An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Modelling after-the-fact leakage for key exchange

Security models for two-party authenticated key exchange (AKE) protocols have developed over time to prove the security of AKE protocols even when the adversary learns certain secret values. In this work, we address more granular leakage: partial leakage of long-term secrets of protocol principals, even after the session key is established. We introduce a generic key exchange security model, which can be instantiated allowing bounded or continuous leakage, even when the adversary learns certain ephemeral secrets or session keys. Our model is the strongest known partial-leakage-based security model for key exchange protocols. We propose a generic construction of a two-pass leakage-resilient key exchange protocol that is secure in the proposed model, by introducing a new concept: the leakage-resilient NAXOS trick. We identify a special property for public-key cryptosystems: pair generation indistinguishability, and show how to obtain the leakage-resilient NAXOS trick from a pair generation indistinguishable leakage-resilient public-key cryptosystem.

Preventing pollution attacks in multi-source network coding

Network coding is a method for achieving channel capacity in networks. The key idea is to allow network routers to linearly mix packets as they traverse the network so that recipients receive linear combinations of packets. Network coded systems are vulnerable to pollution attacks where a single malicious node floods the network with bad packets and prevents the receiver from decoding correctly. Cryptographic defenses to these problems are based on homomorphic signatures and MACs. These proposals, however, cannot handle mixing of packets from multiple sources, which is needed to achieve the full benefits of network coding. In this paper we address integrity of multi-source mixing. We propose a security model for this setting and provide a generic construction.

Distributed public-key cryptography from weak secrets

We introduce the notion of distributed password-based public-key cryptography, where a virtual high-entropy private key is implicitly defined as a concatenation of low-entropy passwords held in separate locations. The users can jointly perform private-key operations by exchanging messages over an arbitrary channel, based on their respective passwords, without ever sharing their passwords or reconstituting the key. Focusing on the case of ElGamal encryption as an example, we start by formally defining ideal functionalities for distributed public-key generation and virtual private-key computation in the UC model. We then construct efficient protocols that securely realize them in either the RO model (for efficiency) or the CRS model (for elegance). We conclude by showing that our distributed protocols generalize to a broad class of “discrete-log”-based public-key cryptosystems, which notably includes identity-based encryption. This opens the door to a powerful extension of IBE with a virtual PKG made of a group of people, each one memorizing a small portion of the master key.

Flexible IBE and beyond in the commutative-blinding framework

The cryptographic community has, of late, shown much inventiveness in the creation of powerful new IBE-like primitives that go beyond the basic IBE notion and extend it in many new directions. Virtually all of these “super-IBE” schemes rely on bilinear pairings for their implementation, which they tend to use in a surprisingly small number of different ways: three of them as of this writing. What is interesting is that, among the three main frameworks that we know of so far, one has acted as a veritable magnet for the construction of many of these “generalized IBE” primitives, whereas the other two have not been nearly as fruitful in that respect. This refers to the Commutative Blinding framework defined by the Boneh-Boyen [Bscr ][Bscr ]1 IBE scheme from 2004. The aim of this chapter is to try to shed some light on this approach's popularity, first by comparing its key properties with those of the competing frameworks, and then by providing a number of examples that illustrate how those properties have been used.

Lattice-based certificateless public-key encryption in the standard model

The notion of certificateless public-key encryption (CL-PKE) was introduced by Al-Riyami and Paterson in 2003 that avoids the drawbacks of both traditional PKI-based public-key encryption (i.e., establishing public-key infrastructure) and identity-based encryption (i.e., key escrow). So CL-PKE like identity-based encryption is certificate-free, and unlike identity-based encryption is key escrow-free. In this paper, we introduce simple and efficient CCA-secure CL-PKE based on (hierarchical) identity-based encryption. Our construction has both theoretical and practical interests. First, our generic transformation gives a new way of constructing CCA-secure CL-PKE. Second, instantiating our transformation using lattice-based primitives results in a more efficient CCA-secure CL-PKE than its counterpart introduced by Dent in 2008.

The resistance of PRESENT-80 against related-key differential attacks

We examine the security of the 64-bit lightweight block cipher PRESENT-80 against related-key differential attacks. With a computer search we are able to prove that for any related-key differential characteristic on full-round PRESENT-80, the probability of the characteristic only in the 64-bit state is not higher than 2−64. To overcome the exponential (in the state and key sizes) computational complexity of the search we use truncated differences, however as the key schedule is not nibble oriented, we switch to actual differences and apply early abort techniques to prune the tree-based search. With a new method called extended split approach we are able to make the whole search feasible and we implement and run it in real time. Our approach targets the PRESENT-80 cipher however,with small modifications can be reused for other lightweight ciphers as well.

New security notions and relations for public-key encryption

Since their introduction, the notions of indistinguishability and non-malleability have been changed and extended by different authors to support different goals. In this paper, we propose new flavors of these notions, investigate their relative strengths with respect to previous notions, and provide the full picture of relationships (i.e., implications and separations) among the security notions for public-key encryption schemes. We take into account the two general security goals of indistinguishability and non-malleability, each in the message space, key space, and hybrid message-key space to find six specific goals, a couple of them, namely complete indistinguishability and key non-malleability, are new. Then for each pair of goals, coming from the indistinguishability or non-malleability classes, we prove either an implication or a separation, completing the full picture of relationships among all these security notions. The implications and separations are respectively supported by formal proofs (i.e., reductions) in the concrete-security framework and by counterexamples.

Lattice-based completely non-malleable public-key encryption in the standard model

An encryption scheme is non-malleable if giving an encryption of a message to an adversary does not increase its chances of producing an encryption of a related message (under a given public key). Fischlin introduced a stronger notion, known as complete non-malleability, which requires attackers to have negligible advantage, even if they are allowed to transform the public key under which the related message is encrypted. Ventre and Visconti later proposed a comparison-based definition of this security notion, which is more in line with the well-studied definitions proposed by Bellare et al. The authors also provide additional feasibility results by proposing two constructions of completely non-malleable schemes, one in the common reference string model using non-interactive zero-knowledge proofs, and another using interactive encryption schemes. Therefore, the only previously known completely non-malleable (and non-interactive) scheme in the standard model, is quite inefficient as it relies on generic NIZK approach. They left the existence of efficient schemes in the common reference string model as an open problem. Recently, two efficient public-key encryption schemes have been proposed by Libert and Yung, and Barbosa and Farshim, both of them are based on pairing identity-based encryption. At ACISP 2011, Sepahi et al. proposed a method to achieve completely non-malleable encryption in the public-key setting using lattices but there is no security proof for the proposed scheme. In this paper we review the mentioned scheme and provide its security proof in the standard model. Our study shows that Sepahi’s scheme will remain secure even for post-quantum world since there are currently no known quantum algorithms for solving lattice problems that perform significantly better than the best known classical (i.e., non-quantum) algorithms.

Cryptanalysis of WG-7 : a lightweight stream cipher

WG-7 is a stream cipher based on WG stream cipher and has been designed by Luo et al. (2010). This cipher is designed for low cost and lightweight applications (RFID tags and mobile phones, for instance). This paper addresses cryptographic weaknesses of WG-7 stream cipher. We show that the key stream generated by WG-7 can be distinguished from a random sequence after knowing 213.5 keystream bits and with a negligible error probability. Also, we investigate the security of WG-7 against algebraic attacks. An algebraic key recovery attack on this cipher is proposed. The attack allows to recover both the internal state and the secret key with the time complexity about 2/27.

Teaching Teachers for the Future (TTF) Project TPACK Survey : summary of the key findings

This paper presents a summary of the key findings of the TTF TPACK Survey developed and administered for the Teaching the Teachers for the Future (TTF) Project implemented in 2011. The TTF Project, funded by an Australian Government ICT Innovation Fund grant, involved all 39 Australian Higher Education Institutions which provide initial teacher education. TTF data collections were undertaken at the end of Semester 1 (T1) and at the end of Semester 2 (T2) in 2011. A total of 12881 participants completed the first survey (T1) and 5809 participants completed the second survey (T2). Groups of like-named items from the T1 survey were subject to a battery of complementary data analysis techniques. The psychometric properties of the four scales: Confidence - teacher items; Usefulness - teacher items; Confidence - student items; Usefulness- student items, were confirmed both at T1 and T2. Among the key findings summarised, at the national level, the scale: Confidence to use ICT as a teacher showed measurable growth across the whole scale from T1 to T2, and the scale: Confidence to facilitate student use of ICT also showed measurable growth across the whole scale from T1 to T2. Additional key TTF TPACK Survey findings are summarised.

Cryptanalysis of RC4(n, m) stream cipher

RC4(n, m) is a stream cipher based on RC4 and is designed by G. Gong et al. It can be seen as a generalization of the famous RC4 stream cipher designed by Ron Rivest. The authors of RC4(n, m) claim that the cipher resists all the attacks that are successful against the original RC4. The paper reveals cryptographic weaknesses of the RC4(n, m) stream cipher. We develop two attacks. The first one is based on non-randomness of internal state and allows to distinguish it from a truly random cipher by an algorithm that has access to 24·n bits of the keystream. The second attack exploits low diffusion of bits in the KSA and PRGA algorithms and recovers all bytes of the secret key. This attack works only if the initial value of the cipher can be manipulated. Apart from the secret key, the cipher uses two other inputs, namely, initial value and initial vector. Although these inputs are fixed in the cipher specification, some applications may allow the inputs to be under the attacker control. Assuming that the attacker can control the initial value, we show a distinguisher for the cipher and a secret key recovery attack that for the L-bit secret key, is able to recover it with about (L/n) · 2n steps. The attack has been implemented on a standard PC and can reconstruct the secret key of RC(8, 32) in less than a second.

NTRUCCA : how to strengthen NTRUEncrypt to chosen-ciphertext security in the standard model

NTRUEncrypt is a fast and practical lattice-based public-key encryption scheme, which has been standardized by IEEE, but until recently, its security analysis relied only on heuristic arguments. Recently, Stehlé and Steinfeld showed that a slight variant (that we call pNE) could be proven to be secure under chosen-plaintext attack (IND-CPA), assuming the hardness of worst-case problems in ideal lattices. We present a variant of pNE called NTRUCCA, that is IND-CCA2 secure in the standard model assuming the hardness of worst-case problems in ideal lattices, and only incurs a constant factor overhead in ciphertext and key length over the pNE scheme. To our knowledge, our result gives the first IND-CCA2 secure variant of NTRUEncrypt in the standard model, based on standard cryptographic assumptions. As an intermediate step, we present a construction for an All-But-One (ABO) lossy trapdoor function from pNE, which may be of independent interest. Our scheme uses the lossy trapdoor function framework of Peikert and Waters, which we generalize to the case of (k − 1)-of-k-correlated input distributions.

Known and chosen key differential distinguishers for block ciphers

In this paper we investigate the differential properties of block ciphers in hash function modes of operation. First we show the impact of differential trails for block ciphers on collision attacks for various hash function constructions based on block ciphers. Further, we prove the lower bound for finding a pair that follows some truncated differential in case of a random permutation. Then we present open-key differential distinguishers for some well known round-reduced block ciphers.

Expressive cryptography : lattice perspectives

The invention of asymmetric encryption back in the seventies was a conceptual leap that vastly increased the expressive power of encryption of the times. For the first time, it allowed the sender of a message to designate the intended recipient in an cryptographic way, expressed as a “public key” that was related to but distinct from the “private key” that, alone, embodied the ability to decrypt. This made large-scale encryption a practical and scalable endeavour, and more than anything else—save the internet itself—led to the advent of electronic commerce as we know and practice it today.