This paper considers asymptotic perfect secrecy and asymptotic perfect estimation in distributed estimation for large sensor networks under threat of an eavesdropper, which has access to all sensor outputs. To measure secrecy, we compare the estimation performance at the fusion center and at eavesdropper in terms of their respective Fisher Information. We analyze the Fisher Information ratio between the fusion center and eavesdropper and derive the maximum achievable ratio when the channels between sensors and eavesdropper are noisy binary symmetric channels. Furthermore, when the fusion center has noiseless channels, we show that the Fisher Information ratio can be made arbitrarily large by careful design of the sensor quantization rules. As a result, asymptotic perfect secrecy can be achieved by making the Fisher Information at Eve arbitrarily small while keeping the Fisher Information at the fusion center arbitrarily large. The secrecy design method in this paper might greatly enhance the secrecy in distributed estimation for large sensor networks.