Practical Quantum-Safe Stateful Hybrid Key Exchange Protocol

Shor\u27s quantum algorithm, running in quantum computers, can efficiently solve integer factorization problem and discrete logarithm problem in polynomial time. This poses an urgent and serious threat to long-term security with recent accelerated evolution of quantum computing. However, National Institute of Standards and Technology (NIST) plans to release its standard of post-quantum cryptography between 2022 and 2024. It is crucially important to propose an early solution, which is likely secure against quantum attacks and classical attacks, and likely to comply with the future NIST standard. A robust combiner combines a set of 2 or more cryptography primitives into a new primitive of the same type, and guarantees that if anyone of the ingredient primitive is secure, then the resulting primitive is secure. This work proposes the first construction of robust combiner for Key Encapsulation Mechanism (KEM), with optimal amortized performance. From our robust combiner of KEMs, we construct efficient stateful hybrid Key Exchange Protocol (KEP), which is more suitable for two parties who will communicate with each other frequently

Evaluating the Security of Merkle-Damgård Hash Functions and Combiners in Quantum Settings

In this work, we evaluate the security of Merkle-Damgård (MD) hash functions and their combiners (XOR and concatenation combiners) in quantum settings. Two main quantum scenarios are considered, including the scenario where a substantial amount of cheap quantum random access memory (qRAM) is available and where qRAM is limited and expensive to access. We present generic quantum attacks on the MD hash functions and hash combiners, and carefully analyze the complexities under both quantum scenarios. The considered securities are fundamental requirements for hash functions, including the resistance against collision and (second-)preimage. The results are consistent with the conclusions in the classical setting, that is, the considered resistances of the MD hash functions and their combiners are far less than ideal, despite the significant differences in the expected security bounds between the classical and quantum settings. Particularly, the generic attacks can be improved significantly using quantum computers under both scenarios. These results serve as an indication that classical hash constructions require careful security re-evaluation before being deployed to the post-quantum cryptography schemes

The Sum Can Be Weaker Than Each Part

International audienceIn this paper we study the security of summing the outputs of two independent hash functions, in an effort to increase the security of the resulting design, or to hedge against the failure of one of the hash functions. The exclusive-or (XOR) combiner H1(M)⊕H2(M) is one of the two most classical combiners, together with the concatenation combiner H1(M) H2(M). While the security of the concatenation of two hash functions is well understood since Joux's seminal work on multicollisions, the security of the sum of two hash functions has been much less studied. The XOR combiner is well known as a good PRF and MAC combiner, and is used in practice in TLS versions 1.0 and 1.1. In a hash function setting, Hoch and Shamir have shown that if the compression functions are modeled as random oracles, or even weak random oracles (i.e. they can easily be inverted – in particular H1 and H2 offer no security), H1 ⊕ H2 is indifferentiable from a random oracle up to the birthday bound. In this work, we focus on the preimage resistance of the sum of two narrow-pipe n-bit hash functions, following the Merkle-Damgård or HAIFA structure (the internal state size and the output size are both n bits). We show a rather surprising result: the sum of two such hash functions, e.g. SHA-512 ⊕ Whirlpool, can never provide n-bit security for preimage resistance. More precisely, we present a generic preimage attack with a complexity of O(2 5n/6). While it is already known that the XOR combiner is not preserving for preimage resistance (i.e. there might be some instantiations where the hash functions are secure but the sum is not), our result is much stronger: for any narrow-pipe functions, the sum is not preimage resistant. Besides, we also provide concrete preimage attacks on the XOR combiner (and the concatenation combiner) when one or both of the compression functions are weak; this complements Hoch and Shamir's proof by showing its tightness for preimage resistance. Of independent interests, one of our main technical contributions is a novel structure to control simultaneously the behavior of independent hash computations which share the same input message. We hope that breaking the pairwise relationship between their internal states will have applications in related settings

Functional Graph Revisited: Updates on (Second) Preimage Attacks on Hash Combiners

This paper studies functional-graph-based (second) preimage attacks against hash combiners. By exploiting more properties of cyclic nodes of functional graph, we find an improved preimage attack against the XOR combiner with a complexity of $2^{5n/8}$, while the previous best-known complexity is $2^{2n/3}$. Moreover, we find the first generic second-preimage attack on Zipper hash with an optimal complexity of $2^{3n/5}$

Proving the TLS Handshake Secure (As It Is)

International audienceThe TLS Internet Standard features a mixed bag of cryptographic algorithms and constructions, letting clients and servers negotiate their use for each run of the handshake. Although many ciphersuites are now well-understood in isolation, their composition remains problematic, and yet it is critical to obtain practical security guarantees for TLS, as all mainstream implementations support multiple related runs of the handshake and share keys between algorithms.We study the provable security of the TLS handshake, as it is implemented and deployed. To capture the details of the standard and its main extensions, we rely on miTLS, a verified reference implementation of the protocol. We propose new agile security definitions and assumptions for the signatures, key encapsulation mechanisms (KEM), and key derivation algorithms used by the TLS handshake. To validate our model of key encapsulation, we prove that both RSA and Diffie-Hellman ciphersuites satisfy our definition for the KEM. In particular, we formalize the use of PKCS#1v1.5 and build a 3,000-line EasyCrypt proof of the security of the resulting KEM against replayable chosen-ciphertext attacks under the assumption that ciphertexts are hard to re-randomize.Based on our new agile definitions, we construct a modular proof of security for the miTLS reference implementation of the handshake, including ciphersuite negotiation, key exchange, renegotiation, and resumption, treated as a detailed 3,600-line executable model. We present our main definitions, constructions, and proofs for an abstract model of the protocol, featuring series of related runs of the handshake with different ciphersuites. We also describe its refinement to account for the whole reference implementation, based on automated verification tools

New Attacks on the Concatenation and XOR Hash Combiners

We study the security of the concatenation combiner $H_1(M) \| H_2(M)$ for two independent iterated hash functions with $n$-bit outputs that are built using the Merkle-Damgård construction. In 2004 Joux showed that the concatenation combiner of hash functions with an $n$-bit internal state does not offer better collision and preimage resistance compared to a single strong $n$-bit hash function. On the other hand, the problem of devising second preimage attacks faster than $2^n$ against this combiner has remained open since 2005 when Kelsey and Schneier showed that a single Merkle-Damgård hash function does not offer optimal second preimage resistance for long messages. In this paper, we develop new algorithms for cryptanalysis of hash combiners and use them to devise the first second preimage attack on the concatenation combiner. The attack finds second preimages faster than $2^n$ for messages longer than $2^{2n/7}$ and has optimal complexity of $2^{3n/4}$. This shows that the concatenation of two Merkle-Damgård hash functions is not as strong a single ideal hash function. Our methods are also applicable to other well-studied combiners, and we use them to devise a new preimage attack with complexity of $2^{2n/3}$ on the XOR combiner $H_1(M) \oplus H_2(M)$ of two Merkle-Damgård hash functions. This improves upon the attack by Leurent and Wang (presented at Eurocrypt 2015) whose complexity is $2^{5n/6}$ (but unlike our attack is also applicable to HAIFA hash functions). Our algorithms exploit properties of random mappings generated by fixing the message block input to the compression functions of $H_1$ and $H_2$. Such random mappings have been widely used in cryptanalysis, but we exploit them in new ways to attack hash function combiners

Maintaining Security and Trust in Large Scale Public Key Infrastructures

In Public Key Infrastructures (PKIs), trusted Certification Authorities (CAs) issue public key certificates which bind public keys to the identities of their owners. This enables the authentication of public keys which is a basic prerequisite for the use of digital signatures and public key encryption. These in turn are enablers for e-business, e-government and many other applications, because they allow for secure electronic communication. With the Internet being the primary communication medium in many areas of economic, social, and political life, the so-called Web PKI plays a central role. The Web PKI denotes the global PKI which enables the authentication of the public keys of web servers within the TLS protocol and thus serves as the basis for secure communications over the Internet. However, the use of PKIs in practice bears many unsolved problems. Numerous security incidents in recent years have revealed weaknesses of the Web PKI. Because of these weaknesses, the security of Internet communication is increasingly questioned. Central issues are (1) the globally predefined trust in hundreds of CAs by browsers and operating systems. These CAs are subject to a variety of jurisdictions and differing security policies, while it is sufficient to compromise a single CA in order to break the security provided by the Web PKI. And (2) the handling of revocation of certificates. Revocation is required to invalidate certificates, e.g., if they were erroneously issued or the associated private key has been compromised. Only this can prevent their misuse by attackers. Yet, revocation is only effective if it is published in a reliable way. This turned out to be a difficult problem in the context of the Web PKI. Furthermore, the fact that often a great variety of services depends on a single CA is a serious problem. As a result, it is often almost impossible to revoke a CA's certificate. However, this is exactly what is necessary to prevent the malicious issuance of certificates with the CA's key if it turns out that a CA is in fact not trustworthy or the CA's systems have been compromised. In this thesis, we therefore turn to the question of how to ensure that the CAs an Internet user trusts in are actually trustworthy. Based on an in depth analysis of the Web PKI, we present solutions for the different issues. In this thesis, the feasibility and practicality of the presented solutions is of central importance. From the problem analysis, which includes the evaluation of past security incidents and previous scientific work on the matter, we derive requirements for a practical solution. For the solution of problem (1), we introduce user-centric trust management for the Web PKI. This allows to individually reduce the number of CAs a user trusts in to a fraction of the original number. This significantly reduces the risk to rely on a CA, which is actually not trustworthy. The assessment of a CA's trustworthiness is user dependent and evidence-based. In addition, the method allows to monitor the revocation status for the certificates relevant to a user. This solves the first part of problem (2). Our solution can be realized within the existing infrastructure without introducing significant overhead or usability issues. Additionally, we present an extension by online service providers. This enables to share locally collected trust information with other users and thus, to improve the necessary bootstrapping of the system. Moreover, an efficient detection mechanism for untrustworthy CAs is realized. In regard to the second part of problem (2), we present a CA revocation tolerant PKI construction based on forward secure signature schemes (FSS). Forward security means that even in case of a key compromise, previously generated signatures can still be trusted. This makes it possible to implement revocation mechanisms such that CA certificates can be revoked, without compromising the availability of dependent web services. We describe how the Web PKI can be transitioned to a CA revocation tolerant PKI taking into account the relevant standards. The techniques developed in this thesis also enable us to address the related problem of ``non-repudiation'' of digital signatures. Non-repudiation is an important security goal for many e-business and e-government applications. Yet, non-repudiation is not guaranteed by standard PKIs. Current solutions, which are based on time-stamps generated by trusted third parties, are inefficient and costly. In this work, we show how non-repudiation can be made a standard property of PKIs. This makes time-stamps obsolete. The techniques presented in this thesis are evaluated in terms of practicality and performance. This is based on theoretical results as well as on experimental analyses. Our results show that the proposed methods are superior to previous approaches. In summary, this thesis presents mechanisms which make the practical use of PKIs more secure and more efficient and demonstrates the practicability of the presented techniques