Hybrid Encryption in a Multi-user Setting, Revisited

This paper contributes to understanding the interplay of security notions for PKE, KEMs, and DEMs, in settings with multiple users, challenges, and instances. We start analytically by first studying (a) the tightness aspects of the standard hybrid KEM+DEM encryption paradigm, (b) the inherent weak security properties of all deterministic DEMs due to generic key-collision attacks in the multi-instance setting, and (c) the negative effect of deterministic DEMs on the security of hybrid encryption. We then switch to the constructive side by (d) introducing the concept of an augmented data encapsulation mechanism (ADEM) that promises robustness against multi-instance attacks, (e) proposing a variant of hybrid encryption that uses an ADEM instead of a DEM to alleviate the problems of the standard KEM+DEM composition, and (f) constructing practical ADEMs that are secure in the multi-instance setting

Tightness Subtleties for Multi-user PKE Notions

Public key encryption schemes are increasingly being studied concretely, with an emphasis on tight bounds even in a multi-user setting. Here, two types of formalization have emerged, one with a single challenge bit and one with multiple challenge bits. Another modelling choice is whether to allow key corruptions or not. How tightly the various notions relate to each other has hitherto not been studied in detail. We show that in the absence of corruptions, single-bit left-or-right indistinguishability is the preferred notion, as it tightly implies the other (corruption-less) notions. However, in the presence of corruptions, this implication no longer holds; we suggest the use of a more general notion that tightly implies both existing options. Furthermore, for completeness we study how the relationship between left-or-right versus real-or-random evolves in the multi-user PKE setting

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

Towards post-quantum secure PAKE - A tight security proof for OCAKE in the BPR model

We revisit OCAKE (ACNS 23), a generic recipe that constructs password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEMs) in a black-box way. This allows to potentially achieve post-quantum security by instantiating the KEM with a post-quantum KEM like KYBER. It was left as an open problem to further adapt the proof such that it also holds against quantum attackers. The security proof is given in the universal composability (UC) framework, which is common for PAKE. So far, however, it is not known how to model or prove computational UC security against quantum adversaries, let alone if the proof uses idealized primitives like random oracles or ideal ciphers. To pave the way towards reasoning post-quantum security, we therefore resort to a (still classical) game-based security proof in the BPR model (EUROCRYPT 2000). We consider this a crucial stepping stone towards a full proof of post-quantum security. We prove security of (a minor variation of) OCAKE, assuming the underlying KEM satisfies notions of ciphertext indistinguishability, anonymity, and (computational) public-key uniformity. To achieve tight security bounds, we use multi-user variants of the aforementioned properties. We provide a full detailed proof – something often omitted in publications on game-based security of PAKE. As a side-contribution, we demonstrate in detail how to handle password guesses, which is something we were unable to find in the existing literature on game-based PAKE proofs

Critical Perspectives on Provable Security: Fifteen Years of Another Look Papers

We give an overview of our critiques of “proofs” of security and a guide to our papers on the subject that have appeared over the past decade and a half. We also provide numerous additional examples and a few updates and errata

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)