Relations Among Complexity Measures
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Note on probabilistic algorithms in integer and polynomial arithmetic
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
A lower bound to palindrome recognition by probabilistic Turing machines
A lower bound to palindrome recognition by probabilistic Turing machines
A note on probabilistically verifying integer and polynomial products
Journal of the ACM (JACM)
The Poly1305-AES message-authentication code
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
Algebraic improvements of numerical algorithms: Interpolation and economization of Taylor series
Mathematical and Computer Modelling: An International Journal
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An algorithm is presented to compute the residue of a polynomial over a finite field of degree n modulo a polynomial of degree O(log n) in O(n) algebraic operations. This algorithm can be implemented on a Turing machine. The implementation is based on Turing machine procedure that divides a polynomial of degree n by a sparse polynomial with k nonzero coefficients in O(kn) steps. This algorithm can be adapted to compute the residue of a number of length n modulo a number of length O(log n) in O(n) bit operations.