SUMMARYIn 2009, Lee and Chang proposed an electronic t‐out‐of‐n lottery protocol over the Internet based on the Chinese remainder theorem and blind signature. However, a security flaw exists in Lee–Chang's protocol that the lottery agent and the malicious purchaser can collude to control the winning result, which is unfair for the honest participants. On the basis of a verifiable random number generated by using the Lagrange interpolation formula over a finite field, an improved t‐out‐of‐n e‐lottery protocol is proposed, which guarantees that each participant can generate the winning result equally. The improved protocol achieves public verifiability and fairness without a trusted third party and a delaying function, which makes it more robust and more efficient. Copyright © 2013 John Wiley & Sons, Ltd.