Residue number system arithmetic: modern applications in digital signal processing
Residue number system arithmetic: modern applications in digital signal processing
Handbook of theoretical computer science (vol. A)
A course in computational algebraic number theory
A course in computational algebraic number theory
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Reconstructing Algebraic Functions from Mixed Data
SIAM Journal on Computing
Chinese remaindering with errors
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Oblivious transfer and polynomial evaluation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Finding smooth integers in short intervals using CRT decoding
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Elliptic curves in cryptography
Elliptic curves in cryptography
Finding Small Roots of Univariate Modular Equations Revisited
Proceedings of the 6th IMA International Conference on Cryptography and Coding
Learning polynomials with queries: The highly noisy case
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
"Soft-decision" decoding of Chinese remainder codes
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Cryptanalysis of RSA with private key d less than N0:292
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Noisy Chinese remaindering in the Lee norm
Journal of Complexity - Special issue on coding and cryptography
On RSA Moduli with Prescribed Bit Patterns
Designs, Codes and Cryptography
Client-Server Password Recovery
OTM '09 Proceedings of the Confederated International Conferences, CoopIS, DOA, IS, and ODBASE 2009 on On the Move to Meaningful Internet Systems: Part II
List decoding for binary Goppa codes
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Simplified high-speed high-distance list decoding for alternant codes
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
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We present a new algorithm for CRT list decoding. An instance of the, CRT list decoding problem consists of integers B, 〈p1, ..., pn〉 and 〈r1, ..., rn〉, where p1 2 n is a sequence of relatively prime integers. The CRT list decoding problem is to find all positive integers x such that x = ri mod pi for all but e values of i ∈ {1, ..., n}. Suppose B = Πi=1r pi for some integer k. Goldreich, Ron, and Sudan (in "Proc. of STOC'99", pp. 225-234, 1999) recently gave several applications for this problem and presented the first efficient algorithm that works whenever e (approximately) satisfies e - √2kn log pn/log p1. Our new algorithm achieves the stronger bound e - √kn log pn/log p1 (approximately). The improvement is significant when k is relatively close to n, e.g. k n/3. The bounds we obtain are similar to the bounds obtained by Guruswami and Sudan for Reed-Solomon list decoding. Hence, our algorithm reduces the gap between CRT list decoding and list decoding of Reed-Solomon codes. In addition, we give a new application for CRT list decoding: finding smooth integers in short intervals. Problems of this type come up in several algorithms for factoring large integers. We define and solve a generalized CRT list decoding problem and discuss how it might be used within the quadratic sieve factoring method.