A Uniform Min-Max Theorem with Applications in Cryptography.

This extension enables a number of additional applications in cryptography and complexity theory, often yielding uniform security versions of results that were previously only proved for nonuniform security ... (due to use of the non-constructive Min-Max Theorem). ... Acknowledgments We thank Kai-Min Chung for many helpful discussions, especially on SNARGs. ...

doi:10.1007/978-3-642-40041-4_6 fatcat:onfjuic7vbf5dk45rptnoderme

Metric entropy is a computational variant of entropy, often used as a convenient substitute of HILL Entropy, slightly stronger and standard notion for entropy in cryptographic applications. ... We apply these characterization to simplify and modularize proofs of some important results, in particular: (a) computational dense model theorem, (b) derivation of the improved version of Leftover Hash ... From the lemma it follows now that If we assume that max h E D A (U, h) (which means -security against A with the uniform key) and that max h E D A (U, h) 2 σ with σ = O ( ) (which means σ-square-security ...

doi:10.1007/978-3-319-17470-9_7 fatcat:lhmrsbzq3rcfxc4n5kty2o5rbq

The results have applications in cryptography for unconditionally secure protocols such as quantum key agreement, key agreement from correlated information, oblivious transfer, and bit commitment. ... Smooth entropy is a measure for the number of almost uniform random bits that can be extracted from a random source by probabilistic algorithms. ... Acknowledgment It is a pleasure to thank Ueli Maurer for his motivation and support and Jan Camenisch for helpful remarks. ...

doi:10.1007/3-540-69053-0_14 fatcat:d26pe3jkk5b4bk3yywydvvrh7u

More concretely, we prove that indistinguishability with uniform randomness implies differential indistinguishability with weak randomness. ... Physical randomness sources deployed in practical implementations of these protocols often fall short in meeting this assumption, but instead provide only a steady stream of bits with certain high entropy ... By Definition 2, D n has min-entropy at least n − α and max-entropy at most n + β. We start with (a). ...

doi:10.1007/978-3-319-28166-7_33 fatcat:ahpzefndhngv7ikuf3yle572dq

Our approach combines the standard min-max theorem and convex approximation techniques, offering quantitative improvements over the standard way of using min-max theorems as well as more concise and elegant ... We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. ... The problem is not with the standard min-max theorem but with an inadequate approximation argument in previous works, which do uniform approximation [Hol05] . ...

arXiv:1506.06633v1 fatcat:2i2i674eeffizbpomk3ymhfbwe

Along the way, we develop quantum analogues of some classical techniques (e.g. the Leakage Simulation Lemma, which is proven by a Non-uniform Min-Max Theorem or Boosting). ... Model Theorem (interpreted as the equivalence between two definitions of pseudo-relative-min-entropy) does not extend to quantum states. ... CYL acknowledges useful discussions with Todd A. Brun and Nengkun Yu. ...

arXiv:1704.07309v4 fatcat:tfqaqllhprhepddqrvw7wzytse

Multiple Versions

In particular, we obtain strong relations in terms of the von Neumann (Shannon) entropy as well as the min-entropy for measurements in (almost) unitary 2-designs, a full set of MUBs, and single qubit measurements ... A full version with complete proofs can be found online arXiv:1111.2026. ... The conditional min-entropy of a state ρ AB ∈ S(AB) is defined as H min (A|B) ρ = max σB ∈S(B) H min (A|B) ρ|σ (5) with H min (A|B) ρ|σ = max λ ∈ R : 2 −λ · I A ⊗ σ B ≥ ρ AB . ...

doi:10.1007/978-3-642-32009-5_45 fatcat:urzyxc4uhnfjjcwrc3kmjrrcme

Specifically, the min-entropy measures the amount of entanglement between E and A, and is the relevant measure when analyzing a wide variety of problems ranging from randomness extraction in quantum cryptography ... This is an abridged version of the paper; the full version containing all proofs and further applications can be found in [13] . ... Entropies Next to its operational interpretation given in (1) , the conditional min-entropy of a state ρ AB ∈ S(AB) can also be expressed as H min (A|B) ρ = max σB ∈S(B) H min (A|B) ρ|σ , with H min ( ...

doi:10.1007/978-3-642-40084-1_19 fatcat:rxcrdbarijf6jnm3ys2y2u43je

This material should be accessible to anybody with a minimal background in linear algebra and some familiarity with the computational framework of modern cryptography, but no prior knowledge about point ... So, unlike other areas of mathematical cryptology even a novice can acquire, with modest effort, a good understanding of not only the potential applications, but also the underlying mathematics of lattice ... So, in order to solve ADD (resp. BDD) we need to find a basis B such that s max (B) is small (resp. s min (B) is large). ...

doi:10.1007/978-3-642-23082-0_7 fatcat:fwjkhdpxpvckzewi6bc3kpa3qi

From corollary 6 it can be deduced that: NL((F, G)) ≤ min{NL(F), NL(G)} (19) The corollary 7 is a generalization of the Theorem 16 in Nyberg (1995) . ... {NL(S 1a ), NL(S 1b )} = min{86, 82} (21) Theorem 10. ...

doi:10.5772/34632 fatcat:5md6bvnmxbaqlmldtgbf5io7va

Our version allows for increasing the acceptable length of leakage in applications up to a constant factor compared to the best previous bounds. ... Computational notions of entropy (a.k.a. pseudoentropy) have found many applications, including leakage-resilient cryptography, deterministic encryption or memory delegation. ... Note that for k = n HILL entropy is simply pseudorandomness, as the only distribution over {0, 1} n with n bits of min-entropy is the uniform distribution. ...

doi:10.1007/978-3-319-22174-8_5 fatcat:ign722k3wvcxzjhj2nz7kat4qu

This idea of simulating auxiliary information turns out to be a powerful tool in computer science, finding applications in complexity theory, cryptography, pseudorandomness and zero-knowledge. ... In particular, with our technique we (finally) get meaningful provable security for the EUROCRYPT'09 leakage-resilient stream cipher instantiated with a standard 256-bit block cipher, like AES256. ... s h = O s · 2 ℓ ǫ −2 + 2 ℓ ǫ −4 The proof follows from a general regularity theorem which is based on their uniform min-max theorem. ...

arXiv:1503.00484v3 fatcat:pmfff2c5q5gbdeycqlegbz2wla

Multiple Versions

the subsequent application of a Calderbank-Shor-Steane quantum code. ... basic properties of quantum state purification protocols are investigated which are capable of purifying tensor products of Bell-diagonal states and which are based on B-steps of the Gottesman-Lo-type with ... Informative discussions with Georgios M Nikolopoulos are acknowledged. K S Ranade is supported by a graduate-student scholarship of the Technische Universität Darmstadt. ...

doi:10.1088/1751-8113/40/1/008 fatcat:mlsef3urc5dldhhe5wo4x7vlxq

Szczepanski Multiple Versions

Von Neumann's Min-Max Theorem guarantees that each player of a zero-sum matrix game has an optimal mixed strategy. ... This paper gives an elementary proof that each player has a near-optimal mixed strategy that chooses uniformly at random from a multiset of pure strategies of size logarithmic in the number of pure strategies ... Because of the fundamental role of games, we expect this theorem to have many applications in complexity theory and cryptography. ...

doi:10.1145/195058.195447 dblp:conf/stoc/LiptonY94 fatcat:objzumhl2fbtndimazd3nc5fh4

Multiple Versions

In this paper we derive a new quantum entropic uncertainty relation, bounding the conditional smooth quantum min entropy based on the result of a measurement using a two outcome POVM and the failure probability ... of a classical sampling strategy. ... In quantum cryptography, one may use min-entropy to determine how many uniform independent random bits may be extracted from a quantum state. ...

arXiv:2005.04773v2 fatcat:yeotqfvm5jhmljgmi2fr2isvfe

Multiple Versions

A Uniform Min-Max Theorem with Applications in Cryptography [chapter]

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Metric Pseudoentropy: Characterizations, Transformations and Applications [chapter]

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Smooth Entropy and Rényi Entropy [chapter]

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Secrecy Without Perfect Randomness: Cryptography with (Bounded) Weak Sources [chapter]

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A New Approximate Min-Max Theorem with Applications in Cryptography [article]

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Computational Notions of Quantum Min-Entropy [article]

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Quantum to Classical Randomness Extractors [chapter]

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Achieving the Limits of the Noisy-Storage Model Using Entanglement Sampling [chapter]

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The Geometry of Lattice Cryptography [chapter]

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Cryptographic Criteria on Vector Boolean Functions [chapter]

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The Chain Rule for HILL Pseudoentropy, Revisited [chapter]

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Simulating Auxiliary Inputs, Revisited [article]

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Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography

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Simple strategies for large zero-sum games with applications to complexity theory

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A New High-Dimensional Quantum Entropic Uncertainty Relation with Applications [article]

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