Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
On the existence of pseudorandom generators
SIAM Journal on Computing
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
Cryptographic primitives based on hard learning problems
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Selection of relevant features and examples in machine learning
Artificial Intelligence - Special issue on relevance
On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Hiding Cliques for Cryptographic Security
Designs, Codes and Cryptography
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Secure communications over insecure channels
Communications of the ACM
A personal view of average-case complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
More on Average Case vs Approximation Complexity
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Random Structures & Algorithms
Witnesses for non-satisfiability of dense random 3CNF formulas
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
SIAM Journal on Computing
Cryptography with constant computational overhead
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The Sum of d Small-Bias Generators Fools Polynomials of Degree d
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Linear Level Lasserre Lower Bounds for Certain k-CSPs
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic Barriers from Phase Transitions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
Poly-logarithmic Independence Fools AC^0 Circuits
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Merkle Puzzles Are Optimal -- An O(n2)-Query Attack on Any Key Exchange from a Random Oracle
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Basing weak public-key cryptography on strong one-way functions
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Computational complexity and information asymmetry in election audits with low-entropy randomness
EVT/WOTE'10 Proceedings of the 2010 international conference on Electronic voting technology/workshop on trustworthy elections
Proceedings of the fourth ACM international conference on Web search and data mining
Computational complexity and information asymmetry in financial products
Communications of the ACM
Input locality and hardness amplification
TCC'11 Proceedings of the 8th conference on Theory of cryptography
New algorithms for learning in presence of errors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Candidate one-way functions based on expander graphs
Studies in complexity and cryptography
Approximation algorithms and hardness of the k-route cut problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Cryptography from learning parity with noise
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Pseudorandom generators with long stretch and low locality from random local one-way functions
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A dichotomy for local small-bias generators
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Public-Key cryptography from new multivariate quadratic assumptions
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Statistical algorithms and a lower bound for detecting planted cliques
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Solving the learning parity with noise's open question
Information Processing Letters
Hi-index | 0.02 |
This paper attempts to broaden the foundations of public-key cryptography. We construct new public-key encryption schemes based on new hardness-on-average assumptions for natural combinatorial NP-hard optimization problems. We consider the following assumptions: It is infeasible to solve a random set of sparse linear equations mod 2, of which a small fraction is noisy. It is infeasible to distinguish between a random unbalanced bipartite graph, and such a graph in which we "plant" at random in the large side a set S with only |S|/3 neighbors. There is a pseudorandom generator in NCz where every output depends on a random constant-size subset of the inputs. We obtain semantically secure public key encryption schemes based on several combinations of these assumptions with different parameters. In particular we obtain public key encryption from Assumption~1 on its own, yielding the first noisy-equations type public key scheme in which the noise rate is higher than one over the square root of the number of equations. We also obtain public-key encryption based on a combination of Assumptions~2 and~3. These are arguably of more "combinatorial"/"private-key" nature than any assumptions used before for public-key cryptography. Our proof involves novel "search to decision" and "search to prediction" reductions for sparse noisy linear equations. The strength of our assumptions raise new algorithmic and pseudorandomness questions (and new parameters for old ones). We give some evidence for these assumptions by studying their resistance to certain classes of natural algorithms, including semi-definite programs, ACO circuits, low-degree polynomials, and cycle counting. We also relate our assumptions to other problems such as planted clique and learning juntas.