What a lovely hat

The evasive learning with errors (evasive LWE) assumption is a new assumption recently introduced by Wee (Eurocrypt 2022) and Tsabary (Crypto 2022) independently, as a significant strengthening of the standard LWE assumption. While the assumption is known to imply various strong primitives including witness encryption [Wee22,Tsabary22], the assumption in the most general case (i.e., the private coin variant) is considered quite implausible due to the obfuscation based attack mentioned in...

One-time programs (Goldwasser, Kalai and Rothblum, CRYPTO 2008) are functions that can be run on any single input of a user's choice, but not on a second input. Classically, they are unachievable without trusted hardware, but the destructive nature of quantum measurements seems to provide a quantum path to constructing them. Unfortunately, Broadbent, Gutoski and Stebila showed that even with quantum techniques, a strong notion of one-time programs, similar to ideal obfuscation, cannot be...

We introduce the notion of pseudorandom obfuscation, a way to obfuscate (keyed) pseudorandom functions $f_K$ in an average-case sense. We study several variants of pseudorandom obfuscation and show a number of applications. 1. Applications in the iO World: Our weakest variant of pseudorandom obfuscation, named obfuscation for identical pseudorandom functions (iPRO), is weaker than indistinguishability obfuscation (iO): rather than obfuscating arbitrary circuits as in iO, iPRO only...

This paper introduces a heuristic ideal obfuscation scheme grounded in the lattice problems, which differs from that proposed by Jain, Lin, and Luo ([JLLW23], CRYPTO 2023). The approach in this paper follows a methodology akin to that of Brakerski, Dottling, Garg, and Malavolta ([BDGM20], EUROCRYPT 2020) for building indistinguishable obfuscation (iO). The proposal is achieved by leveraging a variant of learning with rounding (LWR) to build linearly homomorphic encryption (LHE) and employing...

Additive randomized encodings (ARE), introduced by Halevi, Ishai, Kushilevitz, and Rabin (CRYPTO 2023), reduce the computation of a k-party function $f (x_1, . . . , x_k )$ to locally computing encodings $\hat{x}_i$ of each input xi and then adding them together over some Abelian group into an output encoding $\hat{y} = ∑ \hat{x}_i$, which reveals nothing but the result. In robust ARE (RARE) the sum of any subset of $\hat{x}_i$, reveals only the residual function obtained by restricting the...

Addition of $n$ inputs is often the easiest nontrivial function to compute securely. Motivated by several open questions, we ask what can be computed securely given only an oracle that computes the sum. Namely, what functions can be computed in a model where parties can only encode their input locally, then sum up the encodings over some Abelian group $\G$, and decode the result to get the function output. An *additive randomized encoding* (ARE) of a function $f(x_1,\ldots,x_n)$ maps...

Distributed samplers, introduced by Abram, Scholl and Yakoubov (Eurocrypt ’22), are a one-round, multi-party protocol for securely sampling from any distribution. We give new lower and upper bounds for constructing distributed samplers in challenging scenarios. First, we consider the feasibility of distributed samplers with a malicious adversary in the standard model; the only previous construction in this setting relies on a random oracle. We show that for any UC-secure construction in the...

A (single server) private information retrieval (PIR) allows a client to read data from a public database held on a remote server, without revealing to the server which locations she is reading. In a doubly efficient PIR (DEPIR), the database is first preprocessed, but the server can subsequently answer any client's query in time that is sub-linear in the database size. Prior work gave a plausible candidate for a public-key variant of DEPIR, where a trusted party is needed to securely...

We investigate the optimal (asymptotic) efficiency of functional encryption (FE) and attribute-based encryption (ABE) by proving inherent space-time trade-offs and constructing nearly optimal schemes. We consider the general notion of partially hiding functional encryption (PHFE), capturing both FE and ABE, and the most efficient computation model of random-access machines (RAM). In PHFE, a secret key $\mathsf{sk}_f$ is associated with a function $f$, whereas a...

We introduce a new idealized model of hash functions, which we refer to as the *pseudorandom oracle* (${\mathrm{Pr}\mathcal{O}}$) model. Intuitively, it allows us to model cryptosystems that use the code of an ideal hash function in a non-black-box way. Formally, we model hash functions via a combination of a pseudorandom function (PRF) family and an ideal oracle. A user can initialize the hash function by choosing a PRF key $k$ and mapping it to a public handle $h$ using the oracle. ...

We provide counterexamples to the ``dream'' version of Yao's XOR Lemma. In particular, we put forward explicit candidates for hard predicates, such that the advantage of predicting the XOR of many independent copies does not decrease beyond some fixed negligible function, even as the number of copies gets arbitrarily large. We provide two such constructions: 1) Our first construction is in the ideal obfuscation model (alternatively, assuming virtual black-box obfuscation for a concrete...

The goal of anonymous whistleblowing is to publicly disclose a message while at the same time hiding the identity of the sender in a way that even if suspected of being the sender, this cannot be proven. While many solutions to this problem have been proposed over the years, they all require some form of interaction with trusted or non-colluding parties. In this work, we ask whether this is fundamentally inherent. We put forth the notion of anonymous transfer as a primitive allowing to...

In a witness encryption scheme, to decrypt a ciphertext associated with an NP statement, the decrypter takes as input a witness testifying that the statement is in the language. When the statement is not in the language, then the message is hidden. Thus far, the only provably secure constructions assume the existence of indistinguishability obfuscation (iO) and multilinear maps (MMaps). We make progress towards building polynomially efficient witness encryption for NP without resorting to...

Non-committing encryption (NCE) is a type of public key encryption which comes with the ability to equivocate ciphertexts to encryptions of arbitrary messages, i.e., it allows one to find coins for key generation and encryption which ``explain'' a given ciphertext as an encryption of any message. NCE is the cornerstone to construct adaptively secure multiparty computation [Canetti et al. STOC'96] and can be seen as the quintessential notion of security for public key encryption to realize...

A proof of replication system is a cryptographic primitive that allows a server (or group of servers) to prove to a client that it is dedicated to storing multiple copies or replicas of a file. Until recently, all such protocols required fined-grained timing assumptions on the amount of time it takes for a server to produce such replicas. Damgård, Ganesh, and Orlandi (CRYPTO' 19) proposed a novel notion that we will call proof of replication with client setup. Here, a client first operates...

We propose a candidate ciphertext-policy attribute-based encryption (CP-ABE) scheme for circuits, where the ciphertext size depends only on the depth of the policy circuit (and not its size). This, in particular, gives us a Broadcast Encryption (BE) scheme where the size of the keys and ciphertexts have a poly-logarithmic dependence on the number of users. This goal was previously only known to be achievable assuming ideal multilinear maps (Boneh, Waters and Zhandry, Crypto 2014) or...

In a Single Secret Leader Election (SSLE), a group of participants aim to randomly choose exactly one leader from the group with the restriction that the identity of the leader will be known to the chosen leader and nobody else. At a later time, the elected leader should be able to publicly reveal her identity and prove that she has won the election. The election process itself should work properly even if many registered users are passive and do not send any messages. Among the many...

Among numerous applications, besides cryptocurrencies, the Blockchain offers inherent properties beneficial for the management of supply chains, where data is shared between trusted and untrusted parties. Electronics supply chain serves as a prime example of such chains, where one of the major players, i.e., a foundry, can be untrusted. Hardware obfuscation techniques, namely logic locking, and IC camouflaging have been developed to mislead an adversary aiming at reverse- engineering and...

We present a new cryptanalytic algorithm on obfuscations based on GGH15 multilinear map. Our algorithm, statistical zeroizing attack, directly distinguishes two distributions from obfuscation while it follows the zeroizing attack paradigm, that is, it uses evaluations of zeros of obfuscated programs. Our attack breaks the recent indistinguishability obfuscation candidate suggested by Chen et al. (CRYPTO'18) for the optimal parameter settings. More precisely, we show that there are two...

We initiate the study of computational problems on elliptic curve isogeny graphs defined over RSA moduli. We conjecture that several variants of the neighbor-search problem over these graphs are hard, and provide a comprehensive list of cryptanalytic attempts on these problems. Moreover, based on the hardness of these problems, we provide a construction of groups with infeasible inversion, where the underlying groups are the ideal class groups of imaginary quadratic orders. Recall that in a...

Constructing indistinguishability obfuscation (iO) [BGI+01] is a central open question in cryptography. We provide new methods to make progress towards this goal. Our contributions may be summarized as follows: 1. {\textbf Bootstrapping}. In a recent work, Lin and Tessaro [LT17] (LT) show that iO may be constructed using i) Functional Encryption (FE) for polynomials of degree $L$ , ii) Pseudorandom Generators (PRG) with blockwise locality $L$ and polynomial expansion, and iii) Learning With...

We present a quantum polynomial time attack against the GMMSSZ branching program obfuscator of Garg et al. (TCC'16), when instantiated with the GGH13 multilinear map of Garg et al. (EUROCRYPT'13). This candidate obfuscator was proved secure in the weak multilinear map model introduced by Miles et al. (CRYPTO'16). Our attack uses the short principal ideal solver of Cramer et al. (EUROCRYPT'16), to recover a secret element of the GGH13 multilinear map in quantum polynomial time. We then use...

The notion of Functional Encryption (FE) has recently emerged as a strong primitive with several exciting applications. In this work, we initiate the study of the following question: Can existing public key encryption schemes be ``upgraded'' to Functional Encryption schemes without changing their public keys or the encryption algorithm? We call a public-key encryption with this property to be FE-compatible. Indeed, assuming ideal obfuscation, it is easy to see that every CCA-secure...

Recently, Albrecht, Davidson and Larraia described a variant of the GGH13 without ideals and presented the distinguishing attacks in simplified branching program security model. Their result partially demonstrates that there seems to be a structural defect in the GGH13 encoding that is not related to the ideal $\langle g \rangle$. However, it is not clear whether a variant of the CGH attack described by Chen, Gentry and Halevi can be used to break a branching program obfuscator instantiated...

All known multilinear map candidates have suffered from a class of attacks known as ``zeroizing'' attacks, which render them unusable for many applications. We provide a new construction of polynomial-degree multilinear maps and show that our scheme is provably immune to zeroizing attacks under a strengthening of the Branching Program Un-Annihilatability Assumption (Garg et al., TCC 2016-B). Concretely, we build our scheme on top of the CLT13 multilinear maps (Coron et al., CRYPTO 2013). ...

We investigate the merits of altering the Garg, Gentry and Halevi (GGH13) graded encoding scheme to remove the presence of the ideal \(\langle g \rangle\). In particular, we show that we can alter the form of encodings so that effectively a new \(g_i\) is used for each source group \(\mathbb{G}_i\), while retaining correctness. This would appear to prevent all known attacks on indistinguishability obfuscation (IO) candidates instantiated using GGH13. However, when analysing security in...

We consider the following strong variant of private information retrieval (PIR). There is a large database x that we want to make publicly available. To this end, we post an encoding X of x together with a short public key pk in a publicly accessible repository. The goal is to allow any client who comes along to retrieve a chosen bit x_i by reading a small number of bits from X, whose positions may be randomly chosen based on i and pk, such that even an adversary who can fully observe the...

At EUROCRYPT 2013, Garg, Gentry and Halevi proposed a candidate construction (later referred as GGH13) of cryptographic multilinear map (MMap). Despite weaknesses uncovered by Hu and Jia (EUROCRYPT 2016), this candidate is still used for designing obfuscators. The naive version of the GGH13 scheme was deemed susceptible to averaging attacks, i.e., it could suffer from a statistical leak (yet no precise attack was described). A variant was therefore devised, but it remains heuristic....

In this work, we present a new obfuscator using a Graded Encoding Scheme (GES) with a binary slot. We characterize a class of circuits taking locally keyed input (each input bit of the circuit is a keyed function over c>1 bits of a binary-variable vector X of length n, where c is called the locality), called ideal functions, such that any function of algebraic degree d (called d-function) over them, can be obfuscated with multilinearity \mu=(d+1)n/c. Next we show that obfuscation of a...

Succinct non-interactive arguments (SNARGs) enable verifying NP computations with substantially lower complexity than that required for classical NP verification. In this work, we first construct a lattice-based SNARG candidate with quasi-optimal succinctness (where the argument size is quasilinear in the security parameter). Further extension of our methods yields the first SNARG (from any assumption) that is quasi-optimal in terms of both prover overhead (polylogarithmic in the security...

We describe new cryptanalytic attacks on the candidate branching program obfuscator proposed by Garg, Gentry, Halevi, Raykova, Sahai and Waters (GGHRSW) using the GGH13 graded encoding, and its variant using the GGH15 graded encoding as specified by Gentry, Gorbunov and Halevi. All our attacks require very specific structure of the branching programs being obfuscated, which in particular must have some input-partitioning property. Common to all our attacks are techniques to extract...

Functional encryption (FE) has emerged as an outstanding concept. By now, we know that beyond the immediate application to computation over encrypted data, variants with {\em succinct ciphertexts} are so powerful that they yield the full might of indistinguishability obfuscation (IO). Understanding how, and under which assumptions, such succinct schemes can be constructed has become a grand challenge of current research in cryptography. Whereas the first schemes were based themselves on IO,...

We construct a general-purpose indistinguishability obfuscation (IO) scheme for all polynomial-size circuits from {\em constant-degree} graded encoding schemes in the plain model, assuming the existence of a subexponentially secure Pseudo-Random Generator (PRG) computable by constant-degree arithmetic circuits (or equivalently in $\NC^0)$, and the subexponential hardness of the Learning With Errors (LWE) problems. In contrast, previous general-purpose IO schemes all rely on...

We show general transformations from subexponentially-secure approximate indistinguishability obfuscation (IO) where the obfuscated circuit agrees with the original circuit on a $1/2+\epsilon$ fraction of inputs, into exact indistinguishability obfuscation where the obfuscated circuit and the original circuit agree on all inputs (except for a negligible probability over the coin tosses of the obfuscator). As a step towards our results, which is of independent interest, we also obtain an...

The multiple ideal query (MIQ) model was introduced by Goyal, Jain and Ostrovsky [Crypto'10] as a relaxed notion of security which allows one to construct concurrently secure protocols in the plain model. The main question relevant to the MIQ model is how many queries must we allow to the ideal world adversary? The importance of the above question stems from the fact that if the answer is positive, then it would enable meaningful security guarantees in many application scenarios, as well as,...

A celebrated result by Barak et al (JACM’12) shows the impossibility of general-purpose virtual black-box (VBB) obfuscation in the plain model. A recent work by Canetti, Kalai, and Paneth (TCC’15) extends this result also to the random oracle model (assuming trapdoor per- mutations). In contrast, Brakerski-Rothblum (TCC’15) and Barak et al (EuroCrypt’14) show that in idealized graded encoding models, general-purpose VBB obfuscation indeed is possible; these construction require graded...

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are "noisy" and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels. The security of our construction depends on new hardness assumptions.

In the last few years, cryptographic multilinear maps have proved their tremendous potential as building blocks for new constructions, in particular the first viable approach to general program obfuscation. After the first candidate construction by Garg, Gentry and Halevi (GGH) based on ideal lattices, a second construction over the integers was described by Coron, Lepoint and Tibouchi (CLT). However the CLT scheme was recently broken by Cheon et al.; the attack works by computing the...

We present a candidate obfuscator based on composite-order Graded Encoding Schemes (GES), which are a generalization of multilinear maps. Our obfuscator operates on circuits directly without converting them into formulas or branching programs as was done in previous solutions. As a result, the time and size complexity of the obfuscated program, measured by the number of GES elements, is directly proportional to the circuit complexity of the program being obfuscated. This improves upon...

We show that it is possible to upgrade an obfuscator for a weak complexity class $\weak$ into an obfuscator for arbitrary polynomial size circuits, assuming that the class $\weak$ can compute pseudorandom functions. Specifically, under standard intractability assumptions (e.g., hardness of factoring, Decisional Diffie-Hellman, or Learning with Errors), the existence of obfuscators for $\NC^1$ or even $\TC^0$ implies the existence of general-purpose obfuscators for $\classP$. Previously, such...

We show that the class of polynomial-size branching programs can be obfuscated according to a virtual black-box notion akin to that of Barak et al. [Crypto 01], in an idealized black-box group model over pseudo-free groups. This class is known to lie between $NC^1$ and $P$ and includes most interesting cryptographic algorithms. The construction is rather simple and is based on Kilian's randomization technique for Barrington's branching programs. The black-box group model over pseudo-free...