Public-key cryptography and invariant theory

We suggest public-key cryptosystems based on groups invariants. We also give an overview of known cryptosystems that involve groups. Bibliography: 33 titles.

[1]  Leonid A. Levin,et al.  Average Case Complete Problems , 1986, SIAM J. Comput..

[2]  Oded Goldreich,et al.  Public-Key Cryptosystems from Lattice Reduction Problems , 1996, CRYPTO.

[3]  Yechezkel Zalcstein,et al.  The Complexity of Grigorchuk Groups with Application to Cryptography , 1991, Theor. Comput. Sci..

[4]  Lajos Rónyai.  Computations in Associative Algebras , 1991, Groups And Computation.

[5]  Jacques Stern,et al.  A New Public-Key Cryptosystem , 1997, EUROCRYPT.

[6]  Tatsuaki Okamoto,et al.  A New Public-Key Cryptosystem as Secure as Factoring , 1998, EUROCRYPT.

[7]  Mihir Bellare,et al.  Lecture Notes on Cryptography , 2001 .

[8]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[9]  Ueli Maurer,et al.  Lower Bounds on Generic Algorithms in Groups , 1998, EUROCRYPT.

[10]  A. Yao,et al.  Fair exchange with a semi-trusted third party (extended abstract) , 1997, CCS '97.

[11]  Andreas Blass,et al.  Matrix Transformation Is Complete for the Average Case , 1995, SIAM J. Comput..

[12]  Jung Hee Cheon,et al.  New Public-Key Cryptosystem Using Braid Groups , 2000, CRYPTO.

[13]  Joan Feigenbaum,et al.  Open Questions, Talk Abstracts, and Summary of Discussions , 1989, Distributed Computing And Cryptography.

[14]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[15]  Neal R. Wagner,et al.  A Public Key Cryptosystem Based on the Word Problem , 1985, CRYPTO.

[16]  Valeri V.Dolotin.  On Invariant Theory , 1995, alg-geom/9512011.

[17]  Tatsuaki Okamoto,et al.  New Public-Key Schemes Based on Elliptic Curves over the Ring Zn , 1991, CRYPTO.

[18]  V. Rich.  Personal communication , 1989, Nature.

[19]  Oded Goldreich,et al.  Modern Cryptography, Probabilistic Proofs and Pseudorandomness , 1998, Algorithms and Combinatorics.

[20]  Neal Koblitz,et al.  Algebraic aspects of cryptography , 1998, Algorithms and computation in mathematics.

[21]  Bernd Sturmfels,et al.  Algorithms in invariant theory , 1993, Texts and monographs in symbolic computation.

[22]  Cynthia Dwork,et al.  A public-key cryptosystem with worst-case/average-case equivalence , 1997, STOC '97.

[23]  Dima Grigoriev,et al.  On non-Abelian homomorphic public-key cryptosystems , 2002, ArXiv.

[24]  Jacques Stern,et al.  A new public key cryptosystem based on higher residues , 1998, CCS '98.

[25]  D. Goldfeld,et al.  An algebraic method for public-key cryptography , 1999 .

[26]  William Hugh Murray,et al.  Modern Cryptography , 1995, Information Security Journal.

[27]  From the Post-Markov Theorem Through Decision Problems to Public-Key Cryptography , 1993 .

[28]  Daesung Kwon,et al.  Improved Public Key Cryptosystem using Finite non Abelian Groups , 2001, IACR Cryptol. ePrint Arch..

[29]  Josh Benaloh,et al.  Dense Probabilistic Encryption , 1999 .

[30]  Eugene M. Luks,et al.  Permutation Groups and Polynomial-Time Computation , 1996, Groups And Computation.

[31]  J. Dieudonne,et al.  Invariant theory, old and new , 1971 .