Progress in Cryptology – AFRICACRYPT 2016

Combining the efficient cross-polytope locality-sensitive hash family of Terasawa and Tanaka with the heuristic lattice sieve algorithm of Micciancio and Voulgaris, we show how to obtain heuristic and practical speedups for solving the shortest vector problem (SVP) on both arbitrary and ideal lattices. In both cases, the asymptotic time complexity for solving SVP in dimension n is \(2^{0.298n + o(n)}\).

For any lattice, hashes can be computed in polynomial time, which makes our CPSieve algorithm much more practical than the SphereSieve of Laarhoven and de Weger, while the better asymptotic complexities imply that this algorithm will outperform the GaussSieve of Micciancio and Voulgaris and the HashSieve of Laarhoven in moderate dimensions as well. We performed tests to show this improvement in practice.

For ideal lattices, by observing that the hash of a shifted vector is a shift of the hash value of the original vector and constructing rerandomization matrices which preserve this property, we obtain not only a linear decrease in the space complexity, but also a linear speedup of the overall algorithm. We demonstrate the practicability of our cross-polytope ideal lattice sieve ICPSieve by applying the algorithm to cyclotomic ideal lattices from the ideal SVP challenge and to lattices which appear in the cryptanalysis of NTRU.

The security of many cryptographic schemes has been based on special instances of the Learning with Errors (LWE) problem, e.g., Ring-LWE, LWE with binary secret, or LWE with ternary error. However, recent results show that some subclasses are weaker than expected. In this work we show that LWE with binary error, introduced by Micciancio and Peikert, is one such subclass. We achieve this by applying the Howgrave-Graham attack on NTRU, which is a combination of lattice techniques and a Meet-in-the-Middle approach, to this setting. We show that the attack outperforms all other currently existing algorithms for several natural parameter sets. For instance, for the parameter set \(n=256\), \(m=512\), \(q=256\), this attack on LWE with binary error only requires \(2^{85}\) operations, while the previously best attack requires \(2^{117}\) operations. We additionally present a complete and improved analysis of the attack, using analytic techniques. Finally, based on the attack, we give concrete hardness estimations that can be used to select secure parameters for schemes based on LWE with binary error.

Elliptic curve cryptography (ECC) provides high security with shorter keys than other public-key cryptosystems and it has been successfully used in security critical embedded systems. We present an FPGA-based coprocessor that communicates with the host processor via a 32-bit bus. It implements ECC over an elliptic curve that offers roughly 128-bit security. It is the first hardware implementation that uses the recently introduced lambda coordinates and the Galbraith-Lin-Scott (GLS) technique with fast endomorphisms. One scalar multiplication requires 65,000 clock cycles with a maximum clock frequency of 274 MHz on a Xilinx Virtex-5 FPGA, which gives a computation time of 0.24 ms. The area utilization is 1552 slices and 4 BlockRAMs. Our coprocessor compares favorably to other published works both in terms of speed and area, which makes it a good choice for embedded systems that rety public-key cryptography.

Elliptic Curve Cryptography is an important alternative to traditional public key schemes such as RSA. This paper presents

We investigate two attacks on the PRINCE block cipher in the most realistic scenario, when the attacker only has a minimal amount of known plaintext available. The first attack is called Accelerated Exhaustive Search, and is able to recover the key for up to the full 12-round PRINCE with a complexity slightly lower than the security claim given by the designers. The second attack is a meet-in-the-middle attack, where we show how to successfully attack 8- and 10-round PRINCE with only two known plaintext/ciphertext pairs. Both attacks take advantage of the fact that the two middle rounds in PRINCE are unkeyed, so guessing the state before the first middle round gives the state after the second round practically for free. These attacks are the fastest until now in the known plaintext scenario for the 8 and 10 reduced-round versions and the full 12-round of PRINCE.

GCM is used in a vast amount of security protocols and is quickly becoming the de facto mode of operation for block ciphers due to its exceptional performance. In this paper we analyze the NIST standardized version (SP 800-38D) of GCM, and in particular the use of short tag lengths. We show that feedback of successful or unsuccessful forgery attempt is almost always possible, contradicting the NIST assumptions for short tags. We also provide a complexity estimation of Ferguson’s authentication key recovery method on short tags, and suggest several novel improvements to Fergusons’s attacks that significantly reduce the security level for short tags. We show that for many truncated tag sizes; the security levels are far below, not only the current NIST requirement of 112-bit security, but also the old NIST requirement of 80-bit security. We therefore strongly recommend NIST to revise SP 800-38D.

This paper presents a novel framework for the automatic pipelining of AES S-boxes using composite field representations. The framework is capable of finding positions to insert flip-flops in an almost optimal way, resulting in S-boxes with an almost optimal critical path. Our novel method is using memetic algorithms and is shown to be fast, reliable and successful. We demonstrate our framework for composite field S-boxes using a polynomial and a normal basis, respectively. Our results prove that this method should be consulted when an optimal solution is of interest. Besides experimental results with the new memetic algorithms, we also discuss the ideal model of a circuit, which can be used when assessing the quality of the obtained solutions. We emphasize that this method can be used for any circuit of interest and not only for AES S-boxes.

In this paper, we study the behavior of the XOR count distributions under different bases of finite field. XOR count of a field element is a simplified metric to estimate the hardware implementation cost to compute the finite field multiplication of an element. It is an important criterion in the design of lightweight cryptographic primitives, typically to estimate the efficiency of the diffusion layer in a block cipher. Although several works have been done to find lightweight MDS diffusion matrices, to the best of our knowledge, none has considered finding lightweight diffusion matrices under other bases of finite field apart from the conventional polynomial basis. The main challenge for considering different bases for lightweight diffusion matrix is that the number of bases grows exponentially as the dimension of a finite field increases, causing it to be infeasible to check all possible bases. Through analyzing the XOR count distributions and the relationship between the XOR count distributions under different bases, we find that when all possible bases for a finite field are considered, the collection of the XOR count distribution is invariant to the choice of the irreducible polynomial of the same degree. In addition, we can partition the set of bases into equivalence classes, where the XOR count distribution is invariant in an equivalence class, thus when changing bases within an equivalence class, the XOR count of a diffusion matrix will be the same. This significantly reduces the number of bases to check as we only need to check one representative from each equivalence class for lightweight diffusion matrices. The empirical evidence from our investigation says that the bases which are in the equivalence class of the polynomial basis are the recommended choices for constructing lightweight MDS diffusion matrices.

Zk-SNARKs (succinct non-interactive zero-knowledge arguments of knowledge) are needed in many applications. Unfortunately, all previous zk-SNARKs for interesting languages are either inefficient for the prover, or are non-adaptive and based on a commitment scheme that depends both on the prover’s input and on the language, i.e., they are not commit-and-prove (CaP) SNARKs. We propose a proof-friendly extractable commitment scheme, and use it to construct prover-efficient adaptive CaP succinct zk-SNARKs for different languages, that can all reuse committed data. In new zk-SNARKs, the prover computation is dominated by a linear number of cryptographic operations. We use batch-verification to decrease the verifier’s computation; importantly, batch-verification can be used also in QAP-based zk-SNARKs.

We propose a computationally secure and non-interactive verifiable secret sharing scheme that can be efficiently constructed from any monotone Boolean circuit. By non-interactive we mean that the dealer needs to be active only once, where he posts a public message as well as a private message to each shareholder. In the random oracle model, we can even avoid interaction between shareholders. By efficient, we mean that we avoid generic zero-knowledge techniques. Such efficient constructions were previously only known from linear secret sharing schemes (LSSS). It is believed that the class of access structures that can be handled with polynomial size LSSS is incomparable to the class that can be recognized by polynomial size monotone circuits, so in this sense we extend the class of access structures with efficient and non-interactive VSS.

We present actively secure multi-party computation of the Advanced Encryption Standard (AES). To the best of our knowledge it is the fastest of its kind to date. We start from an efficient actively secure evaluation of general binary circuits that was implemented by the authors of [DLT14]. They presented an optimized implementation of the so-called MiniMac protocol [DZ13] that runs in the pre-processing model, and applied this to a binary AES circuit. In this paper we describe how to dedicate the pre-processing to the structure of AES, which improves significantly the throughput and latency of previous actively secure implementations. We get a latency of about 6 ms and amortised time about 0.4 ms per AES block, which seems completely adequate for practical applications such as verification of 1-time passwords.

For many applications of secure multiparty computation it is natural to demand that the output of the protocol is verifiable. Verifiability should ensure that incorrect outputs are always rejected, even if all parties executing the secure computation collude. Since the inputs to a secure computation are private, and potentially the outputs are private as well, adding verifiability is in general hard and costly.

In this paper we focus on privacy-preserving linear programming as a typical and practically relevant case for verifiable secure multiparty computation. We introduce certificate validation as an effective technique for achieving verifiable linear programming. Rather than verifying the computation proper, which involves many iterations of the simplex algorithm, we extend the output of the secure computation with a certificate. The certificate allows for efficient and direct validation of the correctness of the output. The overhead incurred by the computation of the certificate is marginal. For the validation of a certificate we design particularly efficient distributed-prover zero-knowledge proofs, fully exploiting the fact that we can use ElGamal encryption for this purpose, hence avoiding the use of more elaborate cryptosystems such as Paillier encryption.

We also formulate appropriate security definitions for our approach, and prove security for our protocols in this model, paying special attention to ensuring properties such as input independence. By means of several experiments performed in a real multi-cloud-provider environment, we show that the overall performance for verifiable linear programming is very competitive, incurring minimal overhead compared to protocols providing no correctness guarantees at all.

In most password-based authentication protocols, the server owns a value, the so-called verifier, that depends on the registered password. This verifier is often a one-way function of the password. Despite this protection, an unauthorized person who gets access to the verifier can mount a brute-force attack to recover the password. If the entropy of the password is low, which is often the case in practice, such an attack might be successful. Motivated by the growing need to face databases compromises, we propose a two-factor password-based authentication protocol where no information about the password leak from the server’s side nor from the client’s side, and where the password is not sent to the server when the user authenticates. During the registration, a user gets a value, called the token, while the server records the verifier. Our security model ensures that brute-force attacks are impossible if the server is compromised. Moreover, only on-line attempts are possible if a token is stolen. The solutions that we describe fit well into scenarios where the token is stored on a mobile phone. We provide constructions, proven secure in the random-oracle model, under standard assumptions.

The only known way to achieve Attribute-based Fully Homomorphic Encryption (ABFHE) is through indistinguishability obfuscation. The best we can do at the moment without obfuscation is Attribute-Based Leveled FHE which allows circuits of an a priori bounded depth to be evaluated. This has been achieved from the Learning with Errors (LWE) assumption. However we know of no other way without obfuscation of constructing a scheme that can evaluate circuits of unbounded depth. In this paper, we present an ABFHE scheme that can evaluate circuits of unbounded depth but with one limitation: there is a bound N on the number of inputs that can be used in a circuit evaluation. The bound N could be thought of as a bound on the number of independent senders. Our scheme allows N to be exponentially large so we can set the parameters so that there is no limitation on the number of inputs in practice. Our construction relies on multi-key FHE and leveled ABFHE, both of which have been realized from LWE, and therefore we obtain a concrete scheme that is secure under LWE.

Providing an efficient revocation mechanism for attribute-based encryption (ABE) is of utmost importance since over time a user’s credentials may be revealed or expired. All previously known revocable ABE (RABE) constructions (a) essentially utilize the complete subtree (CS) scheme for revocation purpose, (b) are restricted in the sense that the size of the public parameters depends linearly on the size of the attribute universe and logarithmically on the number of users in the system, and (c) are either selectively secure, which seems unrealistic in a dynamic system such as RABE, or fully secure but built in a composite order bilinear group setting, which results in high computational cost. This paper presents the first adaptively secure unrestricted RABE using subset difference (SD) mechanism for revocation which greatly improves the broadcast efficiency compared to the CS scheme. Our RABE scheme is built on a prime order bilinear group setting resulting in practical computation cost, and its security depends on the Decisional Linear assumption.