Generic Hardness of Inversion on Ring and Its Relation to Self-Bilinear Map

[1]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[2]  Adi Shamir,et al.  Factoring Numbers in O(log n) Arithmetic Steps , 1979, Inf. Process. Lett..

[3]  Endre Szemerédi,et al.  On the Complexity of Matrix Group Problems I , 1984, FOCS.

[4]  H. W. Lenstra,et al.  Factoring integers with elliptic curves , 1987 .

[5]  Silvio Micali,et al.  How to construct random functions , 1986, JACM.

[6]  Michael Luby,et al.  How to Construct Pseudo-Random Permutations from Pseudo-Random Functions (Abstract) , 1986, CRYPTO.

[7]  Leonid A. Levin,et al.  A hard-core predicate for all one-way functions , 1989, STOC '89.

[8]  Richard J. Lipton,et al.  Straight-line complexity and integer factorization , 1994, ANTS.

[9]  V. Nechaev.  Complexity of a determinate algorithm for the discrete logarithm , 1994 .

[10]  M. Shub,et al.  On The Intractability Of Hilbert's Nullstellensatz And An Algebraic Version Of . . , 1995 .

[11]  Victor Shoup,et al.  Lower Bounds for Discrete Logarithms and Related Problems , 1997, EUROCRYPT.

[12]  Leonid A. Levin,et al.  A Pseudorandom Generator from any One-way Function , 1999, SIAM J. Comput..

[13]  Amit Sahai,et al.  On the (im)possibility of obfuscating programs , 2001, JACM.

[14]  Ivan Damgård,et al.  Generic Lower Bounds for Root Extraction and Signature Schemes in General Groups , 2002, EUROCRYPT.

[15]  Dawn Xiaodong Song,et al.  Homomorphic Signature Schemes , 2002, CT-RSA.

[16]  Dan Boneh,et al.  Applications of Multilinear Forms to Cryptography , 2002, IACR Cryptol. ePrint Arch..

[17]  Susan Rae Hohenberger,et al.  The cryptographic impact of groups with infeasible inversion , 2003 .

[18]  Ronald L. Rivest.  On the Notion of Pseudo-Free Groups , 2004, TCC.

[19]  Qi Cheng.  On the ultimate complexity of factorials , 2004, Theor. Comput. Sci..

[20]  Hyang-Sook Lee.  A self-pairing map and its applications to cryptography , 2004, Appl. Math. Comput..

[21]  Daniele Micciancio,et al.  The RSA Group is Pseudo-Free , 2005, Journal of Cryptology.

[22]  Gregor Leander,et al.  On the Equivalence of RSA and Factoring Regarding Generic Ring Algorithms , 2006, ASIACRYPT.

[23]  Kevin S. McCurley,et al.  A key distribution system equivalent to factoring , 1988, Journal of Cryptology.

[24]  Tibor Jager,et al.  On Black-Box Ring Extraction and Integer Factorization , 2008, ICALP.

[25]  Eike Kiltz,et al.  The Group of Signed Quadratic Residues and Applications , 2009, CRYPTO.

[26]  Dong Hoon Lee,et al.  A NOTE ON SELF-BILINEAR MAPS , 2009 .

[27]  U. Maurer,et al.  The Equivalence of Strong RSA and Factoring in the Generic Ring Model of Computation , 2011 .

[28]  Nir Bitansky,et al.  From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again , 2012, ITCS '12.

[29]  Tibor Jager,et al.  On the Analysis of Cryptographic Assumptions in the Generic Ring Model , 2009, Journal of Cryptology.

[30]  Yannick Seurin,et al.  New Constructions and Applications of Trapdoor DDH Groups , 2013, Public Key Cryptography.

[31]  Craig Gentry,et al.  Candidate Multilinear Maps from Ideal Lattices , 2013, EUROCRYPT.

[32]  Daniel R. L. Brown,et al.  Breaking RSA May Be As Difficult As Factoring , 2014, Journal of Cryptology.

[33]  Bogdan Warinschi,et al.  Homomorphic Signatures with Efficient Verification for Polynomial Functions , 2014, CRYPTO.

[34]  Daniel Wichs,et al.  Leveled Fully Homomorphic Signatures from Standard Lattices , 2015, IACR Cryptol. ePrint Arch..

[35]  Sungwook Kim,et al.  Multilinear Map via Scale-Invariant FHE: Enhancing Security and Efficiency , 2015, IACR Cryptol. ePrint Arch..

[36]  Klas Markström.  The straight line complexity of small factorials and primorials , 2015, Integers.

[37]  Amit Sahai,et al.  Multi-party Key Exchange for Unbounded Parties from Indistinguishability Obfuscation , 2015, ASIACRYPT.

[38]  Omer Paneth,et al.  On the Equivalence of Obfuscation and Multilinear Maps , 2015, IACR Cryptol. ePrint Arch..

[39]  Kenneth G. Paterson,et al.  Multilinear Maps from Obfuscation , 2016, Journal of Cryptology.

[40]  Goichiro Hanaoka,et al.  Self-Bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications , 2014, Algorithmica.

[41]  Ueli Maurer,et al.  Breaking RSA Generically Is Equivalent to Factoring , 2009, IEEE Transactions on Information Theory.

[42]  Eric Miles,et al.  Secure Obfuscation in a Weak Multilinear Map Model , 2016, TCC.

[43]  Goichiro Hanaoka,et al.  Generalized Hardness Assumption for Self-bilinear Map with Auxiliary Information , 2016, ACISP.

[44]  Eric Miles,et al.  Annihilation Attacks for Multilinear Maps: Cryptanalysis of Indistinguishability Obfuscation over GGH13 , 2016, CRYPTO.

[45]  Mark Zhandry,et al.  Multiparty Key Exchange, Efficient Traitor Tracing, and More from Indistinguishability Obfuscation , 2014, Algorithmica.

[46]  Dennis Hofheinz,et al.  Graded Encoding Schemes from Obfuscation , 2018, Public Key Cryptography.

[47]  Yilei Chen,et al.  A Candidate Group with Infeasible Inversion , 2018, IACR Cryptol. ePrint Arch..

[48]  Mark Zhandry,et al.  The Distinction Between Fixed and Random Generators in Group-Based Assumptions , 2019, IACR Cryptol. ePrint Arch..