lattice-based instantiations of homomorphic signatures and commitments, we obtain the first multi-theorem NIZKs in the preprocessing and designated-prover models from standard lattice assumptions. Finally, we show how to generalize our construction to obtain a universally composable NIZK (UC-NIZK) in the preprocessing model from standard lattice assumptions. Our UC-NIZK relies on a simple preprocessing protocol based on a new primitive we call blind homomorphic signatures.

2019

JOFC

TFHE: Fast Fully Homomorphic Encryption Over the Torus
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 $${\mathrm {RingGSW}}$$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 $$\mathrm {TBSR}$$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 $$\mathsf {LWE}$$LWE ciphertexts into low-noise $${\mathrm {RingGSW}}$$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.

2019

JOFC

Constant-Round Maliciously Secure Two-Party Computation in the RAM Model
Abstract

The random-access memory model of computation allows program constant-time memory lookup and is more applicable in practice today, covering many important algorithms. This is in contrast to the classic setting of secure 2-party computation (2PC) that mostly follows the approach for which the desired functionality must be represented as a Boolean circuit. In this work, we design the first constant-round maliciously secure two-party protocol in the RAM model. Our starting point is the garbled RAM construction of Gentry et al. (EUROCRYPT, pp 405–422, 2014) that readily induces a constant round semi-honest two-party protocol for any RAM program assuming identity-based encryption schemes. We show how to enhance the security of their construction into the malicious setting while facing several challenges that stem due to handling the data memory. Next, we show how to apply our techniques to a more recent garbled RAM construction by Garg et al. (STOC, pp 449–458, 2015) that is based on one-way functions.

2019

JOFC

Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting
Abstract

The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first non-generic fully simulatable protocol for distributively generating an RSA composite with security against malicious behavior. Our second contribution is a complete Paillier (in: EUROCRYPT, pp 223–238, 1999) threshold encryption scheme in the two-party setting with security against malicious attacks. We further describe how to extend our protocols to the multiparty setting with dishonest majority. Our RSA key generation protocol is comprised of the following subprotocols: (i) a distributed protocol for generation of an RSA composite and (ii) a biprimality test for verifying the validity of the generated composite. Our Paillier threshold encryption scheme uses the RSA composite for the public key and is comprised of the following subprotocols: (i) a distributed generation of the corresponding secret key shares and (ii) a distributed decryption protocol for decrypting according to Paillier.

2019

JOFC

Hardness-Preserving Reductions via Cuckoo Hashing
Abstract

The focus of this work is hardness-preserving transformations of somewhat limited pseudorandom functions families (PRFs) into ones with more versatile characteristics. Consider the problem of domain extension of pseudorandom functions: given a PRF that takes as input elements of some domain $$\mathcal {U}$$U, we would like to come up with a PRF over a larger domain. Can we do it with little work and without significantly impacting the security of the system? One approach is to first hash the larger domain into the smaller one and then apply the original PRF. Such a reduction, however, is vulnerable to a “birthday attack”: after $$\sqrt{\left| \mathcal {U}\right| }$$U queries to the resulting PRF, a collision (i.e., two distinct inputs having the same hash value) is very likely to occur. As a consequence, the resulting PRF is insecure against an attacker making this number of queries. In this work, we show how to go beyond the aforementioned birthday attack barrier by replacing the above simple hashing approach with a variant of cuckoo hashing, a hashing paradigm that resolves collisions in a table by using two hash functions and two tables, cleverly assigning each element to one of the two tables. We use this approach to obtain: (i) a domain extension method that requires just two calls to the original PRF can withstand as many queries as the original domain size, and has a distinguishing probability that is exponentially small in the amount of non-cryptographic work; and (ii) a security-preserving reduction from non-adaptive to adaptive PRFs.

2019

JOFC

(Efficient) Universally Composable Oblivious Transfer Using a Minimal Number of Stateless Tokens
Abstract

We continue the line of work initiated by Katz (Eurocrypt 2007) on using tamper-proof hardware tokens for universally composable secure computation. As our main result, we show an oblivious-transfer (OT) protocol in which two parties each create and transfer a single, stateless token and can then run an unbounded number of OTs. We also show a more efficient protocol, based only on standard symmetric-key primitives (block ciphers and collision-resistant hash functions), that can be used if a bounded number of OTs suffice. Motivated by this result, we investigate the number of stateless tokens needed for universally composable OT. We prove that our protocol is optimal in this regard for constructions making black-box use of the tokens (in a sense we define). We also show that nonblack-box techniques can be used to obtain a construction using only a single stateless token.

2019

JOFC

Cryptanalysis of the CLT13 Multilinear Map
Abstract

In this paper, we describe a polynomial time cryptanalysis of the (approximate) multilinear map proposed by Coron, Lepoint, and Tibouchi in Crypto13 (CLT13). This scheme includes a zero-testing functionality that determines whether the message of a given encoding is zero or not. This functionality is useful for designing several of its applications, but it leaks unexpected values, such as linear combinations of the secret elements. By collecting the outputs of the zero-testing algorithm, we construct a matrix containing the hidden information as eigenvalues, and then recover all the secret elements of the CLT13 scheme via diagonalization of the matrix. In addition, we provide polynomial time algorithms to directly break the security assumptions of many applications based on the CLT13 scheme. These algorithms include solving subgroup membership, decision linear, and graded external Diffie–Hellman problems. These algorithms mainly rely on the computation of the determinants of the matrices and their greatest common divisor, instead of performing their diagonalization.