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12:56 [PhD][New] Juraj Šarinay: Cryptographic Hash Functions in Groups and Provable Properties

  Name: Juraj Šarinay
Topic: Cryptographic Hash Functions in Groups and Provable Properties
Category: (no category)


We consider several “provably secure” hash functions that compute simple sums in a well chosen group (G, ?). Security properties of such functions provably translate in a natural way to computational problems in G\r\nthat are simple to define and possibly also hard to solve. Given k disjoint lists Li of group elements, the k-sum problem asks for gi ? Li such that\r\ng1 ? g2 ? . . . ? gk = 1G. Hardness of the problem in the respective groups follows from some “standard” assumptions used in public-key cryptology such\r\nas hardness of integer factoring, discrete logarithms, lattice reduction and syndrome decoding. We point out evidence that the k-sum problem may even be harder than the above problems.


Two hash functions based on the group k-sum problem, SWIFFTX and FSB, were submitted to NIST as candidates for the future SHA-3 standard. Both submissions were supported by some sort of a security proof. We show\r\nthat the assessment of security levels provided in the proposals is not related to the proofs included. The main claims on security are supported exclusively\r\nby considerations about available attacks. By introducing “second-order” bounds on bounds on security, we expose the limits of such an approach to\r\nprovable security.


A problem with the way security is quantified does not necessarily mean a problem with security itself. Although FSB does have a history of failures,\r\nrecent versions of the two above functions have resisted cryptanalytic efforts well. This evidence, as well as the several connections to more standard\r\nproblems, suggests that the k-sum problem in some groups may be considered hard on its own and possibly lead to provable bounds on security. Complexity of the non-trivial tree algorithm is becoming a standard tool for measuring the associated hardness.


We propose modifications to the multiplicative Very Smooth Hash and derive security from multiplicative k-sums in contra[...]

00:17 [Pub][ePrint] Cryptanalysis of GGH Map, by Yupu Hu and Huiwen Jia

  Multilinear map is a novel primitive which has many cryptographic applications, and GGH map is a major candidate of multilinear maps. GGH map has two classes of applications, which are respectively applications for public tools of encoding and hidden tools of encoding. In this paper we show that applications of GGH map for public tools of encoding are not secure. We present an efficient attack on GGH map, aiming at multi-party key exchange (MPKE) and the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. First, for the secret of each user, we obtain an equivalent secret, which is the sum of original secret and a noise. The noise is an element of the specific principal ideal, but its size is not small. To do so, we use weak-DL attack presented by authors of GGH map. Second, we use special modular operations, which we call modified encoding/decoding, to filter the decoded noise much smaller. Such filtering is enough to break MPKE. Moreover, such filtering negates K-GMDDH assumption, which is the security basis of an ABE. The procedure almost breaks away from those lattice attacks and looks like an ordinary algebra. The key point is our special tools for modular operations. Finally, we break the instance of WE based on the hardness of 3-exact cover problem. To do so, we not only use modified encoding/decoding, but also (1) introduce and solve \"combined 3-exact cover problem\", which is a problem never hard to be solved; and (2) compute Hermite normal form of the specific principal ideal. The attack on the instance of WE is under an assumption, which seems at least nonnegligible.

00:17 [Pub][ePrint] Boosting OMD for Almost Free Authentication of Associated Data, by Reza Reyhanitabar and Serge Vaudenay and Damian Vizár

  We propose \\emph{pure} OMD (p-OMD) as a new variant of the Offset Merkle-Damg{\\aa}rd (OMD) authenticated encryption scheme. Our new scheme inherits all desirable security features of OMD while having a more compact structure and providing higher efficiency. The original OMD scheme, as submitted to the CAESAR competition, couples a single pass of a variant of the Merkle-Damg{\\aa}rd (MD) iteration with the counter-based XOR MAC algorithm to provide privacy and authenticity. Our improved p-OMD scheme dispenses with the XOR MAC algorithm and is \\emph{purely} based on the MD iteration; hence, the name ``pure\'\' OMD. To process a message of $\\ell$ blocks and associated data of $a$ blocks, OMD needs $\\ell+a+2$ calls to the compression function while p-OMD only requires $\\max\\left\\{\\ell, a\\right\\}+2$ calls. Therefore, for a typical case where $\\ell \\geq a$, p-OMD makes just $\\ell+2$ calls to the compression function; that is, associated data is processed almost freely compared to OMD. We prove the security of p-OMD under the same standard assumption (pseudo-randomness of the compression function) as made in OMD; moreover, the security bound for p-OMD is the same as that of OMD, showing that the modifications made to boost the performance are without any loss of security.

00:17 [Pub][ePrint] The Design Space of Lightweight Cryptography, by Nicky Mouha

  For constrained devices, standard cryptographic algorithms can be too big, too slow or too energy-consuming. The area of lightweight cryptography studies new algorithms to overcome these problems. In this paper, we will focus on symmetric-key encryption, authentication and hashing. Instead of providing a full overview of this area of research, we will highlight three interesting topics. Firstly, we will explore the generic security of lightweight constructions. In particular, we will discuss considerations for key, block and tag sizes, and explore the topic of instantiating a pseudorandom permutation (PRP) with a non-ideal block cipher construction. This is inspired by the increasing prevalence of lightweight designs that are not secure against related-key attacks, such as PRINCE, PRIDE or Chaskey. Secondly, we explore the efficiency of cryptographic primitives. In particular, we investigate the impact on efficiency when the input size of a primitive doubles. Lastly, we provide some considerations for cryptographic design. We observe that applications do not always use cryptographic algorithms as they were intended, which negatively impacts the security and/or efficiency of the resulting implementations.

00:17 [Pub][ePrint] Communication-Optimal Proactive Secret Sharing for Dynamic Groups, by Joshua Baron and Karim El Defrawy and Joshua Lampkins and Rafail Ostrovsky

  Proactive secret sharing (PSS) schemes are designed for settings where long-term confidentiality of secrets has to be guaranteed, specifically, when all participating parties may eventually be corrupted. PSS schemes periodically refresh secrets and reset corrupted parties to an uncorrupted state; in PSS the corruption threshold $t$ is replaced with a corruption rate which cannot be violated. In dynamic proactive secret sharing (DPSS) the number of parties can vary during the course of execution. DPSS is ideal when the set of participating parties changes over the lifetime of the secret or where removal of parties is necessary if they become severely corrupted. This paper presents the first DPSS schemes with optimal amortized, $O(1)$, per-secret communication compared to $O(n^4)$ or $\\exp(n)$ in number of parties, $n$, required by existing schemes. We present perfectly and statistically secure schemes with near-optimal threshold in each case. We also describe how to construct a communication-efficient dynamic proactively-secure multiparty computation (DPMPC) protocol which achieves the same thresholds.

00:17 [Pub][ePrint] Foundations of Reconfigurable PUFs (Full Version), by Jonas Schneider and Dominique Schröder

  A Physically Unclonable Function (PUF) can be seen as a source of randomness that can be challenged with a stimulus and responds in a way that is to some extent unpredictable. PUFs can be used to provide efficient solutions for common cryptographic primitives such as identification/authentication schemes, key storage, and hardware-entangled cryptography.

Moreover, Brzuska et al.~have recently shown, that PUFs can be used to construct UC secure protocols (CRYPTO 2011). Most PUF instantiations, however, only provide a static challenge/response space which limits their usefulness for practical instantiations. To overcome this limitation, Katzenbeisser et al. (CHES 2011) introduced Logically Reconfigurable PUFs (LR-PUFs), with the idea to introduce an ``update\'\' mechanism that changes the challenge/response behaviour without physically replacing or modifying the hardware.

In this work, we revisit LR-PUFs. We propose several new ways to characterize the unpredictability of LR-PUFs covering a broader class of realistic attacks and examine their relationship to each other.

In addition, we reconcile existing constructions with these new characterizations and show that they can withstand stronger adversaries than originally shown.

Since previous constructions are insecure with respect to our strongest unpredictability notion, we propose a secure construction which relies on the same assumptions and is almost as efficient as previous solutions.

00:17 [Pub][ePrint] Analysis of VAES3 (FF2), by Morris Dworkin and Ray Perlner

  The National Institute of Standards and Technology (NIST) specified three methods for format-preserving encryption (FPE) in Draft NIST Special Publication (SP) 800-38G, which was released for public comment in July, 2013. Each method was a mode of operation of the Advanced Encryption Standard (AES). One of the three modes, VAES3, was specified under the name FF2 in the NIST draft. This note describes a theoretical chosen-plaintext attack that shows the security strength of FF2 is less than 128 bits.

00:17 [Pub][ePrint] Black-Box Garbled RAM, by Sanjam Garg and Steve Lu and Rafail Ostrovsky

  Garbled RAM, introduced by Lu and Ostrovsky, enables the task of garbling a RAM (Random Access Machine) program directly, there by avoiding the inefficient process of first converting it into a circuit. Garbled RAM can be seen as a RAM analogue of Yao\'s garbled circuit construction, except that known realizations of Garbled RAM make non-black-box use of the underlying cryptographic primitives.

In this paper we remove this limitation and provide the first black-box construction of Garbled RAM with polylogarithmic overhead. Our scheme allows for garbling multiple RAM programs being executed on a persistent database and its security is based only on the existence of one-way functions. We also obtain the first secure RAM computation protocol that is both constant round and makes only black-box use of one-way functions in the OT-hybrid model.

00:17 [Pub][ePrint] Authenticated Key Exchange over Bitcoin, by Patrick McCorry and Siamak F. Shahandashti and Dylan Clarke and Feng Hao

  Bitcoin is designed to protect user anonymity (or pseudonymity) in a financial transaction, and has been increasingly adopted by major e-commerce websites such as Dell, Payal and Expedia. While the anonymity of Bitcoin transactions has been extensively studied, little attention has been paid to the security of post-transaction correspondence. In a commercial application, the merchant and the user often need to engage in follow-up correspondence after a Bitcoin transaction is completed, e.g., to acknowledge the receipt of payment, to confirm the billing address, to arrange the product delivery, to discuss refund and so on. Currently, such follow-up correspondence is typically done in plaintext via email with no guarantee on confidentiality. Obviously, leakage of sensitive data from the correspondence (e.g., billing address) can trivially compromise the anonymity of Bitcoin users. In this paper, we initiate the first study on how to realise end-to-end secure communication between Bitcoin users in a post-transaction scenario without requiring any trusted third party or additional authentication credentials. We first point out that none of the existing PKI-based or password-based AKE schemes are suitable for the purpose. Instead, our idea is to leverage the Bitcoin\'s append-only ledger as an additional layer of authentication between previously confirmed transactions. This naturally leads to a new category of AKE protocols that bootstrap trust entirely from the block chain. We call this new category ``Bitcoin-based AKE\'\' and present two concrete protocols: one is non-interactive with no forward secrecy, while the other is interactive with additional guarantee of forward secrecy. Finally, we present proof-of-concept prototypes for both protocols with experimental results to demonstrate their practical feasibility.

00:17 [Pub][ePrint] TinyLEGO: An Interactive Garbling Scheme for Maliciously Secure Two-party Computation, by Tore Kasper Frederiksen and Thomas P. Jakobsen and Jesper Buus Nielsen and Roberto Trifiletti

  This paper reports on a number of conceptual and technical contributions to the currently very lively field of two-party computation (2PC) based on garbled circuits. Our main contributions are as follows:

1. We propose a notion of an interactive garbling scheme, where the garbled circuit is

generated as an interactive protocol between the garbler and the evaluator. The garbled circuit is correct and privacy preserving even if one of the two parties was acting maliciously during garbling. The security notion is game based.

2. We show that an interactive garbling scheme combined with a Universally Composable (UC) secure oblivious transfer protocol can be used in a black-box manner to implement two-party computation (2PC) UC securely against a static and malicious adversary. The protocol abstracts many recent protocols for implementing 2PC from garbled circuits and will allow future designers of interactive garbling schemes to prove security with the simple game based definitions, as opposed to directly proving UC security for each new scheme.

3. We propose a new instantiation of interactive garbling by designing a new protocol in the LEGO family of protocols for efficient garbling against a malicious adversary. The new protocol is based on several new technical contributions and many optimizations, including a highly efficient UC commitment scheme. A theoretical evaluation of the efficiency shows that the instantiation is one to two orders of magnitude faster than the previously most efficient LEGO protocol and that it in general compares favorably to all existing garbling-based 2PC protocols for malicious adversaries.

00:17 [Pub][ePrint] New algorithm for the discrete logarithm problem on elliptic curves, by Igor Semaev

  A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of Boolean equations. Under a first fall degree assumption

the regularity degree of the system is at most $4$. Extensive experimental data which supports the assumption is provided. An heuristic analysis suggests a new asymptotical complexity bound $2^{c\\sqrt{n\\ln n}}, c\\approx 1.69$ for computing discrete logarithms on an elliptic curve over a field of size $2^n$. For several binary elliptic curves recommended by FIPS the new method performs better than Pollard\'s.