Positive applications of lattices to cryptography

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1295, Issue , 1997, Pages 44-51

  Dwork, Cynthia ^a  

^a IBM ALMADEN RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NUMBER THEORY; PUBLIC KEY CRYPTOGRAPHY;

AVERAGE-CASE HARDNESS; CRYPTOGRAPHIC PRIMITIVES; PSEUDO RANDOM BIT GENERATORS; PUBLIC KEY CRYPTOSYSTEMS;

NETWORK SECURITY;

EID: 38349062340     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0029948     Document Type: Conference Paper

References (26)

1. L. Adleman, On Breaking Generalized Knapsack Public Key Cryptosystems, Proceedings 15th Annual ACM Symposium on Theory of Computing, 1983, pp. 402-412
2. M. Ajtai, Generating Hard Instances of Lattice Problems, Proceedings 28th Annual ACM Symposium on Theory of Computing, 1996, pp. 99-108 Electronic Colloquium on Computational Complexity TR96-007, http://www.eccc.uni-trier.de/eccc-local/Lists/TR-1996.html
3. M. Ajtai, discussion with the author, 1996
4. M. Ajtai, C. Dwork, A Public-Key Cryptosystem with Average-Case/Worst-Case Equivalence, Proceedings 29th Annual ACM Symposium on Theory of Computing, 1997; see also Electronic Colloquium on Computational Complexity TR96-065, http://www.eccc.uni-trier.de/eccc-local/Lists/TR-1996.html
5. L. Babai, On Lovasz’ Lattice Reduction and the Nearest Lattice Point Problem, Combinatorica. 6(1), 1986, pp. 1-13
6. M. Blum and S. Micali, How to Generate Cryptographically Strong Sequences of PseudoRandom Bits, SIAM J. Computing 13, 1984, pp. 850-864
7. J.-Y. Cai and A. P. Nerurkar, An Improved Worst-Case to Average-Case Connection for Lattice Problems, private communication, 1997
8. J.W.S. Cassels, An Introduction to the Geometry of Numbers, Springer, 1959
9. D. Coppersmith, Finding a Small Root of a Univariate Modular Equation, Proc. EVRO-CRYPT’96
10. D. Coppersmith, M. Franklin. J. Patarin, and M. Reiter, Low Exponent RSA with Related Messages, Pioc. EUROCRYPT'96
11. D. Dolev, C. Dwork, and M. Naor. Non-Malleable Cryptography, Proceedings 23th Annual ACM Symposium on Theory of Computing, 1991, pp. 542-550
12. O. Goldreich, Foundations of Cryptography (Fragments of a Book), http://www.wisdom.weizmann.ac.il/people/homepages/oded/frag.html
13. O. Goldreich, S. Goldwasser, and S. Halevi, Collision-Free Hashing from Lattice Problems, Electronic Colloquium on Computational Complexity TR96-042, http://www.eccc.uni-trier.de/eccc-local/Lists/TR-1996.html
14. O. Goldreich, S. Goldwasser, and S. Halevi, Public-Key Cryptosystems from Lattice Reduction Problems, Electronic Colloquium on Computational Complexity TR96-056, http://www.eccc.aiu-trier.de/eccc-local/Lists/TR-1996.html
15. O. Goldreich, S. Goldwasser, and S. Halevi, Eliminating the Decryption Error in the Ajtai-Dwork Cryptosystem, to appear, Proc. CRYPTO'97
16. S. Goldwasser and S. Micali, Probabilistic Encryption, J. Comput. System Sd. 28, 1984, pp. 270-299
17. S. Goldwasser, S. Micali, and R. Rivest, A “Paradoxical” Solution to the Signature Problem, SIAM J. Computing IT, 1988, pp. 281-308
18. M. Grotschel, Lovasz, A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer, Algorithms and Combinatorics 2, 1988
19. P.M. Gruber, C.G. Lekkerkerker, Geometry of Numbers, North-Holland, 1987
20. J. Hastad, Solving Simultaneous Modular Equations of Low Degree, SIAM J, Computing 17(2), pp.336-341, 1988
21. R. Impagliazzo and M. Naor, Efficient Cryptographic Schemes Provably as Secure as Subset Sum, J. Cryptology 9, pp. 199-216, 1996
22. J.C. Lagarias, A.M. Odlyzko, Solving low-density subset sum problems, Journal of the Association for Computing Machinery 32 pp. 229-246, 1985. An earlier version appeared in Proc. 24th Annual Symposium on Foundations of Computer Science, 1983
23. M. Luby, Pseudo-randomness and, applications, Princeton University Press, 1996.
24. M. Naor and M. Yung, Universal One-Way Hash Functions and Their Cryptographic Applies tions, Proceedings 21th Annual ACM Symposium on Theory of Computing, 1989, pp. 33-43
25. A. Shamir, A Polynomial-Time Algorithm for Breaking the Basic Merkle-Hellman Cryptosystem, Proc. 23rd Annual Symposium on Foundations of Computer Science, 1982, pp. 145-152
26. A. C. Yao, Theory and Applications of Trapdoor Functions, Proc. 23rd Annual Symposium on Foundations of Computer Science, 1982, pp. 80-91014