We show very efficient constructions for a pseudo-random generator and for a universal one-way hash function based on the intractability of the subset sum problem for certain dimensions. (Pseudo-random generators can be used for private key encryption and universal one-way hash functions for signature schemes). The increase in efficiency in our construction is due to the fact that many bits can be generated/hashed with one application of the assumed one-way function. All our construction can be implemented in NC using an optimal number of processors.
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844
|
Probabilistic encryption
– Goldwasser, Micali
- 1984
|
|
480
|
How to construct random functions
– Goldreich, Goldwasser, et al.
- 1986
|
|
474
|
A pseudorandom generator from any one-way function
– stad, Impagliazzo, et al.
- 1999
|
|
470
|
Universal classes of hash functions
– Carter, Wegman
- 1979
|
|
466
|
How to generate Cryptographically Strong Sequences of Pseudo-Random Bits
– Blum, Micali
- 1984
|
|
415
|
Theory and applications of trapdoor functions
– Yao
- 1982
|
|
407
|
Factoring polynomials with rational coefficients
– Lenstra, Lenstra, et al.
- 1982
|
|
232
|
Reducibility among combinatorial problems, Complexity of Computer Computations
– Karp
- 1972
|
|
230
|
A hard-core predicate for all one-way functions
– Goldreich, Levin
- 1989
|
|
219
|
Minimum disclosure proofs of knowledge
– Brassard, Chaum, et al.
- 1988
|
|
202
|
How to construct pseudorandom permutations from pseudorandom functions
– Luby, Rackoff
- 1988
|
|
199
|
Constant depth circuits, Fourier transform, and learnability
– Linial, Mansour, et al.
- 1993
|
|
167
|
How to recycle random bits
– Impagliazzo, Zuckerman
- 1989
|
|
166
|
A Simple Unpredictable PseudoRandom Number Generator
– Blum, Blum, et al.
- 1986
|
|
157
|
Bit Commitment Using Pseudo-Randomness
– Naor
- 1991
|
|
149
|
One-way Functions are Necessary and Sufficient for Secure Signatures
– Rompel
- 1990
|
|
142
|
A “Proofs that Yield Nothing but Their Validity and a Methodology of Cryptographic
– Goldreich, Micali, et al.
- 1986
|
|
115
|
Parity, circuits and the polynomial time hierarchy
– Furst, Saxe, et al.
- 1984
|
|
96
|
Sigma 1 -formulae on finite structures
– Ajtai
- 1983
|
|
87
|
Hiding information and signatures in trapdoor knapsacks
– Merkle, Hellman
- 1978
|
|
58
|
Cryptographic hardness of distribution-specific learning
– Kharitonov
- 1993
|
|
54
|
Pseudo-random generation under uniform assumptions
– H˚astad
- 1990
|
|
50
|
Coin Flipping by Telephone
– Blum
- 1982
|
|
50
|
Improved low-density subset sum algorithms
– Coster, Joux, et al.
|
|
48
|
On the existence of pseudorandom generators
– Goldreich, Krawczyk, et al.
- 1993
|
|
47
|
Generating Quasi-Random Sequences from Slightly Random Sources
– Santha, Vazirani
- 1986
|
|
46
|
Perfect zero-knowledge arguments for NP can be based on general complexity assumptions
– Naor, Ostrovsky, et al.
- 1998
|
|
43
|
Attacking the Chor-Rivest cryptosystem by improved lattice reduction
– Schnorr, Hörner
- 1995
|
|
36
|
Crypt analysis: A Survey of Recent Results
– Brickell, Odlyzko
- 1991
|
|
29
|
Secret Sharing Made Short
– Krawczyk
- 1994
|
|
23
|
Random oracles separate PSPACE from the polynomial-time hierarchy
– Babai
- 1987
|
|
23
|
The rise and fall of knapsack cryptosystems
– Odlyzko
- 1990
|
|
19
|
Solving Low Density Knapsacks
– Brickell
- 1984
|
|
17
|
A knapsack type public key cryptosystem based on arithmetic in finite fields
– Chor, Rivest
- 1988
|
|
17
|
How to Prove Yourself
– Fiat, Shamir
- 1976
|
|
15
|
Cryptographic lower bounds for learnability of boolean functions on the uniform distribution
– Kharitonov
- 1992
|
|
13
|
Separating the polynomial time hierarchy by oracles
– Yao
- 1985
|
|
12
|
One-way functions and circuit complexity
– Boppana, Lagarias
- 1987
|
|
12
|
Solving Low Density Subset Sum Problems
– Lagarias, Odlyzko
- 1985
|
|
10
|
Succinct certificates for almost all subset sum problems
– Furst, Kannan
- 1989
|
|
9
|
Improved lower bounds for small depth circuits
– Hastad
- 1986
|
|
5
|
Efficient, Perfect Polynomial Random Number Generators
– Micali, Schnorr
- 1991
|
|
4
|
Universal One Way Hash Functions and Their Cryptographic Applications
– Naor, Yung
- 1989
|
|
4
|
A T \Delta S = O(2 n ) time/space tradeoff for certain NP-Complete problems
– Schroeppel, Shamir
- 1979
|
|
1
|
On the Lagarias Odlyzko algorithm for the subset sum problem
– Frieze
- 1986
|
|
1
|
An almost linear time algorithm for the dense subset sum problem
– Galil, Margalit
- 1991
|
|
1
|
Improving the critical complexity of the Lagarias Odlyzko attack against subset sum problems
– Joux, Stern
- 1991
|
|
1
|
Lattice base reduction: improved practical algorithms for solving subset sum problems
– Schnorr, Euchner
- 1994
|
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