SDEs may be incorporated into an NITF file while maintaining backward compatibility because the identifier and byte count mechanisms allow applications developed prior to the addition of newly defined data to skip over extension fields they are not designed to interpret.
22.
Recover the Private Key ( Shamir-Kipnis ) : The key point of this attack is to recover the private key as sparse univariate polynomials over the extension field \ mathbb { F } _ { q ^ n }.
23.
A draft proposal for an X509v3 extension field, which expired in April 2013, specified that a compliant server presenting a certificate carrying the extension must return a valid OCSP token in its response if the status _ request extension is specified in the TLS client hello.
24.
With the " Hasse Weil theorem " it is possible to receive the group order of any extension field \ mathbb { F } _ { q ^ n } by using the complex roots ? i of ? ( " T " ):
25.
CSAs rings over a field, which are simple algebras ( have no non-trivial 2-sided ideals, just as with fields ) whose center is exactly the field are a noncommutative analog of extension fields, and are more restrictive than general ring extensions.
26.
Every field " K " has an algebraic closure; this is essentially the largest extension field of " K " which is algebraic over " K " and which contains all roots of all polynomial equations with coefficients in " K ".
27.
In the case of fields, this analogy can be formalized by the field with one element, considering any field with a primitive " n " th root of unity as an algebra over the extension field \ mathbf { F } _ { 1 ^ n }.
28.
Extended format extends the { tagaddress } field under certain circumstances to include a set of extension fields embedded in an " ex " comment immediately appended to the " ex " command, which leaves it backward-compatible with original " vi " implementations.
29.
It is also defined over " F ", but has somewhat different properties : finding the form requires factorization of polynomials, and as a consequence the primary rational canonical form may change when the same matrix is considered over an extension field of " F ".
30.
Then " V " is semisimple as a module over \ mathfrak { g } if and only if ( i ) it is a direct sum of the center and a semisimple ideal and ( ii ) the elements of the center are diagonalizable ( over some extension field ).
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