"Properly implemented strong crypto systems are one of the few things that you can rely on," declared Edward Snowden, the former computer technician at America's National Security Agency (NSA) responsible for leaking a trove of documents about his erstwhile employer's activities, in an online question-and-answer session in June.

The revelations published on 5 September by the Guardian, the New York Times and ProPublica, explain his careful choice of words. Many cryptographic systems in use on the internet, it seems, are not "properly implemented", but have been weakened by flaws deliberately introduced by the NSA as part of a decade-long programme to ensure it can read encrypted traffic.

The extent and nature of the programme is still unclear, but it appears to involve getting software companies and internet service providers to insert secret vulnerabilities, or backdoors, into apparently secure systems. This can be done by introducing deliberate errors into software or hardware designs, many of which are developed in collaboration with the NSA; or by recommending the use of security protocols that the NSA knows to be insecure, in its dual role as cryptographic standards-setter and codebreaker.

It is naive to think that signals-intelligence agencies, whose job is to intercept and decrypt messages, are not going to try to do everything to ensure that they can read as much encoded traffic as possible. And there are good reasons why governments should be able to snoop, in the interests of national security and within agreed legal limits. But the latest allegations are worrying for three reasons.

First, the NSA's actions may have weakened overall internet security, on which billions of people rely for banking and payments, with backdoors that can be exploited by criminals, not just intelligence agencies. Second, this undermines confidence in American technology companies, none of which can now be trusted when they say their products are secure, and makes it very difficult for America to criticise authoritarian regimes for interfering with the internet, or to claim (as it does) that it is the best guardian of the internet's addressing system. Third, the NSA seems to have done by stealth what it could not do openly. During the 1990s the agency unsuccessfully lobbied for backdoors to be added to all communications systems. Having lost the argument, it has apparently gone ahead and implemented them on the sly.

All this adds to the impression that oversight of the NSA has not kept pace with the rapid expansion of its activities. Having once spied on a small number of specific targets, it now conducts online surveillance on a vast scale. It has spied on drug dealers, tax evaders and foreign firms, none of which pose a threat to national security. NSA employees have used its systems to spy on their former lovers. Snowden's ability to walk off with a stash of NSA documents is grave evidence of a woeful lack of internal controls. He has gone public, but could just as easily have put his stolen documents to criminal use – as others in his position may already have done.

Barack Obama says he welcomes debate about the activities of America's spooks. There are indeed arguments to be had about the appropriate levels of snooping and degrees of oversight. But any deliberate subversion of cryptographic systems by the NSA is simply a bad idea, and should stop. That would make life harder for the spooks, true, but there are plenty of other more targeted techniques they can use that do not reduce the security of the internet for all of its users, damage the reputation of America's technology industry and leave its government looking untrustworthy and hypocritical.

• This article first appeared as a leader column in The Economist and is republished here with permission