Filters








250,246 Hits in 6.2 sec

Determinant Equivalence Test over Finite Fields and over Q

Ankit Garg, Nikhil Gupta, Neeraj Kayal, Chandan Saha, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
But, to our knowledge, the complexity of the problem over finite fields and over Q was not well understood.  ...  In this work, we give a randomized poly(n, log |F|) time determinant equivalence test over finite fields F (under mild restrictions on the characteristic and size of F).  ...  The test for the permanent holds over finite fields and Q, but the same is not true for the determinant equivalence test in [16] .  ... 
doi:10.4230/lipics.icalp.2019.62 dblp:conf/icalp/GargGK019 fatcat:xe3hhmbxxrclxb5v47akljjtjy

Determinant equivalence test over finite fields and over $\mathbf{Q}$ [article]

Ankit Garg, Nikhil Gupta, Neeraj Kayal, Chandan Saha
2019 Electronic colloquium on computational complexity  
In [Kay12], a randomized polynomial time determinant equivalence test was given over F = C. But, to our knowledge, the complexity of the problem over finite fields and over Q was not well understood.  ...  A polynomial f is equivalent to Det n (x) over a field F if there exists a over F, and if so then output a transformation matrix A ∈ GL(n 2 , F).  ...  The test for the permanent holds over finite fields and Q, but the same is not true for the determinant equivalence test in [Kay12] .  ... 
dblp:journals/eccc/GargGKS19 fatcat:f75f3eh5qrbqdcyictvc3ylpce

Giesbrecht's algorithm, the HFE cryptosystem and Ore's p^s-polynomials [article]

Robert S. Coulter, George Havas, Marie Henderson
2016 arXiv   pre-print
We also discuss the equivalence between factoring polynomials in a skew-polynomial ring and decomposing p^s-polynomials over a finite field, and how Giesbrecht's algorithm is outlined in some detail by  ...  We end with some observations on the security of the Hidden Field Equation (HFE) cryptosystem, where p-polynomials play a central role.  ...  Choose a finite field F q , q = p e , and a basis (β 1 , . . . , β e ) for F q over F p . 2.  ... 
arXiv:1611.04479v1 fatcat:3c23gi6vsbhhxbhoxu5dxzfg4a

Detecting Infinitely Many Semisimple Representations in a Fixed Finite Dimension [article]

Edward S. Letzter
2008 arXiv   pre-print
We describe an algorithmic test for determining whether or not a finitely presented k-algebra R has infinitely many equivalence classes of semisimple representations R → M_n(k'), where k' is the algebraic  ...  The test reduces the problem to computational commutative algebra over k, via famous results of Artin, Procesi, and Shirshov. The test is illustrated by explicit examples, with n = 3.  ...  Setup and Proof of Test In this section we develop and prove our test to determine whether a finitely presented algebra over a field has infinitely many distinct equivalence classes of ndimensional semisimple  ... 
arXiv:0708.3190v3 fatcat:yxpdp252p5cbzljrsndpufo2by

Detecting infinitely many semisimple representations in a fixed finite dimension

E.S. Letzter
2008 Journal of Algebra  
We describe an algorithmic test for determining whether or not a finitely presented k-algebra R has infinitely many equivalence classes of semisimple representations R → M n (k ), where k is the algebraic  ...  The test reduces the problem to computational commutative algebra over k, via famous results of Artin, Procesi, and Shirshov. The test is illustrated by explicit examples, with n = 3.  ...  Setup and proof of test In this section we develop and prove our test to determine whether a finitely presented algebra over a field has infinitely many distinct equivalence classes of n-dimensional semisimple  ... 
doi:10.1016/j.jalgebra.2008.06.035 fatcat:dqyaurodvnfrtdkok7p2uecot4

GIESBRECHT'S ALGORITHM, THE HFE CRYPTOSYSTEM AND ORE'S ps-POLYNOMIALS

ROBERT S. COULTER, GEORGE HAVAS, MARIE HENDERSON
2001 Computer Mathematics  
We also discuss the equivalence between factoring polynomials in a skew-polynomial ring and decomposing p s -polynomials over a finite field, and how Giesbrecht's algorithm is outlined in some detail by  ...  We end with some observations on the security of the Hidden Field Equation (HFE) cryptosystem, where p-polynomials play a central role.  ...  Choose a finite field F q , q = p e , and a basis (β 1 , . . . , β e ) for F q over F p . 2.  ... 
doi:10.1142/9789812799661_0004 fatcat:no5fe3ndxnb63omlmyvd43e6di

A test for additive decomposability of irreducibles over a finite field

J.V. Brawley, L. Carlitz
1989 Discrete Mathematics  
This paper derives a test for determining whether or not a given irreducible over a finite field is additively decomposable. 0012-36W89/$3.50 @ 1989, Elsevier Science Publishers B.V. (North-Holland)  ...  A polynomial h over a field F is said to be additively decomposable over F if there exist polynomials f and g in F[x] each of degree ~1 sue% l h L at the roots of h are precisely all sums Q!  ...  Carlitz, Irreducibles and the composed product for polynomials over a finite field, Discrete Math. 65 (1987) 115-139. [3] R. Lid1 and H.  ... 
doi:10.1016/0012-365x(89)90289-6 fatcat:5ieb4tib7jbc3m6bagmbztq5iy

Page 67 of Mathematical Reviews Vol. , Issue 83a [page]

1983 Mathematical Reviews  
There is a finite set of polynomials in K which determine the Galois group by testing whether they are invariant under substitution of roots.  ...  Two extensions K,, K, of k are said to be Kronecker equivalent over k if D(K,/k) and D( K,/k) differ by finite sets. W. Jehne has studied properties of these Kronecker equivalence classes [J.  ... 

On the Symmetries of and Equivalence Test for Design Polynomials

Nikhil Gupta, Chandan Saha, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
A useful example of such a polynomial, introduced in [34], is the following: where d is a prime, F d is the finite field with d elements, and k d.  ...  We give an efficient equivalence test for N W in the case where the transformation A is a block-diagonal permutation-scaling matrix.  ...  We also thank anonymous reviewers for their comments. 53:11 Algorithm 3 Block-diagonal permutation equivalence test for N W . Input: Black-box access to f ∈ F[x].  ... 
doi:10.4230/lipics.mfcs.2019.53 dblp:conf/mfcs/GuptaS19 fatcat:46awkhafpfghhnr5p47z6kc4gq

Randomized Polynomial-Time Equivalence Between Determinant and Trace-IMM Equivalence Tests

Janaky Murthy, Vineet Nair, Chandan Saha, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
The above result may appear a bit surprising as the complexity of equivalence testing for IMM and that for Det are quite different over : a randomized poly-time equivalence testing for IMM over is known  ...  We show that, despite the syntactic similarity between IMM and Tr-IMM, equivalence testing for Tr-IMM and that for Det are randomized poly-time Turing reducible to each other over any field of characteristic  ...  Except for the determinant, the algorithms in [24, 25] work over C, Q, and finite fields 6 , and for the determinant it works only over C.  ... 
doi:10.4230/lipics.mfcs.2020.72 dblp:conf/mfcs/MurthyN020 fatcat:zrtouth5vrdlxocsieonwvio4q

Page 6648 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
The author determines here all such curves over k = Q(/29) and Q(V37).  ...  /K) (Ay = finite adéles of K). For Y a Mumford curve over K,.  ... 

Page 865 of Mathematical Reviews Vol. 31, Issue 5 [page]

1966 Mathematical Reviews  
Then cd,(@) = 0 for all g#:p, and to determine ed,(@), one need only test the cohomology of the module Z/p.  ...  closure) ; examples are R, finite fields, C((¢)), finite exten- sions of Q,.  ... 

Detecting complex multiplication

Jeffrey D. Achter
2005 Computational Aspects of Algebraic Curves  
From this, we derive an algorithm to compute the endomorphism ring of an elliptic curve over a number field.  ...  We give an efficient, deterministic algorithm to decide if two abelian varieties over a number field are isogenous.  ...  Algorithms for elliptic curves Detecting isogenous elliptic curves The isogeny class of an elliptic curve E over a finite field κ is uniquely determined by |E(κ)|.  ... 
doi:10.1142/9789812701640_0003 fatcat:guvuq35k3bfmnpn2sfkewcpfv4

Conjugacy classes of centralizers in unitary groups [article]

Sushil Bhunia, Anupam Singh
2019 arXiv   pre-print
Further, we count the number of z-classes in the finite unitary group U_n(q), and prove that this number is same as that of GL_n(q) when q>n.  ...  In this paper, we prove that the number of z-classes in the unitary group over such fields is finite.  ...  Special focus is on the unitary group over finite field F = F q 2 of characteristic = 2 with σ given byx = x q and F 0 = F q .  ... 
arXiv:1610.06728v2 fatcat:kic2woswbrfdnki5qf3cdusboq

Deterministic irreducibility testing of polynomials over large finite fields

Erich Kaltofen
1987 Journal of symbolic computation  
We present a sequential deterministic polynomial-time algorithm for testing dense multivariate polynomials over a large finite field for irreducibility.  ...  Our deterministic solution is based on our algorithm for absolute irreducibility testing combined with Berlekamp's algorithm.  ...  Notation: ~:q denotes a finite field with q elements; degx(f) denotes the highest degree of x inf~ IFq[y, xl and deg(f) the total degree off.  ... 
doi:10.1016/s0747-7171(87)80055-x fatcat:m7cbqp7l4jbqvpmrnafsmb6tdu
« Previous Showing results 1 — 15 out of 250,246 results