This paper presents efficient distributed protocols for generating shares of random noise, secure against malicious participants. The primary goal is to create a distributed implementation of privacy-preserving statistical databases, where privacy is achieved by perturbing the true answer to a database query with Gaussian or exponentially distributed random noise. The computational power of these databases, which can handle queries of the form $\sum_i f(d_i)$, has been demonstrated in previous work. The paper introduces techniques for distributing shares of unbiased coins and biased coins, reducing the number of verifiable secret sharings needed compared to previous approaches. Specifically, it uses the Binomial distribution to approximate Gaussian noise and the Poisson distribution to approximate exponential noise. The paper also discusses the structure of the ODO (Our Data, Ourselves) protocol, which involves generating Gaussian and exponential noise, and provides detailed constructions for these distributions. Additionally, it explores generalizations of the basic scheme, including alternatives to full participation and handling queries that are not simple predicates. The results are of independent interest in the fields of cryptography and database security.This paper presents efficient distributed protocols for generating shares of random noise, secure against malicious participants. The primary goal is to create a distributed implementation of privacy-preserving statistical databases, where privacy is achieved by perturbing the true answer to a database query with Gaussian or exponentially distributed random noise. The computational power of these databases, which can handle queries of the form $\sum_i f(d_i)$, has been demonstrated in previous work. The paper introduces techniques for distributing shares of unbiased coins and biased coins, reducing the number of verifiable secret sharings needed compared to previous approaches. Specifically, it uses the Binomial distribution to approximate Gaussian noise and the Poisson distribution to approximate exponential noise. The paper also discusses the structure of the ODO (Our Data, Ourselves) protocol, which involves generating Gaussian and exponential noise, and provides detailed constructions for these distributions. Additionally, it explores generalizations of the basic scheme, including alternatives to full participation and handling queries that are not simple predicates. The results are of independent interest in the fields of cryptography and database security.