All-But-Many Lossy Trapdoor Functions under Decisional RSA Subgroup Assumption and Application

Nanyuan Cao; Zhenfu Cao; Zhen Liu; Xiaolei Dong; Xiaopeng Zhao

doi:10.1093/comjnl/bxz008

All-But-Many Lossy Trapdoor Functions under Decisional RSA Subgroup Assumption and Application

Nanyuan Cao, Zhenfu Cao^*, Zhen Liu, Xiaolei Dong, Xiaopeng Zhao

^*Corresponding author for this work

Software Engineering Institute

Research output: Contribution to journal › Article › peer-review

Abstract

Lossy trapdoor functions (LTDFs) were introduced by Peikert and Waters (STOC 2008) and have a number of applications in cryptography. All-but-many lossy trapdoor functions (ABM-LTDFs) are generalizations of LTDFs studied by Hofheinz (Eurocrypt 2012). Specially, using ABM-LTDFs to construct public key encryption (PKE) scheme with selective opening security has been proven feasible. Existing ABM-LTDFs were built on pairings, lattices and decisional composite residuosity (DCR) assumption. However, pairing-based ABM-LTDFs and DCR-based ABM-LTDFs rely on non-standard assumptions. In this paper, we construct an ABM-LTDF under the decisional RSA subgroup (DRSA) assumption, and we employ it to construct PKE scheme with selective opening security. We also propose a construction of DCR-based ABM-LTDF relying on standard assumption in Appendix.

Original language	English
Pages (from-to)	1148-1157
Number of pages	10
Journal	Gerontologist
Volume	59
Issue number	3
DOIs	https://doi.org/10.1093/comjnl/bxz008
State	Published - 1 Jun 2019

Keywords

Lossy trapdoor function
decisional RSA subgroup assumption
decisional composite residuosity assumption
semi-smooth RSA subgroup modulus

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10.1093/comjnl/bxz008

Cite this

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title = "All-But-Many Lossy Trapdoor Functions under Decisional RSA Subgroup Assumption and Application",

abstract = "Lossy trapdoor functions (LTDFs) were introduced by Peikert and Waters (STOC 2008) and have a number of applications in cryptography. All-but-many lossy trapdoor functions (ABM-LTDFs) are generalizations of LTDFs studied by Hofheinz (Eurocrypt 2012). Specially, using ABM-LTDFs to construct public key encryption (PKE) scheme with selective opening security has been proven feasible. Existing ABM-LTDFs were built on pairings, lattices and decisional composite residuosity (DCR) assumption. However, pairing-based ABM-LTDFs and DCR-based ABM-LTDFs rely on non-standard assumptions. In this paper, we construct an ABM-LTDF under the decisional RSA subgroup (DRSA) assumption, and we employ it to construct PKE scheme with selective opening security. We also propose a construction of DCR-based ABM-LTDF relying on standard assumption in Appendix.",

keywords = "Lossy trapdoor function, decisional RSA subgroup assumption, decisional composite residuosity assumption, semi-smooth RSA subgroup modulus",

author = "Nanyuan Cao and Zhenfu Cao and Zhen Liu and Xiaolei Dong and Xiaopeng Zhao",

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doi = "10.1093/comjnl/bxz008",

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T1 - All-But-Many Lossy Trapdoor Functions under Decisional RSA Subgroup Assumption and Application

AU - Cao, Nanyuan

AU - Cao, Zhenfu

AU - Liu, Zhen

AU - Dong, Xiaolei

AU - Zhao, Xiaopeng

PY - 2019/6/1

Y1 - 2019/6/1

N2 - Lossy trapdoor functions (LTDFs) were introduced by Peikert and Waters (STOC 2008) and have a number of applications in cryptography. All-but-many lossy trapdoor functions (ABM-LTDFs) are generalizations of LTDFs studied by Hofheinz (Eurocrypt 2012). Specially, using ABM-LTDFs to construct public key encryption (PKE) scheme with selective opening security has been proven feasible. Existing ABM-LTDFs were built on pairings, lattices and decisional composite residuosity (DCR) assumption. However, pairing-based ABM-LTDFs and DCR-based ABM-LTDFs rely on non-standard assumptions. In this paper, we construct an ABM-LTDF under the decisional RSA subgroup (DRSA) assumption, and we employ it to construct PKE scheme with selective opening security. We also propose a construction of DCR-based ABM-LTDF relying on standard assumption in Appendix.

AB - Lossy trapdoor functions (LTDFs) were introduced by Peikert and Waters (STOC 2008) and have a number of applications in cryptography. All-but-many lossy trapdoor functions (ABM-LTDFs) are generalizations of LTDFs studied by Hofheinz (Eurocrypt 2012). Specially, using ABM-LTDFs to construct public key encryption (PKE) scheme with selective opening security has been proven feasible. Existing ABM-LTDFs were built on pairings, lattices and decisional composite residuosity (DCR) assumption. However, pairing-based ABM-LTDFs and DCR-based ABM-LTDFs rely on non-standard assumptions. In this paper, we construct an ABM-LTDF under the decisional RSA subgroup (DRSA) assumption, and we employ it to construct PKE scheme with selective opening security. We also propose a construction of DCR-based ABM-LTDF relying on standard assumption in Appendix.

KW - Lossy trapdoor function

KW - decisional RSA subgroup assumption

KW - decisional composite residuosity assumption

KW - semi-smooth RSA subgroup modulus

UR - https://www.scopus.com/pages/publications/85084405001

U2 - 10.1093/comjnl/bxz008

DO - 10.1093/comjnl/bxz008

M3 - 文章

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SN - 0016-9013

VL - 59

SP - 1148

EP - 1157

JO - Gerontologist

JF - Gerontologist

IS - 3

ER -

All-But-Many Lossy Trapdoor Functions under Decisional RSA Subgroup Assumption and Application

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Keywords

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