TY - GEN
T1 - More constructions of lossy and correlation-secure trapdoor functions
AU - Freeman, David Mandell
AU - Goldreich, Oded
AU - Kiltz, Eike
AU - Rosen, Alon
AU - Segev, Gil
PY - 2010
Y1 - 2010
N2 - We propose new and improved instantiations of lossy trapdoor functions (Peikert and Waters, STOC '08), and correlation-secure trapdoor functions (Rosen and Segev, TCC '09). Our constructions widen the set of number-theoretic assumptions upon which these primitives can be based, and are summarized as follows: Lossy trapdoor functions based on the quadratic residuosity assumption. Our construction relies on modular squaring, and whereas previous such constructions were based on seemingly stronger assumptions, we present the first construction that is based solely on the quadratic residuosity assumption. Lossy trapdoor functions based on the composite residuosity assumption. Our construction guarantees essentially any required amount of lossiness, where at the same time the functions are more efficient than the matrix-based approach of Peikert and Waters. Lossy trapdoor functions based on the d-Linear assumption. Our construction both simplifies the DDH-based construction of Peikert and Waters, and admits a generalization to the whole family of d-Linear assumptions without any loss of efficiency. Correlation-secure trapdoor functions related to the hardness of syndrome decoding.
AB - We propose new and improved instantiations of lossy trapdoor functions (Peikert and Waters, STOC '08), and correlation-secure trapdoor functions (Rosen and Segev, TCC '09). Our constructions widen the set of number-theoretic assumptions upon which these primitives can be based, and are summarized as follows: Lossy trapdoor functions based on the quadratic residuosity assumption. Our construction relies on modular squaring, and whereas previous such constructions were based on seemingly stronger assumptions, we present the first construction that is based solely on the quadratic residuosity assumption. Lossy trapdoor functions based on the composite residuosity assumption. Our construction guarantees essentially any required amount of lossiness, where at the same time the functions are more efficient than the matrix-based approach of Peikert and Waters. Lossy trapdoor functions based on the d-Linear assumption. Our construction both simplifies the DDH-based construction of Peikert and Waters, and admits a generalization to the whole family of d-Linear assumptions without any loss of efficiency. Correlation-secure trapdoor functions related to the hardness of syndrome decoding.
KW - Public-key encryption
KW - correlation-secure trapdoor functions
KW - lossy trapdoor functions
UR - http://www.scopus.com/inward/record.url?scp=79955545739&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-13013-7_17
DO - 10.1007/978-3-642-13013-7_17
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AN - SCOPUS:79955545739
SN - 3642130127
SN - 9783642130120
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 279
EP - 295
BT - Public Key Cryptography, PKC 2010 - 13th International Conference on Practice and Theory in Public Key Cryptography, Proceedings
T2 - 13th International Conference on Practice and Theory in Public Key Cryptography, PKC 2010
Y2 - 26 May 2010 through 28 May 2010
ER -