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Lossy Trapdoor Functions and Their Applications
, 2007
"... We propose a new general primitive called lossy trapdoor functions (lossy TDFs), and realize it under a variety of different number theoretic assumptions, including hardness of the decisional DiffieHellman (DDH) problem and the worstcase hardness of lattice problems. Using lossy TDFs, we develop a ..."
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Cited by 126 (21 self)
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We propose a new general primitive called lossy trapdoor functions (lossy TDFs), and realize it under a variety of different number theoretic assumptions, including hardness of the decisional DiffieHellman (DDH) problem and the worstcase hardness of lattice problems. Using lossy TDFs, we develop
A feebly trapdoor function
, 2008
"... In 1992, A. Hiltgen [Hil92] provided the first constructions of provably (slightly) secure cryptographic primitives, namely feebly oneway functions. These functions are provably harder to invert than to compute, but the complexity (viewed as circuit complexity over circuits with arbitrary binary ga ..."
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Cited by 1 (1 self)
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gates) is amplified only by a constant factor (in Hiltgen’s works, the factor approaches 2). In traditional cryptography, oneway functions are the basic primitive of privatekey and digital signature schemes, while publickey cryptosystems are constructed with trapdoor functions. We continue Hiltgen’s
On the Lossiness of the Rabin Trapdoor Function
, 2013
"... Abstract. Lossy trapdoor functions, introduced by Peikert and Waters (STOC ’08), are functions that can be generated in two indistinguishable ways: either the function is injective, and there is a trapdoor to invert it, or the function is lossy, meaning that the size of its range is strictly smaller ..."
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Abstract. Lossy trapdoor functions, introduced by Peikert and Waters (STOC ’08), are functions that can be generated in two indistinguishable ways: either the function is injective, and there is a trapdoor to invert it, or the function is lossy, meaning that the size of its range is strictly
New Candidates for Multivariate Trapdoor Functions
"... Abstract. We present a new method for building pairs of HFE polynomials of high degree, such that the map constructed with one of these pairs is easy to invert. The inversion is accomplished using a low degree polynomial of Hamming weight three, which is derived from a special reduction via Hamming ..."
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weight three polynomials produced by these two HFE polynomials. This allows us to build new candidates for multivariate trapdoor functions in which we use the pair of HFE polynomials to fabricate the core map. We performed the security analysis for the case where the base field is GF (2) and showed
New candidates for multivariate trapdoor functions
"... Abstract. We present a new method for building pairs of HFE polynomials of high degree, such that the map constructed with such a pair is easy to invert. The inversion is accomplished using a low degree polynomial of Hamming weight three, which is derived from a special reduction via Hamming weight ..."
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three polynomials produced by these two HFE polynomials. This allows us to build new candidates for multivariate trapdoor functions in which we use the pair of HFE polynomials to fabricate the core map. We performed the security analysis for the case where the base field is GF (2) and showed
A feebly secure trapdoor function
"... In 1992, A. Hiltgen [1] provided the first constructions of provably (slightly) secure cryptographic primitives, namely feebly oneway functions. These functions are provably harder to invert than to compute, but the complexity (viewed as circuit complexity over circuits with arbitrary binary gates) ..."
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Cited by 5 (3 self)
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) is amplified by a constant factor only (with the factor approaching 2). In traditional cryptography, oneway functions are the basic primitive of privatekey and digital signature schemes, while publickey cryptosystems are constructed with trapdoor functions. We continue Hiltgen’s work by providing an example
More Constructions of Lossy and CorrelationSecure Trapdoor Functions
"... We propose new and improved instantiations of lossy trapdoor functions (Peikert and Waters, STOC ’08), and correlationsecure trapdoor functions (Rosen and Segev, TCC ’09). Our constructions widen the set of numbertheoretic assumptions upon which these primitives can be based, and are summarized as ..."
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We propose new and improved instantiations of lossy trapdoor functions (Peikert and Waters, STOC ’08), and correlationsecure trapdoor functions (Rosen and Segev, TCC ’09). Our constructions widen the set of numbertheoretic assumptions upon which these primitives can be based, and are summarized
IdentityBased (Lossy) Trapdoor Functions and Applications
, 2011
"... We provide the first constructions of identitybased (injective) trapdoor functions. Furthermore, they are lossy. Constructions are given both with pairings (DLIN) and lattices (LWE). Our lossy identitybased trapdoor functions provide an automatic way to realize, in the identitybased setting, many ..."
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Cited by 7 (2 self)
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We provide the first constructions of identitybased (injective) trapdoor functions. Furthermore, they are lossy. Constructions are given both with pairings (DLIN) and lattices (LWE). Our lossy identitybased trapdoor functions provide an automatic way to realize, in the identitybased setting
Short Signatures from Homomorphic Trapdoor Functions
, 2015
"... We present a latticebased stateless signature scheme provably secure in the standard model. Our scheme has a constant number of matrices in the public key and a single lattice vector (plus a tag) in the signatures. The best previous latticebased encryption schemes were the scheme of Ducas and Micc ..."
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) recent construction of homomorphic trapdoor functions into a primitive we call puncturable homomorphic trapdoor functions (PHTDFs). This primitive abstracts out most of the properties required in many different latticebased cryptographic constructions. We then show how to combine a PHTDF along with a
Allbutmany lossy trapdoor functions
 In EUROCRYPT
, 2012
"... We put forward a generalization of lossy trapdoor functions (LTFs). Namely, allbutmany lossy trapdoor functions (ABMLTFs) are LTFs that are parametrized with tags. Each tag can either be injective or lossy, which leads to an invertible or a lossy function. The interesting property of ABMLTFs is ..."
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Cited by 15 (4 self)
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We put forward a generalization of lossy trapdoor functions (LTFs). Namely, allbutmany lossy trapdoor functions (ABMLTFs) are LTFs that are parametrized with tags. Each tag can either be injective or lossy, which leads to an invertible or a lossy function. The interesting property of ABM
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