arXiv subjects

Boris Skoric

Publications and source records attributed to Boris Skoric.

At least 19 recordsLinked to original sources

arXiv2026

Continuous-variable approximate unitary 2-design, with applications to unclonable encryption

We introduce an $\varepsilon$-approximate unitary 2-design that is compatible with the structure of p- and q-quadratures in continuous-variable (CV) quantum systems. The design unitaries are defined on a finite-dimensional discretisation of the CV space and can be physically implemented as operations on the full CV space. This establishes the first approximate unitary design for CV systems. The design alternatingly acts with unitaries based on the quadrature operators $\hat q$ and $\hat p$. We prove that the parameter $\varepsilon$ is given by $1/d^\ell$, where $d$ is the dimension of the truncated Hilbert space and $\ell$ is the number of iterations. We propose an Unclonable Encryption scheme in which the encryption operators are given by the unitaries which constitute the approximate unitary design. We prove its security using recent results on decoupling. This establishes unclonable-indistinguishable security for a CV encryption for the first time.

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arXiv2025

Random coding for long-range continuous-variable QKD

Quantum Key Distribution (QKD) schemes are key exchange protocols based on the physical properties of quantum channels. They avoid the computational-hardness assumptions that underlie the security of classical key exchange. Continuous-Variable QKD (CVQKD), in contrast to qubit-based discrete-variable (DV) schemes, makes use of quadrature measurements of the electromagnetic field. CVQKD has the advantage of being compatible with standard telecom equipment, but at long distances has to deal with very low signal to noise ratios, which necessitates labour-intensive error correction. It is challenging to implement the error correction decoding in realtime. In this paper we introduce a random-codebook error correction method that is suitable for long range Gaussian-modulated CVQKD. We use likelihood ratio scoring with block rejection based on thresholding. For proof-technical reasons, the accept/reject decisions are communicated in encrypted form; in this way we avoid having to deal with non-Gaussian states in the analysis of the leakage. The error correction method is highly parallelisable, which is advantageous for realtime implementation. Under conservative assumptions on the computational resources, we predict a realtime key ratio of at least 8% of the Devetak-Winter value, which outperforms existing reconciliation schemes.

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arXiv2025

Continuous-Variable Quantum Key Distribution with key rates far above the PLOB bound

Continuous-Variable Quantum Key Distribution (CVQKD) at large distances has such high noise levels that the error-correcting code must have very low rate. In this regime it becomes feasible to implement random-codebook error correction, which is known to perform close to capacity. We propose a reverse reconciliation scheme for CVQKD in which the first step is advantage distillation based on random-codebook error correction operated above the Shannon limit. Our scheme has a novel way of achieving statistical decoupling between the public reconciliation data and the secret key. We provide an analysis of the secret key rate for the case of Gaussian collective attacks, and we present numerical results. The best performance is obtained when the message size exceeds the mutual information $I(X;Y)$ between Alice's quadratures $X$ and Bob's measurements $Y$, i.e. the Shannon limit. This somewhat counter-intuitive result is understood from a tradeoff between code rate and frame rejection rate, combined with the fact that error correction for QKD needs to reconcile only random data. We obtain secret key rates that lie far above the Devetak-Winter value $I(X;Y) - I(E;Y)$, which is the upper bound in the case of one-way error correction. Furthermore, our key rates lie above the PLOB bound for Continuous-Variable detection, but below the PLOB bound for Discrete-Variable detection.

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arXiv2024

Continuous-variable Quantum Position Verification secure against entangled attackers

Motivated by the fact that coherent states may offer practical advantages it was recently shown that a continuous-variable (CV) quantum position verification (QPV) protocol using coherent states could be securely implemented if and only if attackers do not pre-share any entanglement. In the discrete-variable (DV) analogue of that protocol it was shown that modifying how the classical input information is sent from the verifiers to the prover leads to a favourable scaling in the resource requirements for a quantum attack. In this work, we show that similar conclusions can be drawn for CV-QPV. By adding extra classical information of size $n$ to a CV-QPV protocol, we show that the protocol, which uses a coherent state and classical information, remains secure, even if the quantum information travels arbitrarily slow, against attackers who pre-share CV (entangled) states with a linear (in $n$) cutoff at the photon number. We show that the protocol remains secure for certain attenuation and excess noise.

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arXiv2024

Implementation of Entropically Secure Encryption: Securing Personal Health Data

Entropically Secure Encryption (ESE) offers unconditional security with shorter keys compared to the One-Time Pad. In this paper, we present the first implementation of ESE for bulk encryption. The main computational bottleneck for bulk ESE is a multiplication in a very large finite field. This involves multiplication of polynomials followed by modular reduction. We have implemented polynomial multiplication based on the gf2x library, with some modifications that avoid inputs of vastly different length, thus improving speed. Additionally, we have implemented a recently proposed efficient reduction algorithm that works for any polynomial degree. We investigate two use cases: X-ray images of patients and human genome data. We conduct entropy estimation using compression methods whose results determine the key lengths required for ESE. We report running times for all steps of the encryption. We discuss the potential of ESE to be used in conjunction with Quantum Key Distribution (QKD), in order to achieve full information-theoretic security of QKD-protected links for these use cases.

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arXiv2023

A simpler security proof for 6-state quantum key distribution

Six-state Quantum Key Distribution (QKD) achieves the highest key rate in the class of qubit-based QKD schemes. The standard security proof, which has been developed since 2005, invokes complicated theorems involving smooth Renyi entropies. In this paper we present a simpler security proof for 6-state QKD that entirely avoids Renyi entropies. This is achieved by applying state smoothing directly in the Bell basis. We furthermore show that the same proof technique can be used for 6-state quantum key recycling.

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arXiv2022

Entropically secure encryption with faster key expansion

Entropically secure encryption is a way to encrypt a large plaintext with a small key and still have information-theoretic security, thus in a certain sense circumventing Shannon's result that perfect encryption requires the key to be at least as long as the entropy of the plaintext. Entropically secure encryption is not perfect, and it works only if a lower bound is known on the entropy of the plaintext. The typical implementation is to expand the short key to the size of the plaintext, e.g. by multiplication with a public random string, and then use one-time pad encryption. This works in the classical as well as the quantum setting. In this paper, we introduce a new key expansion method that is faster than existing ones. We prove that it achieves the same security. The speed gain is most notable when the key length is a sizeable fraction of the message length. In particular, a factor of 2 is gained in the case of approximate randomization of quantum states.

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arXiv2022

Can't Touch This: unconditional tamper evidence from short keys

Storing data on an external server with information-theoretic security, while using a key shorter than the data itself, is impossible. As an alternative, we propose a scheme that achieves information-theoretically secure tamper evidence: The server is able to obtain information about the stored data, but not while staying undetected. Moreover, the client only needs to remember a key whose length is much shorter than the data. We provide a security proof for our scheme, based on an entropic uncertainty relation, similar to QKD proofs. Our scheme works if Alice is able to (reversibly) randomise the message to almost-uniformity with only a short key. By constructing an explicit attack we show that short-key unconditional tamper evidence cannot be achieved without this randomisability.

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arXiv2021

Quantum digital signatures with smaller public keys

We introduce a variant of quantum signatures in which nonbinary symbols are signed instead of bits. The public keys are fingerprinting states, just as in the scheme of Gottesman and Chuang, but we allow for multiple ways to reveal the private key partially. The effect of this modification is a reduction of the number of qubits expended per message bit. We give a security proof and we present numerical results that show how the improvement in public key size depends on the message length.

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arXiv2021

Diagrammatic security proof for 8-state encoding

Dirac notation is the most common way to describe quantum states and operations on states. It is very convenient and allows for quick visual distinction between vectors, scalars and operators. For quantum processes that involve interactions of multiple systems an even better visualisation has been proposed by Coecke and Kissinger, in the form of a diagrammatic formalism [CK2017]. Their notation expresses formulas in the form of diagrams, somewhat similar to Feynman diagrams, and is more general than the circuit notation for quantum computing. This document consists of two parts. (1) We give a brief summary of the diagrammatic notation of quantum processes, tailored to readers who already know quantum physics and are not interested in general process theory. For this audience our summary is less daunting than the encyclopaedic book by Coecke and Kissinger [CK2017], and on the other hand more accessible than the ultra-compact introduction of [KTW2017]. We deviate a somewhat from [CK2017,KTW2017] in that we do not assume basis states to equal their own complex conjugate; this means that we do not use symmetric notation for basis states, and it leads us to explicitly show arrows on wires where they are usually omitted. (2) We extend the work of Kissinger, Tull and Westerbaan [KTW2017] which gives a diagrammatic security proof for BB84 and 6-state Quantum Key Distribution. Their proof is based on a sequence of diagrammatic manipulations that works when the bases used in the protocol are mutually unbiased. We extend this result to 8-state encoding, which has been proposed as a tool in quantum key recycling protocols [SdV2017,LS2018], and which does not have mutually unbiased bases.

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arXiv2020

Two-way Unclonable Encryption with a vulnerable sender

Unclonable Encryption, introduced by Gottesman in 2003, is a quantum protocol that guarantees the secrecy of a successfully transferred classical message even when all keys leak at a later time. We propose an Unclonable Encryption protocol with the additional property that the sender's key material is allowed to leak even in the case of an unsuccessful run. This extra feature makes it possible to achieve secure quantum encryption even when one of the parties is unable to protect its keys against after-protocol theft. Such an asymmetry occurs e.g. in case of server-client scenarios, where the client device is resource-constrained and/or located in a hostile environment. Our protocol makes use of a bidirectional quantum channel in a manner similar to the two-way protocol LM05. Bob sends random qubit states to Alice. Alice flips the states in a way that depends on the message and a shared key, and sends the resulting states back to Bob. Bob recovers Alice's message by measuring the flips. We prove that our protocol satisfies the definition of unclonable encryption and additionally that the message remains secure even if all of Alice's keys leak after the protocol. Furthermore, we show that some of the key material can be safely re-used. Our security proof is formulated in terms of diamond norms, which makes it composable, and allows for noisy quantum channels. We work out the details only for the asymptotics in the limit of long messages. As a side result we construct a two-way QKD scheme with a high key rate. We show that its key rate is higher than the rate of the two-way QKD scheme LM05 proven for the case of independent channel noise.

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arXiv2020

Qubit-based Unclonable Encryption with Key Recycling

We re-visit Unclonable Encryption as introduced by Gottesman in 2003. We look at the combination of Unclonable Encryption and Key Recycling, while aiming for low communication complexity and high rate. We introduce a qubit-based prepare-and-measure Unclonable Encryption scheme with re-usable keys. Our scheme consists of a single transmission by Alice and a single classical feedback bit from Bob. The transmission from Alice to Bob consists entirely of qubits. The rate, defined as the message length divided by the number of qubits, is higher than what can be achieved using Gottesman's scheme. We provide a security proof based on the diamond norm distance, taking noise into account.

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arXiv2020

The Blob: provable incompressibility and traceability in the whitebox model

We introduce a scheme for distributing and storing software with cryptographic functionality in the whitebox attacker model. Our scheme satisfies two relevant properties: incompressibility and traceability. The main idea is to store a large amount of random data (a `blob'), some of which will be randomly sampled in the future to serve as key material, and some of which serves as a watermark. We study two variants: with and without re-use of key material. For both variants we analyse how many decryptions can be performed with the blob, taking into account collusion attacks against the watermark. Our results show that application of blob schemes in the context of pay-TV is feasible.

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arXiv2020

Quantum Alice and Silent Bob: Qubit-based Quantum Key Recycling with almost no classical communication

We answer an open question about Quantum Key Recycling (QKR): Is it possible to put the message entirely in the qubits without increasing the number of qubits? We show that this is indeed possible. We introduce a prepare-and-measure QKR protocol where the communication from Alice to Bob consists entirely of qubits. As usual, Bob responds with an authenticated one-bit accept/reject classical message. Compared to Quantum Key Distribution (QKD), QKR has reduced round complexity. Compared to previous qubit-wise QKR protocols, our scheme has far less classical communication. We provide a security proof in the universal composability framework and find that the communication rate is asymptotically the same as for QKD with one-way postprocessing.

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arXiv2020

Locally Differentially Private Frequency Estimation with Consistency

Local Differential Privacy (LDP) protects user privacy from the data collector. LDP protocols have been increasingly deployed in the industry. A basic building block is frequency oracle (FO) protocols, which estimate frequencies of values. While several FO protocols have been proposed, the design goal does not lead to optimal results for answering many queries. In this paper, we show that adding post-processing steps to FO protocols by exploiting the knowledge that all individual frequencies should be non-negative and they sum up to one can lead to significantly better accuracy for a wide range of tasks, including frequencies of individual values, frequencies of the most frequent values, and frequencies of subsets of values. We consider 10 different methods that exploit this knowledge differently. We establish theoretical relationships between some of them and conducted extensive experimental evaluations to understand which methods should be used for different query tasks.

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arXiv2019

Estimating Numerical Distributions under Local Differential Privacy

When collecting information, local differential privacy (LDP) relieves the concern of privacy leakage from users' perspective, as user's private information is randomized before sent to the aggregator. We study the problem of recovering the distribution over a numerical domain while satisfying LDP. While one can discretize a numerical domain and then apply the protocols developed for categorical domains, we show that taking advantage of the numerical nature of the domain results in better trade-off of privacy and utility. We introduce a new reporting mechanism, called the square wave SW mechanism, which exploits the numerical nature in reporting. We also develop an Expectation Maximization with Smoothing (EMS) algorithm, which is applied to aggregated histograms from the SW mechanism to estimate the original distributions. Extensive experiments demonstrate that our proposed approach, SW with EMS, consistently outperforms other methods in a variety of utility metrics.

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arXiv2018

Fingerprint template protection using minutia-pair spectral representations

Storage of biometric data requires some form of template protection in order to preserve the privacy of people enrolled in a biometric database. One approach is to use a Helper Data System. Here it is necessary to transform the raw biometric measurement into a fixed-length representation. In this paper we extend the spectral function approach of Stanko and Skoric [WIFS2017], which provides such a fixed-length representation for fingerprints. First, we introduce a new spectral function that captures different information from the minutia orientations. It is complementary to the original spectral function, and we use both of them to extract information from a fingerprint image. Second, we construct a helper data system consisting of zero-leakage quantisation followed by the Code Offset Method. We show empirical data which demonstrates that applying our helper data system causes only a small performance penalty compared to fingerprint authentication based on the unprotected spectral functions.

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arXiv2018

Security proof for Round Robin Differential Phase Shift QKD

We give a security proof of the `Round Robin Differential Phase Shift' Quantum Key Distribution scheme, and we give a tight bound on the required amount of privacy amplification. Our proof consists of the following steps. We construct an EPR variant of the scheme. We identify Eve's optimal way of coupling an ancilla to an EPR qudit pair under the constraint that the bit error rate between Alice and Bob should not exceed a value beta. As a function of beta we derive, for finite key size, the trace distance between the real state and a state in which no leakage exists. For asymptotic key size we obtain a bound on the trace distance by computing the von Neumann entropy. Our asymptotic result for the privacy amplification is sharper than existing bounds.

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