Relations among notions of complete non-malleability: indistinguishability characterisation and efficient construction without random oracles

We study relations among various notions of complete non-malleability, where an adversary can tamper with both ciphertexts and public-keys, and ciphertext indistinguishability. We follow the pattern of relations previously established for standard non-malleability. To this end, we propose a more convenient and conceptually simpler indistinguishability-based security model to analyse completely non-malleable schemes. Our model is based on strong decryption oracles, which provide decryptions under arbitrarily chosen public keys. We give the first precise definition of a strong decryption oracle, pointing out the subtleties in different approaches that can be taken. We construct the first efficient scheme, which is fully secure against strong chosen-ciphertext attacks, and therefore completely non-malleable, without random oracles.The authors were funded in part by eCrypt II (EU FP7 - ICT-2007-216646) and FCT project PTDC/EIA/71362/2006. The second author was also funded by FCT grant BPD-47924-2008

Related Randomness Attacks for Public Key Encryption

Abstract. Several recent and high-profile incidents give cause to believe that randomness failures of various kinds are endemic in deployed cryptographic systems. In the face of this, it behoves cryptographic researchers to develop methods to immunise – to the extent that it is possible – cryptographic schemes against such failures. This paper considers the practically-motivated situation where an adversary is able to force a public key encryption scheme to reuse random values, and functions of those values, in encryption computations involving adversarially chosen public keys and messages. It presents a security model appropriate to this situation, along with variants of this model. It also provides necessary conditions on the set of functions used in order to attain this security notation, and demonstrates that these conditions are also sufficient in the Random Oracle Model. Further standard model constructions achieving weaker security notions are also given, with these constructions having interesting connections to other primitives including: pseudo-random functions that are secure in the related key attack setting; Correlated Input Secure hash functions; and public key encryption schemes that are secure in the auxiliary input setting (this being a special type of leakage resilience)

Non-Malleable Functions and Their Applications

We formally study ``non-malleable functions\u27\u27 (NMFs), a general cryptographic primitive which simplifies and relaxes ``non-malleable one-way/hash functions\u27\u27 (NMOWHFs) introduced by Boldyreva et al. (Asiacrypt 2009) and refined by Baecher et al. (CT-RSA 2010). NMFs focus on basic functions, rather than one-way/hash functions considered in the literature of NMOWHFs. We mainly follow Baecher et al. to formalize a game-based definition for NMFs. Roughly, a function $f$ is non-malleable if given an image $y^* \leftarrow f(x^*)$ for a randomly chosen $x^*$, it is hard to output a mauled image $y$ with a transformation $\phi$ from some prefixed transformation class s.t. $y = f(\phi(x^*))$. A distinctive strengthening of our non-malleable notion is that $\phi$ such that $\phi(x^*) = x^*$ is allowed. We also consider adaptive non-malleability, which stipulates that non-malleability holds even when an inversion oracle is available. We investigate the relations between non-malleability and one-wayness in depth. In non-adaptive setting, we show that for any achievable transformation class, non-malleability implies one-wayness for poly-to-one functions but not vise versa.In adaptive setting, we show that for most algebra-induced transformation class, adaptive non-malleability (ANM) is equivalent to adaptive one-wayness (AOW) for injective functions. These results establish theoretical connections between non-malleability and one-wayness for functions, which extend to trapdoor functions as well, and thus resolve the open problems left by Kiltz et al. (Eurocrypt 2010). We also study the relations between standard OW/NM and hinted OW/NM, where the latter notions are typically more useful in practice. Towards efficient realizations of NMFs, we give a deterministic construction from adaptive trapdoor functions and a randomized construction from all-but-one lossy functions and one-time signature. This partially solves an open problem posed by Boldyreva et al. (Asiacrypt 2009). Finally, we explore applications of NMFs in security against related-key attacks (RKA). We first show that the implication AOW $\Rightarrow$ ANM provides key conceptual insight into addressing non-trivial copy attacks in RKA security. We then show that NMFs give rise to a generic construction of continuous non-malleable key derivation functions, which have proven to be very useful in achieving RKA security for numerous cryptographic primitives. Particularly, our construction simplifies and clarifies the construction by Qin et al. (PKC 2015)

The related-key analysis of feistel constructions

Lecture Notes in Computer Science, Volume 8540, 2015.It is well known that the classical three- and four-round Feistel constructions are provably secure under chosen-plaintext and chosen-ciphertext attacks, respectively. However, irrespective of the number of rounds, no Feistel construction can resist related-key attacks where the keys can be offset by a constant. In this paper we show that, under suitable reuse of round keys, security under related-key attacks can be provably attained. Our modification is substantially simpler and more efficient than alternatives obtained using generic transforms, namely the PRG transform of Bellare and Cash (CRYPTO 2010) and its random-oracle analogue outlined by Lucks (FSE 2004). Additionally we formalize Luck’s transform and show that it does not always work if related keys are derived in an oracle-dependent way, and then prove it sound under appropriate restrictions

Careful with Composition: Limitations of Indifferentiability and Universal Composability

We exhibit a hash-based storage auditing scheme which is provably secure in the random-oracle model (ROM), but easily broken when one instead uses typical indifferentiable hash constructions. This contradicts the widely accepted belief that the indifferentiability composition theorem applies to any cryptosystem. We characterize the uncovered limitation of the indifferentiability framework by show- ing that the formalizations used thus far implicitly exclude security notions captured by experiments that have multiple, disjoint adversarial stages. Examples include deterministic public-key encryption (PKE), password-based cryptography, hash function nonmalleability, key-dependent message security, and more. We formalize a stronger notion, reset indifferentiability, that enables an indifferentiability- style composition theorem covering such multi-stage security notions, but then show that practical hash constructions cannot be reset indifferentiable. We discuss how these limitations also affect the universal composability framework. We finish by showing the chosen-distribution attack security (which requires a multi-stage game) of some important public-key encryption schemes built using a hash construction paradigm introduced by Dodis, Ristenpart, and Shrimpton

Cryptographic Analysis of Secure Messaging Protocols

Instant messaging applications promise their users a secure and private way to communicate. The validity of these promises rests on the design of the underlying protocol, the cryptographic primitives used and the quality of the implementation. Though secure messaging designs exist in the literature, for various reasons developers of messaging applications often opt to design their own protocols, creating a gap between cryptography as understood by academic research and cryptography as implemented in practice. This thesis contributes to bridging this gap by approaching it from both sides: by looking for flaws in the protocols underlying real-world messaging applications, as well as by performing a rigorous analysis of their security guarantees in a provable security model.Secure messaging can provide a host of different, sometimes conflicting, security and privacy guarantees. It is thus important to judge applications based on the concrete security expectations of their users. This is particularly significant for higher-risk users such as activists or civil rights protesters. To position our work, we first studied the security practices of protesters in the context of the 2019 Anti-ELAB protests in Hong Kong using in-depth, semi-structured interviews with participants of these protests. We report how they organised on different chat platforms based on their perceived security, and how they developed tactics and strategies to enable pseudonymity and detect compromise.Then, we analysed two messaging applications relevant in the protest context: Bridgefy and Telegram. Bridgefy is a mobile mesh messaging application, allowing users in relative proximity to communicate without the Internet. It was being promoted as a secure communication tool for use in areas experiencing large-scale protests. We showed that Bridgefy permitted its users to be tracked, offered no authenticity, no effective confidentiality protections and lacked resilience against adversarially crafted messages. We verified these vulnerabilities by demonstrating a series of practical attacks.Telegram is a messaging platform with over 500 million users, yet prior to this work its bespoke protocol, MTProto, had received little attention from the cryptographic community. We provided the first comprehensive study of the MTProto symmetric channel as implemented in cloud chats. We gave both positive and negative results. First, we found two attacks on the existing protocol, and two attacks on its implementation in official clients which exploit timing side channels and uncover a vulnerability in the key exchange protocol. Second, we proved that a fixed version of the symmetric MTProto protocol achieves security in a suitable bidirectional secure channel model, albeit under unstudied assumptions. Our model itself advances the state-of-the-art for secure channels