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

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)

Towards Black-Box Accountable Authority IBE with Short Ciphertexts and Private Keys

At Crypto'07, Goyal introduced the concept of Accountable Authority Identity-Based Encryption as a convenient tool to reduce the amount of trust in authorities in Identity-Based Encryption. In this model, if the Private Key Generator (PKG) maliciously re-distributes users' decryption keys, it runs the risk of being caught and prosecuted. Goyal proposed two constructions: the first one is efficient but can only trace well-formed decryption keys to their source; the second one allows tracing obfuscated decryption boxes in a model (called weak black-box model) where cheating authorities have no decryption oracle. The latter scheme is unfortunately far less efficient in terms of decryption cost and ciphertext size. In this work, we propose a new construction that combines the efficiency of Goyal's first proposal with a very simple weak black-box tracing mechanism. Our scheme is described in the selective-ID model but readily extends to meet all security properties in the adaptive-ID sense, which is not known to be true for prior black-box schemes.Comment: 32 page

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

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

Short Group Signatures via Structure-Preserving Signatures: Standard Model Security from Simple Assumptions

International audienceGroup signatures are a central cryptographic primitive which allows users to sign messages while hiding their identity within a crowd of group members. In the standard model (without the random oracle idealization), the most efficient constructions rely on the Groth-Sahai proof systems (Euro-crypt'08). The structure-preserving signatures of Abe et al. (Asiacrypt'12) make it possible to design group signatures based on well-established, constant-size number theoretic assumptions (a.k.a. " simple assumptions ") like the Symmetric eXternal Diffie-Hellman or Decision Linear assumptions. While much more efficient than group signatures built on general assumptions, these constructions incur a significant overhead w.r.t. constructions secure in the idealized random oracle model. Indeed, the best known solution based on simple assumptions requires 2.8 kB per signature for currently recommended parameters. Reducing this size and presenting techniques for shorter signatures are thus natural questions. In this paper, our first contribution is to significantly reduce this overhead. Namely, we obtain the first fully anonymous group signatures based on simple assumptions with signatures shorter than 2 kB at the 128-bit security level. In dynamic (resp. static) groups, our signature length drops to 1.8 kB (resp. 1 kB). This improvement is enabled by two technical tools. As a result of independent interest, we first construct a new structure-preserving signature based on simple assumptions which shortens the best previous scheme by 25%. Our second tool is a new method for attaining anonymity in the strongest sense using a new CCA2-secure encryption scheme which is simultaneously a Groth-Sahai commitment