Jason Leopold, who has written two articles on this topic this week, explains that the basis for the August, 2002 memo appears to be a health benefits statute.

As to who wrote the memo, WAPO recaps:

The signed author of the August 2002 memo was Jay S. Bybee, then the head of the Office of Legal Counsel and now a federal appeals court judge in San Francisco. But the memo was primarily drafted by one of Bybee's deputies, John Yoo, now a law professor at the University of California at Berkeley.

Other secret Justice memos that are known to have dealt with waterboarding and harsh tactics are a pair of opinions penned in 2005 by Steven G. Bradbury, now the acting Office of Legal Counsel chief. Administration officials have said those
opinions authorized a number of techniques, including waterboarding and head-slapping.

Other probes underway by the OPR include one into the authorization of the warrantless NSA wiretap program and the firing of the 9 U.S. Attorneys.

OPR says because of the high interest in the torture investigation, it may break with its usual tradition and release the results publicly when it concludes the investigation.

The August, 2002 memo is titled "Re: Standards of Conduct for Interrogation under 18 U.S.C. 2340-2340A." It was a memo from the Justice Department's Office of Legal Counsel to Alberto R. Gonzales, then counsel to President Bush. A copy is available here (pdf.) Here's a 2004 WaPo article on the memo.

I think the best coverage on the torture memos has been that of law profs Jack Balkin and Marty Lederman at Balkanization -- Their writings through the fall of 2007 are accessible here.