The man was arrested at his home on Friday morning on suspicion of offences under the Computer Misuse Act 1990 and the Regulation of Investigatory Powers Act (Ripa) 2000.
The Metropolitan police said the arrest was not directly linked to any news organisation or the activities of journalists.
The Met police said the man is in custody at a police station in the Cardiff area.
Operation Tuleta is investigating the use of so-called "Trojan" emails which allow a hacker to take over a target's computer.
The team reports to the deputy assistant commissioner, Sue Akers, who will shortly retire as head of the related phone-hacking investigations.
The first arrest under Operation Tuleta was a 52-year-old man in Milton Keynes in November 2011.
To date, Operation Tuleta detectives have made six arrests, while 24 people have been held under Operation Weeting and 41 people have been arrested by Operation Elveden officers investigating inappropriate payments by journalists to police and public officials.
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