Key reconciliation for high performance Quantum Key Distribution

Quantum Key Distribution is carving its place among the tools used to secure communications. While a difficult technology, it enjoys benefits that set it apart from the rest, the most prominent is its provable security based on the laws of physics. QKD requires not only the mastering of signals at the quantum level, but also a classical processing to extract a secret-key from them. This postprocessing has been customarily studied in terms of the efficiency, a figure of merit that offers a biased view of the performance of real devices. Here we argue that it is the throughput the significant magnitude in practical QKD, specially in the case of high speed devices, where the differences are more marked, and give some examples contrasting the usual postprocessing schemes with new ones from modern coding theory. A good understanding of its implications is very important for the design of modern QKD devices.

Information reconciliation for Quantum Key Distribution

Secret-key agreement, a well-known problem in cryptography, allows two parties holding correlated sequences to agree on a secret key communicating over a public channel. It is usually divided into three different procedures: advantage distillation, information reconciliation and privacy amplification. The efficiency of each one of these procedures is needed if a positive key rate is to be attained from the legitimate parties? correlated sequences. Quantum key distribution (QKD) allows the two parties to obtain correlated sequences, provided that they have access to an authenticated channel. The new generation of QKD devices is able to work at higher speeds and in noisier or more absorbing environments. This exposes the weaknesses of current information reconciliation protocols, a key component to their performance. Here we present a new protocol based in low-density parity-check (LDPC) codes that presents the advantages of low interactivity, rate adaptability and high efficiency,characteristics that make it highly suitable for next generation QKD devices.

Fundamental finite key limits for information reconciliation in quantum key distribution

The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during one-way information reconciliation is flawed and we propose an improved estimate.

Rate-Adaptive LDPC-based key reconciliation for high performance quantum key distribution

The postprocessing or secret-key distillation process in quantum key distribution (QKD) mainly involves two well-known procedures: information reconciliation and privacy amplification. Information or key reconciliation has been customarily studied in terms of efficiency. During this, some information needs to be disclosed for reconciling discrepancies in the exchanged keys. The leakage of information is lower bounded by a theoretical limit, and is usually parameterized by the reconciliation efficiency (or inefficiency), i.e. the ratio of additional information disclosed over the Shannon limit. Most techniques for reconciling errors in QKD try to optimize this parameter. For instance, the well-known Cascade (probably the most widely used procedure for reconciling errors in QKD) was recently shown to have an average efficiency of 1.05 at the cost of a high interactivity (number of exchanged messages). Modern coding techniques, such as rate-adaptive low-density parity-check (LDPC) codes were also shown to achieve similar efficiency values exchanging only one message, or even better values with few interactivity and shorter block-length codes.

No-switching quantum key distribution using broadband modulated coherent light

We realize an end-to-end no-switching quantum key distribution protocol using continuous-wave coherent light. We encode weak broadband Gaussian modulations onto the amplitude and phase quadratures of light beams. Our no-switching protocol achieves high secret key rate via a post-selection protocol that utilizes both quadrature information simultaneously. We establish a secret key rate of 25 Mbits/s for a lossless channel and 1 kbit/s for 90% channel loss, per 17 MHz of detected bandwidth, assuming individual Gaussian eavesdropping attacks. Since our scheme is truly broadband, it can potentially deliver orders of magnitude higher key rates by extending the encoding bandwidth with higher-end telecommunication technology.

Long-range, high bit-rate secure key distribution link utilizing Raman Ultra-long fiber laser (UFL)

The distribution of the secret key is the weakest link of many data encryption systems. Quantum key distribution (QKD) schemes provide attractive solutions [1], however their implementation remains challenging and their range and bit-rate are limited. Moreover, practical QKD systems, employ real-life components and are, therefore, vulnerable to diverse attack schemes [2]. Ultra-Long fiber lasers (UFLs) have been drawing much attention recently because of their fundamentally different properties compared to conventional lasers as well as their unique applications [3]. Here, we demonstrate a 100Bps, practically secure key distribution, over a 500km link, employing Raman gain UFL. Fig. 1(a) depicts a schematic of the UFL system. Each user has an identical set of two wavelength selective mirrors centered at l0 and l 1. In order to exchange a key-bit, each user independently choose one of these mirrors and introduces it as a laser reflector at their end. If both users choose identical mirrors, a clear signal develops and the bits in these cases are discarded. However if they choose complementary mirrors, (1, 0 or 0, 1 states), the UFL remains below lasing threshold and no signal evolves. In these cases, an eavesdropper can only detect noise and is unable to determine the mirror choice of the users, where the choice of mirrors represent a single key bit (e.g. Alice's choice of mirror is the key-bit). These bits are kept and added to the key. The absence of signal in the secure states faxilitates fast measurements to distinguish between the non-secure and the secure states and to determine the key-bit in the later case, Sequentially reapeating the single bit exchange protocol generate the entire keys of any desirable length. © 2013 IEEE.

Fixed argument pairings

A common scenario in many pairing-based cryptographic protocols is that one argument in the pairing is fixed as a long term secret key or a constant parameter in the system. In these situations, the runtime of Miller's algorithm can be significantly reduced by storing precomputed values that depend on the fixed argument, prior to the input or existence of the second argument. In light of recent developments in pairing computation, we show that the computation of the Miller loop can be sped up by up to 37 if precomputation is employed, with our method being up to 19.5 faster than the previous precomputation techniques.

Optimally increasing secure connectivity in multihop wireless ad hoc networks

We consider the problem of how to maximize secure connectivity of multi-hop wireless ad hoc networks after deployment. Two approaches, based on graph augmentation problems with nonlinear edge costs, are formulated. The first one is based on establishing a secret key using only the links that are already secured by secret keys. This problem is in NP-hard and does not accept polynomial time approximation scheme PTAS since minimum cutsets to be augmented do not admit constant costs. The second one is based of increasing the power level between a pair of nodes that has a secret key to enable them physically connect. This problem can be formulated as the optimal key establishment problem with interference constraints with bi-objectives: (i) maximizing the concurrent key establishment flow, (ii) minimizing the cost. We show that both problems are NP-hard and MAX-SNP (i.e., it is NP-hard to approximate them within a factor of 1 + e for e > 0 ) with a reduction to MAX3SAT problem. Thus, we design and implement a fully distributed algorithm for authenticated key establishment in wireless sensor networks where each sensor knows only its one- hop neighborhood. Our witness based approaches find witnesses in multi-hop neighborhood to authenticate the key establishment between two sensor nodes which do not share a key and which are not connected through a secure path.

Complexity of increasing the secure connectivity in wireless ad hoc networks

We consider the problem of maximizing the secure connectivity in wireless ad hoc networks, and analyze complexity of the post-deployment key establishment process constrained by physical layer properties such as connectivity, energy consumption and interference. Two approaches, based on graph augmentation problems with nonlinear edge costs, are formulated. The first one is based on establishing a secret key using only the links that are already secured by shared keys. This problem is in NP-hard and does not accept polynomial time approximation scheme PTAS since minimum cutsets to be augmented do not admit constant costs. The second one extends the first problem by increasing the power level between a pair of nodes that has a secret key to enable them physically connect. This problem can be formulated as the optimal key establishment problem with interference constraints with bi-objectives: (i) maximizing the concurrent key establishment flow, (ii) minimizing the cost. We prove that both problems are NP-hard and MAX-SNP with a reduction to MAX3SAT problem.

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.

Reversible and blind database watermarking using difference expansion

There has been significant research in the field of database watermarking recently. However, there has not been sufficient attention given to the requirement of providing reversibility (the ability to revert back to original relation from watermarked relation) and blindness (not needing the original relation for detection purpose) at the same time. This model has several disadvantages over reversible and blind watermarking (requiring only the watermarked relation and secret key from which the watermark is detected and the original relation is restored) including the inability to identify the rightful owner in case of successful secondary watermarking, the inability to revert the relation to the original data set (required in high precision industries) and the requirement to store the unmarked relation at a secure secondary storage. To overcome these problems, we propose a watermarking scheme that is reversible as well as blind. We utilize difference expansion on integers to achieve reversibility. The major advantages provided by our scheme are reversibility to a high quality original data set, rightful owner identification, resistance against secondary watermarking attacks, and no need to store the original database at a secure secondary storage. We have implemented our scheme and results show the success rate is limited to 11% even when 48% tuples are modified.

Reversible and blind database watermarking using difference expansion

There has been significant research in the field of database watermarking recently. However, there has not been sufficient attention given to the requirement of providing reversibility (the ability to revert back to original relation from watermarked relation) and blindness (not needing the original relation for detection purpose) at the same time. This model has several disadvantages over reversible and blind watermarking (requiring only the watermarked relation and secret key from which the watermark is detected and the original relation is restored) including the inability to identify the rightful owner in case of successful secondary watermarking, the inability to revert the relation to the original data set (required in high precision industries) and the requirement to store the unmarked relation at a secure secondary storage. To overcome these problems, we propose a watermarking scheme that is reversible as well as blind. We utilize difference expansion on integers to achieve reversibility. The major advantages provided by our scheme are reversibility to a high quality original data set, rightful owner identification, resistance against secondary watermarking attacks, and no need to store the original database at a secure secondary storage. We have implemented our scheme and results show the success rate is limited to 11% even when 48% tuples are modified.

Cryptanalysis of LASH

We show that the LASH-x hash function is vulnerable to attacks that trade time for memory, including collision attacks as fast as 2(4x/11) and preimage attacks as fast as 2(4x/7). Moreover, we briefly mention heuristic lattice based collision attacks that use small memory but require very long messages that are expected to find collisions much faster than 2 x/2. All of these attacks exploit the designers’ choice of an all zero IV. We then consider whether LASH can be patched simply by changing the IV. In this case, we show that LASH is vulnerable to a 2(7x/8) preimage attack. We also show that LASH is trivially not a PRF when any subset of input bytes is used as a secret key. None of our attacks depend upon the particular contents of the LASH matrix – we only assume that the distribution of elements is more or less uniform.

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.

Security evaluation of Rakaposhi Stream Cipher

Rakaposhi is a synchronous stream cipher, which uses three main components: a non-linear feedback shift register (NLFSR), a dynamic linear feedback shift register (DLFSR) and a non-linear filtering function (NLF). NLFSR consists of 128 bits and is initialised by the secret key K. DLFSR holds 192 bits and is initialised by an initial vector (IV). NLF takes 8-bit inputs and returns a single output bit. The work identifies weaknesses and properties of the cipher. The main observation is that the initialisation procedure has the so-called sliding property. The property can be used to launch distinguishing and key recovery attacks. The distinguisher needs four observations of the related (K,IV) pairs. The key recovery algorithm allows to discover the secret key K after observing 29 pairs of (K,IV). Based on the proposed related-key attack, the number of related (K,IV) pairs is 2(128 + 192)/4 pairs. Further the cipher is studied when the registers enter short cycles. When NLFSR is set to all ones, then the cipher degenerates to a linear feedback shift register with a non-linear filter. Consequently, the initial state (and Secret Key and IV) can be recovered with complexity 263.87. If DLFSR is set to all zeros, then NLF reduces to a low non-linearity filter function. As the result, the cipher is insecure allowing the adversary to distinguish it from a random cipher after 217 observations of keystream bits. There is also the key recovery algorithm that allows to find the secret key with complexity 2 54.