Low-Complexity Cryptographic Hash Functions

Cryptographic hash functions are efficiently computable functions that shrink a long input into a shorter output while achieving some of the useful security properties of a random function. The most common type of such hash functions is collision resistant hash functions (CRH), which prevent an efficient attacker from finding a pair of inputs on which the function has the same output

SoK: Privacy-Preserving Signatures

Modern security systems depend fundamentally on the ability of users to authenticate their communications to other parties in a network. Unfortunately, cryptographic authentication can substantially undermine the privacy of users. One possible solution to this problem is to use privacy-preserving cryptographic authentication. These protocols allow users to authenticate their communications without revealing their identity to the verifier. In the non-interactive setting, the most common protocols include blind, ring, and group signatures, each of which has been the subject of enormous research in the security and cryptography literature. These primitives are now being deployed at scale in major applications, including Intel\u27s SGX software attestation framework. The depth of the research literature and the prospect of large-scale deployment motivate us to systematize our understanding of the research in this area. This work provides an overview of these techniques, focusing on applications and efficiency

Secure equality testing protocols in the two-party setting

Protocols for securely testing the equality of two encrypted integers are common building blocks for a number of proposals in the literature that aim for privacy preservation. Being used repeatedly in many cryptographic protocols, designing efficient equality testing protocols is important in terms of computation and communication overhead. In this work, we consider a scenario with two parties where party A has two integers encrypted using an additively homomorphic scheme and party B has the decryption key. Party A would like to obtain an encrypted bit that shows whether the integers are equal or not but nothing more. We propose three secure equality testing protocols, which are more efficient in terms of communication, computation or both compared to the existing work. To support our claims, we present experimental results, which show that our protocols achieve up to 99% computation-wise improvement compared to the state-of-the-art protocols in a fair experimental set-up

Extension Field Cancellation: a New Central Trapdoor for Multivariate Quadratic Systems

This paper introduces a new central trapdoor for multivariate quadratic (MQ) public-key cryptosystems that allows for encryption, in contrast to time-tested MQ primitives such as Unbalanced Oil and Vinegar or Hidden Field Equations which only allow for signatures. Our construction is a mixed-field scheme that exploits the commutativity of the extension field to dramatically reduce the complexity of the extension field polynomial implicitly present in the public key. However, this reduction can only be performed by the user who knows concise descriptions of two simple polynomials, which constitute the private key. After applying this transformation, the plaintext can be recovered by solving a linear system. We use the minus and projection modifiers to inoculate our scheme against known attacks. A straightforward C++ implementation confirms the efficient operation of the public key algorithms

Another Look at the Cost of Cryptographic Attacks

This paper makes the case for considering the cost of cryptographic attacks as the main measure of their efficiency, instead of their time complexity. This allows, in our opinion, a more realistic assessment of the "risk" these attacks represent. This is half-and-half a position and a technical paper. Cryptographic attacks described in the literature are rarely implemented. Most exist only "on paper", and their main characteristic is that their estimated time complexity is small enough to break a given security property. However, when a cryptanalyst actually considers implementing an attack, she soon realizes that there is more to the story than time complexity. For instance, Wiener has shown that breaking the double-DES costs 2 6n/5 , asymptotically more than exhaustive search on n bits. We put forward the asymptotic cost of cryptographic attacks as a measure of their practicality. We discuss the shortcomings of the usual computational model and propose a simple abstract cryptographic machine on which it is easy to estimate the cost. We then study the asymptotic cost of several relevant algorithm: collision search, the three-list birthday problem (3XOR) and solving multivariate quadratic polynomial equations. We find that some smart algorithms cost much more than what their time complexity suggest, while naive and simple algorithms may cost less. Some algorithms can be tuned to reduce their cost (this increases their time complexity). Foreword A celebrated High Performance Computing paper entitled "Hitting the Memory Wall: Implications of the Obvious" [47] opens with these words: This brief note points out something obvious-something the authors "knew" without really understanding. With apologies to those who did understand, we offer it to those others who, like us, missed the point. We would like to do the same-but this note is not so short

PFE: Linear Active Security, Double-Shuffle Proofs, and Low-Complexity Communication

We consider private function evaluation (PFE) in malicious adversary model. Current state-of-the-art in PFE from Valiant\u27s universal circuits (Liu, Yu, et al., CRYPTO 2021) does not avoid the logarithmic factor in circuit size. In constructing linear active PFE, one essential building block is to prove the correctness of an extended permutation (EP, Mohassel and Sadeghian at EUROCRYPT 2013) by zero-knowledge protocols with linear complexity. The linear instantiation $\mathcal{ZK}_{EP}$ by Mohassel, Sadeghian, and Smart (ASIACRYPT 2014) is a three-phase protocol, and each phase (dummy placement, replication, and permutation) is of size $2g$. Its overhead thus seems really outrageous, reducing its practicability. We present in this paper a novel and efficient framework $\mathcal{ZK}_{DS}$ for proving the correct EP. We show that \underline{d}ouble \underline{s}huffles suffice for EP (exponentiations and communication overheads are about 27% and 31% of $\mathcal{ZK}_{EP}$, respectively). Data owner(s) generates the randomness for the first shuffle whose outputs determine outgoing wires of the circuit defined by the function. Function owner reuses and extends the randomness in the second shuffle whose outputs determine the incoming wires. From $\mathcal{ZK}_{DS}$, we build an online/offline PFE framework with linear active security. The online phase could be instantiated by any well-studied secure function evaluation (SFE) with linear active security (e.g., Tiny-OT at CRYPTO 2012). The offline phase depends only on the private function $f$ and uses $\mathcal{ZK}_{DS}$ to prove the EP relationship between outgoing wires and incoming wires in the circuit $\mathcal{C}_f$ derived from $f$

Randomness Recoverable Secret Sharing Schemes

It is well-known that randomness is essential for secure cryptography. The randomness used in cryptographic primitives is not necessarily recoverable even by the party who can, e.g., decrypt or recover the underlying secret/message. Several cryptographic primitives that support randomness recovery have turned out useful in various applications. In this paper, we study randomness recoverable secret sharing schemes (RR-SSS), in both information-theoretic and computational settings and provide two results. First, we show that while every access structure admits a perfect RR-SSS, there are very simple access structures (e.g., in monotone AC?) that do not admit efficient perfect (or even statistical) RR-SSS. Second, we show that the existence of efficient computational RR-SSS for certain access structures in monotone AC? implies the existence of one-way functions. This stands in sharp contrast to (non-RR) SSS schemes for which no such results are known. RR-SSS plays a key role in making advanced attributed-based encryption schemes randomness recoverable, which in turn have applications in the context of designated-verifier non-interactive zero knowledge

Faster binary-field multiplication and faster binary-field MACs

This paper shows how to securely authenticate messages using just 29 bit operations per authenticated bit, plus a constant overhead per message. The authenticator is a standard type of "universal" hash function providing information-theoretic security; what is new is computing this type of hash function at very high speed. At a lower level, this paper shows how to multiply two elements of a field of size 2^128 using just 9062 \approx 71 * 128 bit operations, and how to multiply two elements of a field of size 2^256 using just 22164 \approx 87 * 256 bit operations. This performance relies on a new representation of field elements and new FFT-based multiplication techniques. This paper's constant-time software uses just 1.89 Core 2 cycles per byte to authenticate very long messages. On a Sandy Bridge it takes 1.43 cycles per byte, without using Intel's PCLMULQDQ polynomial-multiplication hardware. This is much faster than the speed records for constant-time implementations of GHASH without PCLMULQDQ (over 10 cycles/byte), even faster than Intel's best Sandy Bridge implementation of GHASH with PCLMULQDQ (1.79 cycles/byte), and almost as fast as state-of-the-art 128-bit prime-field MACs using Intel's integer-multiplication hardware (around 1 cycle/byte). Keywords: Performance, FFTs, Polynomial multiplication, Universal hashing, Message authenticatio