Modulus Computational Entropy

Skorski, Maciej

doi:10.1007/978-3-319-04268-8_11

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…Leakage Chain Rule for quantum HILL pseudoentropy. The classical Leakage Chain Rule for rHILL pseudoentropy, first proved by [DP08,RTTV08] and improved by [FR12,Sko13], states that for a joint distribution (X, Z, B) where B consists of ℓ = O(log κ) bits,…”

Section: Leakage Chain Rulementioning

confidence: 99%

Computational Notions of Quantum Min-Entropy

Chen¹,

Chung²,

Lai³

et al. 2017

Preprint

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We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold. Our main results are as follows.(1) The classical Leakage Chain Rule for pseudoentropy can be extended to the case that the leakage information is quantum (while the source remains classical). Specifically, if the source has pseudoentropy at least k, then it has pseudoentropy at least k − ℓ conditioned on an ℓqubit leakage. (2) As an application of the Leakage Chain Rule, we construct the first quantum leakage-resilient stream-cipher in the bounded-quantum-storage model, assuming the existence of a quantum-secure pseudorandom generator. (3) We show that the general form of the classical Dense Model Theorem (interpreted as the equivalence between two definitions of pseudo-relativemin-entropy) does not extend to quantum states. Along the way, we develop quantum analogues of some classical techniques (e.g., the Leakage Simulation Lemma, which is proven by a Nonuniform Min-Max Theorem or Boosting). On the other hand, we also identify some classical techniques (e.g., Gap Amplification) that do not work in the quantum setting. Moreover, we introduce a variety of notions that combine quantum information and quantum complexity, and this raises several directions for future work.

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Section: Leakage Chain Rulementioning

confidence: 99%

Computational Notions of Quantum Min-Entropy

Chen¹,

Chung²,

Lai³

et al. 2017

Preprint

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show abstract

“…One of the primary uses of HILL entropy is that applying a randomness extractor [NZ93] yields pseudorandom bits [BSW03, Lemma 4.2]. There are many notions of indistinguishability based pseudoentropy [BSW03,Sko14]. One significant drawback of conditional HILL entropy is that revealing one bit can significantly decrease HILL entropy [KPW13].…”

Section: Pseudoentropymentioning

confidence: 99%

Unifying Leakage Classes: Simulatable Leakage and Pseudoentropy

Fuller

Hamlin

2015

Lecture Notes in Computer Science

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Leakage-resilient cryptography builds systems that withstand partial adversary knowledge of secret state. Ideally, leakage-resilient systems withstand current and future attacks; restoring confidence in the security of implemented cryptographic systems. Understanding the relation between classes of leakage functions is an important aspect.In this work, we consider the memory leakage model, where the leakage class contains functions over the system's entire secret state. Standard classes include functions with bounded output length, functions that retain (pseudo) entropy in the secret, and functions that leave the secret computationally unpredictable.Standaert, Pereira, and Yu (Crypto, 2013) introduced a new class of leakage functions they call simulatable leakage. A leakage function is simulatable if a simulator can produce indistinguishable leakage without access to the true secret state. We extend their notion to general applications and consider two versions. For weak simulatability: the simulated leakage must be indistinguishable from the true leakage in the presence of public information. For strong simulatability, this requirement must also hold when the distinguisher has access to the true secret state. We show the following:

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“…A counterexample to the chain rule using ideas from deniable encryption was recently shown by Krenn et al [42]. Skorski [57] provides a general characterization of when the chain rule applies.…”

Section: Work On Conditional Computational Entropymentioning

confidence: 99%

A Unified Approach to Deterministic Encryption: New Constructions and a Connection to Computational Entropy

2013

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This paper addresses deterministic public-key encryption schemes (DE), which are designed to provide meaningful security when only source of randomness in the encryption process comes from the message itself. We propose a general construction of DE that unifies prior work and gives novel schemes. Specifically, its instantiations include:• The first construction from any trapdoor function that has sufficiently many hardcore bits.• The first construction that provides "bounded" multi-message security (assuming lossy trapdoor functions).The security proofs for these schemes are enabled by three tools that are of broader interest:• A weaker and more precise sufficient condition for semantic security on a high-entropy message distribution. Namely, we show that to establish semantic security on a distribution M of messages, it suffices to establish indistinguishability for all conditional distribution M |E, where E is an event of probability at least 1/4. (Prior work required indistinguishability on all distributions of a given entropy.)• A result about computational entropy of conditional distributions. Namely, we show that conditioning on an event E of probability p reduces the quality of computational entropy by a factor of p and its quantity by log 2 1/p.• A generalization of leftover hash lemma to correlated distributions.We also extend our result about computational entropy to the average case, which is useful in reasoning about leakage-resilient cryptography: leaking λ bits of information reduces the quality of computational entropy by a factor of 2 λ and its quantity by λ.

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Modulus Computational Entropy

Cited by 5 publications

References 16 publications

Computational Notions of Quantum Min-Entropy

Computational Notions of Quantum Min-Entropy

Unifying Leakage Classes: Simulatable Leakage and Pseudoentropy

A Unified Approach to Deterministic Encryption: New Constructions and a Connection to Computational Entropy

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