Tightly SIM-SO-CCA Secure Public Key Encryption from Standard Assumptions

Selective opening security (SO security) is desirable for public key encryption (PKE) in a multi-user setting. {In a selective opening attack, an adversary receives a number of ciphertexts for possibly correlated messages, then it opens a subset of them and gets the corresponding messages together with the randomnesses used in the encryptions. SO security aims at providing security for the unopened ciphertexts.} Among the existing simulation-based, selective opening, chosen ciphertext secure (SIM-SO-CCA secure) PKEs, only one (Libert et al. Crypto\u2717) enjoys tight security, which is reduced to the Non-Uniform LWE assumption. However, their public key and ciphertext are not compact. In this work, we focus on constructing PKE with tight SIM-SO-CCA security based on standard assumptions. We formalize security notions needed for key encapsulation mechanism (KEM) and show how to transform these securities into SIM-SO-CCA security of PKE through a tight security reduction, while the construction of PKE from KEM follows the general framework proposed by Liu and Paterson (PKC\u2715). We present two KEM constructions with tight securities based on the Matrix Decision Diffie-Hellman assumption. These KEMs in turn lead to two tightly SIM-SO-CCA secure PKE schemes. One of them enjoys not only tight security but also compact public key

Generic Constructions of Compact and Tightly Selective-Opening Secure Public-key Encryption Schemes

We propose two generic constructions of public-key encryption (PKE) with tight simulation-based selective-opening security against chosen-ciphertext attacks (SIM-SO-CCA) in the random oracle model. Our constructions can be instantiated with a small constant number of elements in the ciphertext, ignoring smaller contributions from symmetric-key encryption. That is, they have compact ciphertexts. Furthermore, three of our instantiations have compact public keys as well. Known (almost) tightly SIM-SO-CCA secure PKE schemes are due to the work of Lyu et al. (PKC 2018) and Libert et al. (Crypto 2017). They have either linear-size ciphertexts or linear-size public keys. Moreover, they only achieve almost tightness, namely, with security loss depending on the security parameter. In contrast to them, our schemes are the first ones achieving both tight SIM-SO-CCA security and compactness. More precisely, our two generic constructions are: - From Pseudorandom KEM: Our first generic construction is from a key encapsulation mechanism (KEM) with pseudorandom ciphertexts against plaintext-checking attacks. Such a KEM can be constructed directly from the Strong Diffie-Hellman (StDH), Computational DH (CDH), and Decisional DH assumptions. Both their ciphertexts and public keys are compact. Their security loss is a small constant. Interestingly, our CDH-based construction is the first scheme achieving all these advantages based on a weak search assumption. Furthermore, we also give a generic construction of such a KEM, which yields an efficient tightly SIM-SO-CCA PKE from lattices. - From Lossy Encryption: Our second scheme is the well-known Fujisaki-Okamoto transformation. We show that it can turn a lossy encryption scheme into a tightly SIM-SO-CCA secure PKE. This transformation preserves both tightness and compactness of the underlying lossy encryption, which is in contrast to the non-tight proof of Heuer et al. (PKC 2015)

Cryptology in the Crowd

Uhell skjer: Kanskje mistet du nøkkelen til huset, eller hadde PIN-koden til innbruddsalarmen skrevet på en dårlig plassert post-it lapp. Og kanskje endte de slik opp i hendene på feil person, som nå kan påføre livet ditt all slags ugagn: Sikkerhetssystemer gir ingen garantier når nøkler blir stjålet og PIN-koder lekket. Likevel burde naboen din, hvis nøkkel-og-PIN-kode rutiner er heller vanntette, kunne føle seg trygg i vissheten om at selv om du ikke evner å sikre huset ditt mot innbrudd, så forblir deres hjem trygt. Det er tilsvarende for kryptologi, som også lener seg på at nøkkelmateriale hemmeligholdes for å kunne garantere sikkerhet: Intuitivt forventer man at kjennskap til ett systems hemmelige nøkkel ikke burde være til hjelp for å bryte inn i andre, urelaterte systemer. Men det har vist seg overraskende vanskelig å sette denne intuisjonen på formell grunn, og flere konkurrerende sikkerhetsmodeller av varierende styrke har oppstått. Det blir dermed naturlig å spørre seg: Hvilken formalisme er den riktige når man skal modellere realistiske scenarioer med mange brukere og mulige lekkasjer? Eller: hvordan bygger man kryptografi i en folkemengde? Artikkel I begir seg ut på reisen mot et svar ved å sammenligne forskjellige flerbrukervarianter av sikkerhetsmodellen IND-CCA, med og uten evnen til å motta hemmelige nøkler tilhørende andre brukere. Vi finner et delvis svar ved å vise at uten denne evnen, så er noen modeller faktisk å foretrekke over andre. Med denne evnen, derimot, forblir situasjonen uavklart. Artikkel II tar et sidesteg til et sett relaterte sikkerhetsmodeller hvor, heller enn å angripe én enkelt bruker (ut fra en mengde av mulige ofre), angriperen ønsker å bryte kryptografien til så mange brukere som mulig på én gang. Man ser for seg en uvanlig mektig motstander, for eksempel en statssponset aktør, som ikke har problemer med å bryte kryptografien til en enkelt bruker: Målet skifter dermed fra å garantere trygghet for alle brukerne, til å gjøre masseovervåking så vanskelig som mulig, slik at det store flertall av brukere kan forbli sikret. Artikkel III fortsetter der Artikkel I slapp ved å sammenligne og systematisere de samme IND-CCA sikkerhetsmodellene med en større mengde med sikkerhetsmodeller, med det til felles at de alle modellerer det samme (eller lignende) scenarioet. Disse modellene, som går under navnene SOA (Selective Opening Attacks; utvalgte åpningsangrep) og NCE (Non-Committing Encryption; ikke-bindende kryptering), er ofte vesentlig sterkere enn modellene studert i Artikkel I. Med et system på plass er vi i stand til å identifisere en rekke hull i litteraturen; og dog vi tetter noen, etterlater vi mange som åpne problemer.Accidents happen: you may misplace the key to your home, or maybe the PIN to your home security system was written on an ill-placed post-it note. And so they end up in the hands of a bad actor, who is then granted the power to wreak all kinds of havoc in your life: the security of your home grants no guarantees when keys are stolen and PINs are leaked. Nonetheless your neighbour, whose key-and-pin routines leave comparatively little to be desired, should feel safe that just because you can’t keep your house safe from intruders, their home remains secured. It is likewise with cryptography, whose security also relies on the secrecy of key material: intuitively, the ability to recover the secret keys of other users should not help an adversary break into an uncompromised system. Yet formalizing this intuition has turned out tricky, with several competing notions of security of varying strength. This begs the question: when modelling a real-world scenario with many users, some of which may be compromised, which formalization is the right one? Or: how do we build cryptology in a crowd? Paper I embarks on the quest to answer the above questions by studying how various notions of multi-user IND-CCA compare to each other, with and without the ability to adaptively compromise users. We partly answer the question by showing that, without compromise, some notions of security really are preferable over others. Still, the situation is left largely open when compromise is accounted for. Paper II takes a detour to a related set of security notions in which, rather than attacking a single user, an adversary seeks to break the security of many. One imagines an unusually powerful adversary, for example a state-sponsored actor, for whom brute-forcing a single system is not a problem. Our goal then shifts from securing every user to making mass surveillance as difficult as possible, so that the vast majority of uncompromised users can remain secure. Paper III picks up where Paper I left off by comparing and systemizing the same security notions with a wider array of security notions that aim to capture the same (or similar) scenarios. These notions appear under the names of Selective Opening Attacks (SOA) and Non-Committing Encryption (NCE), and are typically significantly stronger than the notions of IND-CCA studied in Paper I. With a system in place, we identify and highlight a number of gaps, some of which we close, and many of which are posed as open problems.Doktorgradsavhandlin

SoK: Public Key Encryption with Openings

When modelling how public key encryption can enable secure communication, we should acknowledge that secret information, such as private keys or the randomness used for encryption, could become compromised. Intuitively, one would expect unrelated communication to remain secure, yet formalizing this intuition has proven challenging. Several security notions have appeared that aim to capture said scenario, ranging from the multi-user setting with corruptions, via selective opening attacks (SOA), to non-committing encryption (NCE). Remarkably, how the different approaches compare has not yet been systematically explored. We provide a novel framework that maps each approach to an underlying philosophy of confidentiality: indistinguishability versus simulatability based, each with an a priori versus an a posteriori variant, leading to four distinct philosophies. In the absence of corruptions, these notions are largely equivalent; yet, in the presence of corruptions, they fall into a hierarchy of relative strengths, from IND-CPA and IND-CCA at the bottom, via indistinguishability SOA and simulatability SOA, to NCE at the top. We provide a concrete treatment for the four notions, discuss subtleties in their definitions and asymptotic interpretations and identify limitations of each. Furthermore, we re-cast the main implications of the hierarchy in a concrete security framework, summarize and contextualize other known relations, identify open problems, and close a few gaps. We end on a survey of constructions known to achieve the various notions. We identify and name a generic random-oracle construction that has appeared in various guises to prove security in seemingly different contexts. It hails back to Bellare and Rogaway\u27s seminal work on random oracles (CCS\u2793) and, as previously shown, suffices to meet one of the strongest notions of our hierarchy (single-user NCE with bi-openings)

Almost-tight Identity Based Encryption against Selective Opening Attack

The paper presented an identity based encryption (IBE) under selective opening attack (SOA) whose security is almost-tightly related to a set of computational assumptions. Our result is a combination of Bellare, Waters, and Yilek\u27s method [TCC, 2011] for constructing (not tightly) SOA secure IBE and Hofheinz, Koch, and Striecks\u27 technique [PKC, 2015] on building almost-tightly secure IBE in the multi-ciphertext setting. In particular, we first tuned Bellare et al.\u27s generic construction for SOA secure IBE to show that a one-bit IBE achieving ciphertext indistinguishability under chosen plaintext attack in the multi-ciphertext setting (with one-sided publicly openability) tightly implies a multi-bit IBE secure under selective opening attack. Next, we almost-tightly reduced such a one-bit IBE to static assumptions in the composite-order bilinear groups employing the technique of Hofheinz et al. This yielded the first SOA secure IBE with almost-tight reduction

Anonymous Public Key Encryption under Corruptions

Anonymity of public key encryption (PKE) requires that, in a multi-user scenario, the PKE ciphertexts do not leak information about which public keys are used to generate them. Corruptions are common threats in the multi-user scenario but anonymity of PKE under corruptions is less studied in the literature. In TCC 2020, Benhamouda et al. first provide a formal characterization for anonymity of PKE under a specific type of corruption. However, no known PKE scheme is proved to meet their characterization. To the best of our knowledge, all the PKE application scenarios which require anonymity also require confidentiality. However, in the work by Benhamouda et al., different types of corruptions for anonymity and confidentiality are considered, which can cause security pitfalls. What\u27s worse, we are not aware of any PKE scheme which can provide both anonymity and confidentiality under the same types of corruptions. In this work, we introduce a new security notion for PKE called ANON-RSO$_k\&$C security, capturing anonymity under corruptions. We also introduce SIM-RSO$_k\&$C security which captures confidentiality under the same types of corruptions. We provide a generic framework of constructing PKE scheme which can achieve the above two security goals simultaneously based on a new primitive called key and message non-committing encryption (KM-NCE). Then we give a general construction of KM-NCE utilizing a variant of hash proof system (HPS) called Key-Openable HPS. We also provide Key-Openable HPS instantiations based on the matrix decisional Diffie-Hellman assumption. Therefore, we can obtain various concrete PKE instantiations achieving the two security goals in the standard model with compact ciphertexts. Furthermore, for some PKE instantiation, its security reduction is tight

Selective Opening Security in the Quantum Random Oracle Model, Revisited

We prove that two variants of the Fujisaki-Okamoto (FO) transformations are selective opening secure (SO) against chosen-ciphertext attacks in the quantum random oracle model (QROM), assuming that the underlying public-key encryption scheme is one-way secure against chosen-plaintext attacks (OW-CPA). The two variants we consider are $\mathsf{FO}^{\not{\bot}}$ (Hofheinz, Hövelmanns, and Kiltz, TCC 2017) and $\mathsf{U}^{\not{\bot}}_\mathsf{m}$ (Jiang et al., CRYPTO 2018). This is the first correct proof in the QROM. The previous work of Sato and Shikata (IMACC 2019) showed the SO security of $\mathsf{FO}^{\not{\bot}}$ in the QROM. However, we identify a subtle gap in their work. To close this gap, we propose a new framework that allows us to adaptively reprogram a QRO with respect to multiple queries that are computationally hard to predict. This is a property that can be easily achieved by the classical ROM, but is very hard to achieve in the QROM. Hence, our framework brings the QROM closer to the classical ROM. Under our new framework, we construct the first tightly SO secure PKE in the QROM using lossy encryption. Our final application is proving $\mathsf{FO}^{\not{\bot}}$ and $\mathsf{U}^{\not{\bot}}_\mathsf{m}$ are bi-selective opening (Bi-SO) secure in the QROM. This is a stronger SO security notion, where an adversary can additionally corrupt some users\u27 secret keys

Simulation-Sound Arguments for LWE and Applications to KDM-CCA2 Security

The Naor-Yung paradigm is a well-known technique that constructs IND-CCA2-secure encryption schemes by means of non-interactive zero-knowledge proofs satisfying a notion of simulation-soundness. Until recently, it was an open problem to instantiate it under the sole Learning-With-Errors (LWE) assumption without relying on random oracles. While the recent results of Canetti {\it et al.} (STOC\u2719) and Peikert-Shiehian (Crypto\u2719) provide a solution to this problem by applying the Fiat-Shamir transform in the standard model, the resulting constructions are extremely inefficient as they proceed via a reduction to an NP-complete problem. In this paper, we give a direct, non-generic method for instantiating Naor-Yung under the LWE assumption outside the random oracle model. Specifically, we give a direct construction of an unbounded simulation-sound NIZK argument system which, for carefully chosen parameters, makes it possible to express the equality of plaintexts encrypted under different keys in Regev\u27s cryptosystem. We also give a variant of our argument that provides tight security. As an application, we obtain an LWE-based public-key encryption scheme for which we can prove (tight) key-dependent message security under chosen-ciphertext attacks in the standard model

Collusion-Resistant Broadcast Encryption with Tight Reductions and Beyond

The issue of tight security for identity-based encryption schemes ($\mathsf{IBE}$) in bilinear groups has been widely investigated and a lot of optimal properties have been achieved. Recently, a tightly secure IBE scheme in bilinear groups under the multi-challenge setting has been achieved by Chen et al. (to appear in PKC 2017), and their scheme even achieves constant-size public parameters and is adaptively secure. However, we note that the issue of tight security for broadcast encryption schemes ($\mathsf{BE}$) in bilinear groups has received less attention so far. Actually current broadcast encryption systems of bilinear groups are either not tightly secure or based on non-static assumptions. In this work we mainly focus on the issue of tight security for standard broadcast encryption schemes \footnote{We utilize the syntax of broadcast encryption schemes under the key-encapsulation setting in this work and it is easy to be transformed into one under the standard setting.}. We construct the \textit{first} tightly secure broadcast encryption scheme from static assumptions (i.e., decisional subgroup assumptions) in the selective security model by utilizing improved techniques derived from the Déjà Q framework (Eurocrypt 2014, TCC-A 2016). The proof of our construction will lead to only $O(\log n)$ or $O(\log \lambda)$ security loss, where $n$ is the number of users in the system and $\lambda$ is the security parameter. Following this result, we present a tightly secure non-zero inner product encryption scheme ($\mathsf{NIPE}$) from decisional subgroup assumptions in the selective security model. This NIPE scheme has the same parameter sizes as our BE scheme and there is only $O(\log n)$ or $O(\log \lambda)$ security loss as well, where $n$ is the dimension of the inner product space and $\lambda$ is the security parameter. Finally, we further present a tightly secure functional commitment scheme ($\mathsf{FC}$) for linear functions, which was introduced by Libert et al. (ICALP 16). In contrast with their scheme, which also suffers $O(n)$ security loss during the reduction, there is only $O(\log n)$ or $O(\log \lambda)$ security loss in our FC scheme

Tightly Secure IBE under Constant-size Master Public Key

International audienceChen and Wee [CRYPTO, 2013] proposed the first almost tightly and adaptively secure IBE in the standard model and left two open problems which called for a tightly secure IBE with (1) constant-size master public key and/or (2) constant security loss. In this paper, we propose an IBE scheme with constant-size master public key and tighter security reduction. This (partially) solves Chen and Wee's first open problem and makes progress on the second one. Technically, our IBE scheme is built based on Wee's petit IBE scheme [TCC, 2016] in the composite-order bilinear group whose order is product of four primes. The sizes of master public key, ciphertexts, and secret keys are not only constant but also nearly optimal as Wee's petit IBE. We can prove its adaptive security in the multi-instance, multi-ciphertext setting [PKC, 2015] based on the decisional subgroup assumption and a subgroup variant of DBDH assumption. The security loss is O(log q) where q is the upper bound of the total number of secret keys and challenge ciphertexts revealed to adversary in each single IBE instance. It's much smaller than those for all known adaptively secure IBE schemes in a concrete sense