Public-Key Cryptographic Primitives Provably as Secure as Subset Sum

Lyubashevsky, Vadim; Palacio, Adriana; Segev, Gil

doi:10.1007/978-3-642-11799-2_23

Cited by 65 publications

(46 citation statements)

References 38 publications

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“…One expects that with high probability at least one of these ways will satisfy Σ(I 11 ) ≡ s 11 (mod M 1 ), implying Σ(I 12 ) ≡ s 12 (mod M 1 ) (since M 1 divides M and s 11 + s 12 = s 1 ). Analogous comments apply to I 2 , I 21 , I 22 .…”

Section: T T T T T T T T T T T T Tmentioning

confidence: 93%

“…For example, Lyubashevsky, Palacio, and Segev in [22] propose a public-key encryption system and prove that being able to break it implies being able to solve modular subset-sum problems of the following type: find a random subset I ⊆ {1, 2, . .…”

Section: Introductionmentioning

confidence: 99%

“…, x n modulo M and given i∈I x i modulo M , where M is roughly (10n log n) n . They claim in [22,Section 1] that "there are currently no known quantum algorithms that perform better than classical ones on the subset sum problem". Contents of this paper.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum Algorithms for the Subset-Sum Problem

Bernstein

Jeffery

Lange

et al. 2013

Post-Quantum Cryptography

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Section: T T T T T T T T T T T T Tmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Algorithms for the Subset-Sum Problem

Bernstein

Jeffery

Lange

et al. 2013

Post-Quantum Cryptography

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“…This limitation was overcome by the work of Lyubashevsky, Palacio, and Segev [22] that proposed a new PKE scheme achieving IND-CPA security with a simple and direct reduction to solving random instances of the Subset Sum problem.…”

Section: Introductionmentioning

confidence: 99%

Chosen-Ciphertext Security from Subset Sum

Faust

Masny

Venturi

2016

Public-Key Cryptography – PKC 2016

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Abstract. We construct a public-key encryption (PKE) scheme whose security is polynomial-time equivalent to the hardness of the Subset Sum problem. Our scheme achieves the standard notion of indistinguishability against chosen-ciphertext attacks (IND-CCA) and can be used to encrypt messages of arbitrary polynomial length, improving upon a previous construction by Lyubashevsky, Palacio, and Segev (TCC 2010) which achieved only the weaker notion of semantic security (IND-CPA) and whose concrete security decreases with the length of the message being encrypted. At the core of our construction is a trapdoor technique which originates in the work of Micciancio and Peikert (Eurocrypt 2012).

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“…Usually the leakage bound is also related to the secret key size, so that a relatively large fraction of the secret key can be leaked. Leakage-resilient schemes in this model include storage schemes [25,30], public-key and identity-based encryption [59,2,56,1,13,27,12,18,47], signature schemes [50,2,13,27,11,57,37,60,61,21], and more (see, e.g., [40,10,63,62]). …”

Section: Introductionmentioning

confidence: 99%

Mind Your Coins: Fully Leakage-Resilient Signatures with Graceful Degradation

Faonio

Nielsen

Venturi

2015

Automata, Languages, and Programming

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We construct new leakage-resilient signature schemes. Our schemes remain unforgeable against an adversary leaking arbitrary (yet bounded) information on the entire state of the signer (sometimes known as fully leakage resilience), including the random coin tosses of the signing algorithm.The main feature of our constructions is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible. This property was recently put forward by Nielsen, Venturi, and Zottarel (PKC 2014) to deal with settings in which the secret key is much larger than the size of a signature. One remarkable such case is the so-called Bounded-Retrieval Model (BRM), where one intentionally inflates the size of the secret key while keeping constant the signature size and the computational complexity of the scheme.Our main constructions have leakage rate 1 − o(1), and are proven secure in the standard model. We additionally give a construction in the BRM, relying on a random oracle. All of our schemes are described in terms of generic building blocks, but also admit efficient instantiations under fairly standard number-theoretic assumptions. Finally, we explain how to extend some of our schemes to the setting of noisy leakage, where the only restriction on the leakage functions is that the output does not decrease the min-entropy of the secret key by too much.

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Public-Key Cryptographic Primitives Provably as Secure as Subset Sum

Cited by 65 publications

References 38 publications

Quantum Algorithms for the Subset-Sum Problem

Quantum Algorithms for the Subset-Sum Problem

Chosen-Ciphertext Security from Subset Sum

Mind Your Coins: Fully Leakage-Resilient Signatures with Graceful Degradation

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