An efficient probabilistic public key encryption scheme which hides all partial information
Proceedings of CRYPTO 84 on Advances in cryptology
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Oblivious transfer and polynomial evaluation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Complete characterization of security notions for probabilistic private-key encryption
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
Learning polynomials with queries: The highly noisy case
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved Decoding of Reed-Solomon and Algebraic-Geometric Codes
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Reed Solomon Codes for Digital Fingerprinting
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
The capacity of ciphers fulfilling the accessibility of cryptograms
Enhanced methods in computer security, biometric and artificial intelligence systems
Cryptanalyzing the polynomial-reconstruction based public-key system under optimal parameter choice
Designs, Codes and Cryptography
Private Interrogation of Devices via Identification Codes
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
A public key encryption scheme based on the polynomial reconstruction problem
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Some applications of polynomials for the design of cryptographic protocols
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Subspace polynomials and limits to list decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
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We investigate the decoding problem of Reed-Solomon Codes (aka: the Polynomial Reconstruction Problem - PR) from a cryptographic hardness perspective. Following the standard methodology for constructing cryptographically strong primitives, we formulate a decisional intractability assumption related to the PR problem. Then, based on this assumption we show: (i) hardness of partial information extraction and (ii) pseudorandomness. This lays the theoretical framework for the exploitation of PR as a basic cryptographic tool which, as it turns out, possesses unique properties. One such property is the fact that in PR, the size of the corrupted codeword (which corresponds to the size of a ciphertext and the plaintext) and the size of the index of error locations (which corresponds to the size of the key) are independent and can even be super-polynomially related. We then demonstrate the power of PR-based cryptographic design by constructing a stateful cipher.