The Diffuse Infrared Background Experiment (DIRBE) is designed to measure the absolute brightness of the entire sky in the 1-300 μm spectral range. It is one of three instruments on NASA's Cosmic Background Explorer (COBE) satellite, to be launched in 1989 on a Delta rocket. The DIRBE will map the entire sky in 10 photometric bands with 1% relative accuracy at a spatial resolution of 0.6 °. Due to the wide dynamic range of signals expected in many bands, this requirement imposes stringent constraints on system linearity, which is particularly difficult to achieve in those spectral channels using photovoltaic or photoconductive detectors. For these detector types, we employ transimpedance amplifiers (TIA) requiring the use of very high impedance feedback elements for low noise operation. Typically, high value resistors used at cryogenic temperatures have quite nonlinear current/voltage relations. We have evaluated several resistor types and found that Victoreen MOX-400 resistors offer good linearity over the relevant signal range, and if procured without epoxy encapsulation, consistently survive repeated cooling to cryogenic temperatures. Approximately 50 flight and flight spare Victoreen MOX-400 resistors were tested for linearity and temperature coefficient of impedance over the 1.5-4.2K temperature range. The devices were found to have small voltage coefficients of impedance, and good uniformity from sample to sample. In this paper, we present a description of the measurement techniques used and show the measured electrical characteristics of the resistors.