How does Prism compute the confidence intervals of a survival curve?

 Prism 5 offers two choices. 

The symmetrical method was the only method offered in prior versions of Prism, and is offered now for compatibility. It uses the method of Greenwood.

The asymmetrical method is more accurate and recommended. It is explained on page 42 and page 43 of Machin (reference below). That book does not give a name or reference for the method, The idea is that it first does a transform (square root and log) that makes the uncertainty of survival close to Gaussian. It then computes the SE and a symmetrical 95% CI on that transformed scale. Then it back transforms the confidence limits back to the original scale. 

Note that when Prism reports the fraction (or percent) survival with its confidence interval, it uses a Prism table that labels the first column "mean". In fact, this value is the observed fraction (or percent) survival and the other two columns give the confidence interval for the true fraction (or percent) survival in the overall population (given the assumptions of survival analysis).