Augmented Random Oracles

We propose a new paradigm for justifying the security of random oracle-based protocols, which we call the Augmented Random Oracle Model (AROM). We show that the AROM captures a wide range of important random oracle impossibility results. Thus a proof in the AROM implies some resiliency to such impossibilities. We then consider three ROM transforms which are subject to impossibilities: Fiat-Shamir (FS), Fujisaki-Okamoto (FO), and Encrypt-with-Hash (EwH). We show in each case how to obtain security in the AROM by strengthening the building blocks or modifying the transform. Along the way, we give a couple other results. We improve the assumptions needed for the FO and EwH impossibilities from indistinguishability obfuscation to circularly secure LWE; we argue that our AROM still captures this improved impossibility. We also demonstrate that there is no best possible hash function, by giving a pair of security properties, both of which can be instantiated in the standard model separately, which cannot be simultaneously satisfied by a single hash function

Lockable Obfuscation

In this paper we introduce the notion of lockable obfuscation. In a lockable obfuscation scheme there exists an obfuscation algorithm $\mathsf{Obf}$ that takes as input a security parameter $\lambda$, a program $P$, a message $\mathsf{msg}$ and ``lock value\u27\u27 $\alpha$ and outputs an obfuscated program $\widetilde{P}$. One can evaluate the obfuscated program $\widetilde{P}$ on any input $x$ where the output of evaluation is the message $\mathsf{msg}$ if $P(x) = \alpha$ and otherwise receives a rejecting symbol $\perp$. We proceed to provide a construction of lockable obfuscation and prove it secure under the Learning with Errors (LWE) assumption. Notably, our proof only requires LWE with polynomial hardness and does not require complexity leveraging. We follow this by describing multiple applications of lockable obfuscation. First, we show how to transform any attribute-based encryption (ABE) scheme into one in which the attributes used to encrypt the message are hidden from any user that is not authorized to decrypt the message. (Such a system is also know as predicate encryption with one-sided security.) The only previous construction due to Gorbunov, Vaikuntanathan and Wee is based off of a specific ABE scheme of Boneh et al. By enabling the transformation of any ABE scheme we can inherent different forms and features of the underlying scheme such as: multi-authority, adaptive security from polynomial hardness, regular language policies, etc. We also show applications of lockable obfuscation to separation and uninstantiability results. We first show how to create new separation results in circular encryption that were previously based on indistinguishability obfuscation. This results in new separation results from learning with error including a public key bit encryption scheme that it IND-CPA secure and not circular secure. The tool of lockable obfuscation allows these constructions to be almost immediately realized by translation from previous indistinguishability obfuscation based constructions. In a similar vein we provide random oracle uninstantiability results of the Fujisaki-Okamoto transformation (and related transformations) from the lockable obfuscation combined with fully homomorphic encryption. Again, we take advantage that previous work used indistinguishability obfuscation that obfuscated programs in a form that could easily be translated to lockable obfuscation

Instantiability of Classical Random-Oracle-Model Encryption Transforms

Extending work leveraging program obfuscation to instantiate random-oracle-based transforms (e.g., Hohenberger et al., EUROCRYPT 2014, Kalai et al., CRYPTO 2017), we show that, using obfuscation and other assumptions, there exist standard-model hash functions that suffice to instantiate the classical RO-model encryption transforms OAEP (Bellare and Rogaway, EUROCRYPT 1994) and Fujisaki-Okamoto (CRYPTO 1999, J. Cryptology 2013) for specific public-key encryption (PKE) schemes to achieve IND-CCA security. Our result for Fujisaki-Okamoto employs a simple modification to the scheme. Our instantiations do not require much stronger assumptions on the base schemes compared to their corresponding RO-model proofs. For example, to instantiate low-exponent RSA-OAEP, the assumption we need on RSA is sub-exponential partial one-wayness, matching the assumption (partial one-wayness) on RSA needed by Fujisaki et al. (J. Cryptology 2004) in the RO model up to sub-exponentiality. For the part of Fujisaki-Okamoto that upgrades public-key encryption satisfying indistinguishability against plaintext checking attack to IND-CCA, we again do not require much stronger assumptions up to sub-exponentiality. We obtain our hash functions in a unified way, extending a technique of Brzuska and Mittelbach (ASIACRYPT 2014). We incorporate into their technique: (1) extremely lossy functions (ELFs), a notion by Zhandry (CRYPTO 2016), and (2) multi-bit auxiliary-input point function obfuscation (MB-AIPO). While MB-AIPO is impossible in general (Brzuska and Mittelbach, ASIACRYPT 2014), we give plausible constructions for the special cases we need, which may be of independent interest

Indistinguishability Obfuscation and UCEs : The Case of Computationally Unpredictable Sources

Random oracles are powerful cryptographic objects. They facilitate the security proofs of an impressive number of practical cryptosystems ranging from KDM-secure and deterministic encryption to point-function obfuscation and many more. However, due to an uninstantiability result of Canetti, Goldreich, and Halevi (STOC 1998) random oracles have become somewhat controversial. Recently, Bellare, Hoang, and Keelveedhi (BHK; CRYPTO 2013 and ePrint 2013/424, August 2013) introduced a new abstraction called Universal Computational Extractors (UCEs), and showed that they suffice to securely replace random oracles in a number of prominent applications, including all those mentioned above, without suffering from the aforementioned uninstantiability result. This, however, leaves open the question of constructing UCEs in the standard model. We show that the existence of indistinguishability obfuscation (iO) implies (non-black-box) attacks on all the definitions that BHK proposed within their UCE framework in the original version of their paper, in the sense that no concrete hash function can satisfy them. We also show that this limitation can be overcome, to some extent, by restraining the class of admissible adversaries via a statistical notion of unpredictability. Following our attack, BHK (ePrint 2013/424, September 2013), independently adopted this approach in their work. In the updated version of their paper, BHK (ePrint 2013/424, September 2013) also introduce two other novel source classes, called bounded parallel sources and split sources, which aim at recovering the computational applications of UCEs that fall outside the statistical fix. These notions keep to a computational notion of unpredictability, but impose structural restrictions on the adversary so that our original iO attack no longer applies. We extend our attack to show that indistinguishability obfuscation is sufficient to also break the UCE security of any hash function against bounded parallel sources. Towards this goal, we use the randomized encodings paradigm of Applebaum, Ishai, and Kushilevitz (STOC 2004) to parallelize the obfuscated circuit used in our attack, so that it can be computed by a bounded parallel source whose second stage consists of constant-depth circuits. BHK, in the latest version of their paper (ePrint 2013/424, May 2014), have subsequently replace bounded parallel sources with new source classes. We conclude by discussing the composability and feasibility of hash functions secure against split sources

A Unified Approach to Idealized Model Separations via Indistinguishability Obfuscation

It is well known that the random oracle model is not sound in the sense that there exist cryptographic systems that are secure in the random oracle model but when instantiated by any family of hash functions become insecure. However, all known separation results require the attacker to send an appropriately crafted message to the challenger in order to break security. Thus, this leaves open the possibility that some cryptographic schemes, such as bit-encryption, are still sound in the random oracle model. In this work we refute this possibility, assuming the existence of indistinguishability obfuscation. We do so in the following way. First, we present a random oracle separation for bit-encryption; namely, we show that there exists a bit-encryption protocol secure in the random oracle model but \emph{completely insecure} when the random oracle is instantiated by any concrete function. Second, we show how to adapt this separation to work for most natural simulation-based and game-based definitions. Our techniques can easily be adapted to other idealized models, and thus we present a \emph{unified approach} to showing separations for most protocols of interest in most idealized models

COA-Secure Obfuscation and Applications

We put forth a new paradigm for program obfuscation, where obfuscated programs are endowed with proofs of ``well-formedness.\u27\u27 In addition to asserting existence of an underlying plaintext program with an attested structure and functionality, these proofs also prevent mauling attacks, whereby an adversary surreptitiously creates an obfuscated program based on secrets which are embedded in a given obfuscated program. We call this new guarantee Chosen Obfuscation Attack (COA) security. We define and construct general-purpose COA-secure Probabilistic Indistinguishability Obfuscators for circuits, assuming sub-exponential IO for circuits and CCA commitments. To demonstrate the power of the new notion, we use it to realize, in the plain model: - Structural Watermarking, which is a new form of software watermarking that provides significantly broader protection than current schemes and features a keyless, public verification process. - Completely CCA encryption, which is a strengthening of completely non-malleable encryption. We also show, based on the same assumptions, a generic method for enhancing any obfuscation mechanism that guarantees any semantic-style form of hiding to one that provides also COA security

New Random Oracle Instantiations from Extremely Lossy Functions

We instantiate two random oracle (RO) transformations using Zhandry\u27s extremely lossy function (ELF) technique (Crypto\u2716). Firstly, using ELFs and indistinguishabililty obfuscation (iO), we instantiate a modified version of the Fujisaki-Okamoto (FO) transform which upgrades a public-key encryption scheme (PKE) from indistinguishability under chosen plaintext attacks (IND-CPA) to indistinguishability under chosen ciphertext attacks (IND-CCA). We side-step a prior uninstantiability result for FO by Brzuska, Farshim, and Mittelbach (TCC\u2715) by (1) hiding the randomness from the (potentially ill-designed) IND-CPA encryption scheme and (2) embedding an additional secret related to the hash-function into the secret-key of the IND-CCA-secure PKE, an idea brought forward by Murphy, O’Neill, Zaheri (Asiacrypt 2022) who also instantiate a modified FO variant also under ELFs and iO for the class of lossy PKE. Our transformation applies to all PKE which can be inverted given their randomness. Secondly, we instantiate the hash-then-evaluate paradigm for pseudorandom functions (PRFs), $\mathsf{PRF}_\mathsf{new}(k,x):=\mathsf{wPRF}(k,\mathsf{RO}(x))$. Our construction replaces $\mathsf{RO}$ by $\mathsf{PRF}_\mathsf{old}(k_\mathsf{pub},\mathsf{elf}(x))$ with a key $k_\mathsf{pub}$, that, unusually, is known to the distinguishing adversary against $\mathsf{PRF}_\mathsf{new}$. We start by observing that several existing weak PRF candidates are plausibly also secure under such distributions of pseudorandom inputs, generated by $\mathsf{PRF}_\mathsf{old}$. Firstly, analogous cryptanalysis applies and/or an attack with such pseudorandom inputs would imply surprising results such as key agreement from the high-noise version of the Learning Parity with Noise (LPN) assumption. Our simple transformation applies to the entire family of PRF-style functions. Specifically, we obtain results for oblivious PRFs, which are a core building block for password-based authenticated key exchange (PAKE) and private set intersection (PSI) protocols, and we also obtain results for pseudorandom correlation functions (PCF), which are a key tool for silent oblivious transfer (OT) extension

Contention in Cryptoland: Obfuscation, Leakage and UCE

This paper addresses the fundamental question of whether or not different, exciting primitives now being considered actually exist. We show that we, unfortunately, cannot have them all. We provide results of the form not(A) OR not(B), meaning one of the primitives A,B cannot exist. (But we don\u27t know which.) Specifically, we show that: (1) VGBO (Virtual Grey Box Obfuscation) for all circuits, which has been conjectured to be achieved by candidate constructions, cannot co-exist with Canetti\u27s 1997 AI-DHI (auxiliary input DH inversion) assumption, which has been used to achieve many goals including point-function obfuscation (2) iO (indistinguishability obfuscation) for all circuits cannot co-exist with KM-LR-SE (key-message leakage-resilient symmetric encryption) (3) iO cannot co-exist with hash functions that are UCE secure for computationally unpredictable split sources

On the Correlation Intractability of Obfuscated Pseudorandom Functions

A family of hash functions is called ``correlation intractable\u27\u27 if it is hard to find, given a random function in the family, an input-output pair that satisfies any ``sparse\u27\u27 relation, namely any relation that is hard to satisfy for truly random functions. Correlation intractability captures a strong and natural Random Oracle-like property. However, it is widely considered to be unobtainable. Indeed, it was shown that correlation intractable functions do not exist for some length parameters [Canetti, Goldreich and Halevi, J.ACM 04]. Furthermore, no candidate constructions have been proposed in the literature for any setting of the parameters. We construct a correlation intractable function ensemble that withstands all relations with a priori bounded polynomial complexity. We assume the existence of sub-exponentially secure indistinguishability obfuscators, puncturable pseudorandom functions, and input-hiding obfuscators for evasive circuits. The existence of the latter is implied by Virtual-Grey-Box obfuscation for evasive circuits [Bitansky et al, CRYPTO 14]

On Constructing One-Way Permutations from Indistinguishability Obfuscation

We prove that there is no black-box construction of a one-way permutation family from a one-way function and an indistinguishability obfuscator for the class of all oracle-aided circuits, where the construction is domain invariant (i.e., where each permutation may have its own domain, but these domains are independent of the underlying building blocks). Following the framework of Asharov and Segev (FOCS \u2715), by considering indistinguishability obfuscation for oracle-aided circuits we capture the common techniques that have been used so far in constructions based on indistinguishability obfuscation. These include, in particular, non-black-box techniques such as the punctured programming approach of Sahai and Waters (STOC \u2714) and its variants, as well as sub-exponential security assumptions. For example, we fully capture the construction of a trapdoor permutation family from a one-way function and an indistinguishability obfuscator due to Bitansky, Paneth and Wichs (TCC \u2716). Their construction is not domain invariant and our result shows that this, somewhat undesirable property, is unavoidable using the common techniques. In fact, we observe that constructions which are not domain invariant circumvent all known negative results for constructing one-way permutations based on one-way functions, starting with Rudich\u27s seminal work (PhD thesis \u2788). We revisit this classic and fundamental problem, and resolve this somewhat surprising gap by ruling out all such black-box constructions -- even those that are not domain invariant