Communications of the ACM
How to construct random functions
Journal of the ACM (JACM)
A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
On the cryptographic applications of random functions
Proceedings of CRYPTO 84 on Advances in cryptology
Two remarks concerning the Goldwasser-Micali-Rivest signature scheme
Proceedings on Advances in cryptology---CRYPTO '86
Modern cryptology
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Appraising two decades of distributed computing theory research
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
A subexponential algorithm for the discrete logarithm problem with applications to cryptography
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Publicly verifiable secret sharing
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Secure hybrid encryption from weakened key encapsulation
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
How to break MD5 and other hash functions
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Collisions of SHA-0 and reduced SHA-1
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Algebraic pseudorandom functions with improved efficiency from the augmented cascade
Proceedings of the 17th ACM conference on Computer and communications security
Pseudorandom functions and permutations provably secure against related-key attacks
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Verifiable delegation of computation over large datasets
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Hardness preserving constructions of pseudorandom functions
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Pseudorandom functions and lattices
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Publicly verifiable delegation of large polynomials and matrix computations, with applications
Proceedings of the 2012 ACM conference on Computer and communications security
The k-BDH assumption family: bilinear map cryptography from progressively weaker assumptions
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
Group homomorphic encryption: characterizations, impossibility results, and applications
Designs, Codes and Cryptography
Verifiable delegation of computation on outsourced data
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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In this paper, we generalize Naor and Reingold's construction of pseudorandom functions under the DDH Assumption [22] to yield a construction of pseudorandom functions under the decisional k-Linear Assumption, for each k › 1. The decisional Linear Assumption was first introduced by Boneh, Boyen, and Shacham in [5] as an alternative assumption for settings where the DDH problem is easy, such as bilinear groups. Shacham [25] and Hofheinz and Kiltz [16] independently introduced the generalized decisional k-Linear Assumptions and showed that the decisional (k+1)-Linear problem is hard for generic groups even when the decisional k-Linear problem is easy. It is thus desirable to have constructions of cryptographic primitives based on the decisional k-Linear Assumption instead of DDH. Not surprisingly, one must pay a small price for added security: as k increases, our constructed functions become slightly less efficient to compute and the key size increases (quadratically in k).