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Using a well-known wire-tap model, novel wireless secrecy analyses under dual correlated Nakagami- $m$ fading with a real fading parameter $m$ are reported. Infinite summations for incomplete gamma functions are employed to derive compact expressions for secrecy capacity and secrecy outage probability (SOP) under noninteger $m$. Independently, using finite summations, corresponding closed-form findings for integer $m$ are also derived. In the current literature, finite summations for the incomplete gamma functions, whose first arguments and hence $m$ must be an integer, are employed to obtain closed-form expressions for, first, the SOP (with an unknown passive wire-tapper's channel state information), and second, ergodic secrecy capacity (with partially known active wire-tapper's channel state information under slow fading). The new secrecy results for noninteger $m$ generalize the proposed findings for integer $m$ , and existing findings under dual correlated Rayleigh fading for $m=1$. The new findings can thus be comprehensively employed for wireless secrecy computation under dual correlated Nakagami- $m$ fading for real $m$. Infinite-summation convergence and cross verification are also obtained for a finite number of terms, which shows the practicality and consistency of the new findings. For the first time, secrecy analyses employing an adaptive encoder with on/off transmission are performed under dual correlated Nakagami- $m$ fading for real $m$ to not only improve wireless secrecy, but also achieve the eventual successful transmission from a source to a destination. The new SOP results for real $m$ can be employed as lower bounds and complete theoretical secrecy analyses, for SOP under dual correlated Nakagami- $m$ fading with integer $m$. Simulation results are employed to show matching between the proposed findings and existing findings. [ABSTRACT FROM AUTHOR]