The convictions of the men involved in one of Scotland's largest uncovered paedophile rings mark the triumphant end of an unusual 18-month investigation that took officers on a trail from Lothian to Boston.

The 13-strong team of specialist officers running Operation Algebra sought the help of electronics experts from the FBI's elite cyber crime squad to untangle a web of deviants who used internet alter egos to hide their crimes.

Operation Algebra, led by Detective Inspector Stuart Hood and Detective Superindendent Allan Jones, was launched in October 2007. The investigation quickly became international as officers uncovered a complex network of paedophiles operating in the UK, Europe and the US.

It took months to unravel the vast trail of email traffic from each of the men's computers. Courts in the US granted warrants to obtain records from Microsoft and internet service provider AOL, leading police to the true identities of the owners of numerous internet accounts.

James Rennie was found to have been in communication with paedophiles in the US, in particular one man using the e-mail address "grasso666". The man was discovered to be 20-year-old Matthew Grasso from Massachusetts, who was convicted and charged with the "prolific distribution" of child pornography.

During the trial a key piece of evidence emerged: the photograph that became known as the Hogmanay Image, showing Strachan seriously sexually assaulting an 18-month-old toddler.

After months of work by experts the picture was unlocked from encrypted computer files and an electronic date stamp showed it had been taken an hour before midnight on December 31, 2005.

First, police took steps to prove the camera used to take the image was owned by Strachan. Detectives contacted Dr Hany Farid, of Dartmouth College in Massachusetts, who is a leading expert in digital forensics.

Dr Farid has aided the CIA and FBI with evidence on computer-based crimes but this is the first time such evidence has been used in a British court. The professor was asked to analyse four digital camera images: the Hogmanay Image and three others known to have been taken by Strachan on a Sony Cybershot camera.

Dr Farid was able to show to the court that it was "highly likely" the four pictures came from the same camera, indicating the equipment was owned by Strachan.

Strachan is only partially seen in the image, so police next approached forensic expert Professor Susan Black, who gave expert evidence at the trial of Slobodan Milosevic, in order to prove he was the man pictured.

After Strachan and Rennie were arrested at the end of 2007, computer experts continued their trawl through the chat-logs, an exercise that led to the detection of the other six men. More than 70 others in Britain have been found to be involved with the eight convicted yesterday; so far more than 40 of those have been arrested.