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Designs, Codes and Cryptography, ISSN 0925-1022, 1/2003, Volume 28, Issue 1, pp. 33 - 44
...}}$$ mod p gives a square root of a when p ≡ 3 mod 4. Let us write p − 1 = 2 n s with s odd. A fast algorithm due to Shanks, with n steps, allows us to compute a square root of a modulo p... 
Information and Communication, Circuits | finite fields | Data Structures, Cryptology and Information Theory | Convex and Discrete Geometry | Shanks algorithm | Mathematics | square root mod p | Combinatorics | Electronic and Computer Engineering | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Algorithms
Journal Article
International Journal of Computational and Mathematical Sciences, ISSN 2010-3905, 06/2009, Volume 3, Issue 3, pp. 101 - 109
Journal Article
by Bach, E and Huber, K
IEEE Transactions on Information Theory, ISSN 0018-9448, 03/1999, Volume 45, Issue 2, pp. 807 - 809
Journal Article
Studia Scientiarum Mathematicarum Hungarica, ISSN 0081-6906, 12/2013, Volume 50, Issue 4, p. 470
Journal Article
Journal of Discrete Mathematical Sciences and Cryptography, ISSN 0972-0529, 01/2016, Volume 19, Issue 1, pp. 93 - 101
..., to the ring of Gaussian integers ℤ[i]. Its security relies on the integer factorization problem and extraction of square roots of a Gaussian integer over ℤ n... 
Zero-knowledge | Gaussian integers | Identification protocol | RSA modulo | Gaussian primes | Square root extraction
Journal Article
Designs, Codes and Cryptography, ISSN 0925-1022, 10/2011, Volume 61, Issue 1, pp. 41 - 69
...>}$$ are obtained, where p and q are distinct odd primes; n ≥ 1 is an integer and q has order $${\frac{\phi(2p^{n})}{2}}$$ modulo 2p n . The generator polynomials, the dimension... 
Information and Communication, Circuits | Generator polynomials | 16S34 | Data Encryption | Group rings | QR codes | 12E20 | Mathematics | Data Structures, Cryptology and Information Theory | Primitive idempotents | Discrete Mathematics in Computer Science | Square root bound | 94B05 | Coding and Information Theory | Combinatorics | Cyclic codes | 20C05 | 94B65 | Dual codes
Journal Article
DESIGNS CODES AND CRYPTOGRAPHY, ISSN 0925-1022, 10/2011, Volume 61, Issue 1, pp. 41 - 69
...(2p(n))/2 modulo 2p(n). The generator polynomials, the dimension, the minimum distance of the minimal cyclic codes of length 2p(n... 
Generator polynomials | MATHEMATICS, APPLIED | Primitive idempotents | Square root bound | Group rings | QR codes | COMPUTER SCIENCE, THEORY & METHODS | Cyclic codes | Dual codes
Journal Article
Journal of Systems Architecture, ISSN 1383-7621, 2008, Volume 54, Issue 10, pp. 957 - 966
Square root is an operation performed by the hardware in recent generations of processors. The hardware implementation of the square root operation is achieved... 
CMOS | Square root | VLSI | Non-restoring algorithm | Expandability | Standard cell | CMOs | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | IMPLEMENTATIONS | ALGORITHM | Very-large-scale integration | Algorithms | Design and construction | Complementary metal oxide semiconductors
Journal Article
Japan Academy Proceedings Series A: Mathematical Sciences, ISSN 0386-2194, 01/2012, Volume 88A, Issue 1, p. 16
... [Z.sub.p]-extension. Denote by [h.sup.-.sub.n] the relative class number of the n-th layer [k.sub.n... 
Fields, Algebraic | Square root | Numbers, Prime | Research
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2014, Volume 83, Issue 285, pp. 435 - 446
.... In the particular case m=2 O(\mathsf {M}(n)\log (p) + \mathsf {C}(n)\log (n)) \mathbb{F}_p \mathsf {M}(n) \mathsf {C}(n) \mathsf {M}(n) = O(n\log (n) \log \log (n)) \mathsf {C... 
Integers | Computer science | Algorithms | Algebra | Cubes | Polynomials | Exponentiation | Logarithms | Cryptography | Factorization | Finite field arithmetic | Square roots | Root extraction | MODULAR COMPOSITION | square roots | MATHEMATICS, APPLIED | MATRIX MULTIPLICATION | finite field arithmetic | FAST POLYNOMIAL FACTORIZATION | ALGORITHM | COMPUTATION
Journal Article
Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, 3/2019, Volume 30, Issue 2, pp. 135 - 145
Journal Article
Results in Mathematics, ISSN 1422-6383, 3/2019, Volume 74, Issue 1, pp. 1 - 33
We investigate the relationship between various choice principles and $$n\hbox {th}$$ nth -root functions in rings... 
root functions in integral domains | finite choice | 13A99 | cycle choice | Mathematics, general | 03E25 | Mathematics | bounded multiple choice | consistency results | Square root functions in rings | axiom of choice | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
SIAM Journal on Computing, ISSN 0097-5397, 2008, Volume 38, Issue 5, pp. 1987 - 2006
...: Given a division-free straight-line program producing an integer N, decide whether N > 0. In the Blum-Shub-Smale model, polynomial-time computation over the reals... 
Straight-line programs | Blum-Shub-Smale model | BPP | Counting hierarchy | Sum of square roots problem | Arithmetic circuits | MATHEMATICS, APPLIED | NUMBER | arithmetic circuits | INFORMATION | MACHINES | counting hierarchy | straight-line programs | THRESHOLD CIRCUITS | COMPUTER SCIENCE, THEORY & METHODS | sum of square roots problem | PROBABILISTIC ALGORITHMS | COMPUTATION
Journal Article
Journal Article
ACM Transactions on Computation Theory (TOCT), ISSN 1942-3454, 11/2012, Volume 4, Issue 4, pp. 1 - 15
The sum of square roots over integers problem is the task of deciding the sign of a nonzero sum, S = ∑ i=1 n Δ i · √ a i , where Δ i ∈ {+1, −1... 
polynomials | Sum of square roots | arithmetic circuits | Polynomials | Arithmetic circuits | Computational geometry
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 01/2001, Volume 22, Issue 4, pp. 1112 - 1125
The standard inverse scaling and squaring algorithm for computing the matrix logarithm begins by transforming the matrix to Schur triangular form in order to... 
Denman-Beavers iteration | Inverse scaling and squaring method | Matrix logarithm | Matrix square root | Padé approximation | matrix logarithm | matrix square root | MATHEMATICS, APPLIED | inverse scaling and squaring method | Pade approximation | SQUARE-ROOT | SIGN FUNCTION
Journal Article
The European Physical Journal C, ISSN 1434-6044, 08/2005, Volume 42, Issue 3, pp. 303 - 308
Journal Article
Designs, Codes and Cryptography, ISSN 0925-1022, 3/2015, Volume 74, Issue 3, pp. 559 - 569
We show how to perform basic operations (arithmetic, square roots, computing isomorphisms) over finite fields of the form $$\mathbb F _{q^{2^k}}$$ F q 2 k in... 
Information and Communication, Circuits | Finite field | 68W30 | Square root | Data Encryption | Mathematics | Complexity | Data Structures, Cryptology and Information Theory | 11Y16 | Discrete Mathematics in Computer Science | 12Y05 | Coding and Information Theory | Combinatorics | Algebraic closure
Journal Article
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