In analog coded computing, encoding basis functions are typically chosen to guarantee exact reconstruction and improve numerical stability. However, the same basis functions also determine the statistical geometry of the observations available to colluding workers, and hence directly influence the privacy of the underlying data. This suggests that basis selection should not be viewed solely as a reconstruction or numerical conditioning problem, but rather as a joint privacy and accuracy co-design problem. Motivated by this observation, we revisit Analog Lagrange Coded Computing (ALCC) and show that the full orthogonality constraints imposed by the conventional Lagrange basis are stronger than what is required for exact recovery. We retain only the interpolation constraints necessary for the data bearing basis functions and require the noise bearing basis functions merely to vanish at the data recovery points. This yields a parameterized family of generalized polynomial encoding bases that preserves exact reconstruction while introducing additional design degrees of freedom. We then derive a basis-dependent characterization of differential privacy for colluding workers and formulate a privacy-calibrated numerical optimization problem that jointly selects the data and noise basis functions to reduce reconstruction error while satisfying a prescribed \((ε,δ)\)-DP requirement. The resulting framework therefore treats the encoding basis itself as a privacy-design variable, rather than selecting a fixed closed-form basis a priori. The same design philosophy is also compatible with alternative privacy metrics such as mutual-information leakage. Numerical results show that, at the same privacy level, optimized basis functions substantially reduce floating-point reconstruction error relative to conventional ALCC.

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