A group known as APT28 and Fancy Bear by U.S. cyber-security researchers released a second batch of data on Wednesday with the British cyclist among 25 athletes to have their Therapeutic Use Exemptions (TUEs) publicised.
"I've openly discussed my TUEs with the media and have no issues with the leak which only confirms my statements," said 2013, 2015 and 2016 Tour winner Froome in a news release.
"In nine years as a professional I've twice required a TUE for exacerbated asthma, the last time was in 2014."
TUEs allow athletes to take banned substances to treat ongoing medical conditions.
Compatriot Bradley Wiggins, who triumphed at the Tour in 2012 and last month landed a team pursuit gold to win a British record eighth Olympic Games medal, was also on the list of 25 athletes.
The Fancy Bear website published Wiggins' TUEs from 2008, 2011, 2012 and 2013 that all refer to asthma-related treatments.
"There's nothing new here," a spokesman for Wiggins said. "Everyone knows Brad suffers from asthma, his medical treatment is (British Cycling) and UCI approved."
Cycling's governing body the UCI joined the condemnation of the cyber attacks and defended the way it issued TUEs.
"The management of Therapeutic Use Exemptions ... is robust and fully safeguarded," it said.
"The UCI TUE Committee (TUEC) is composed of independent experts in the fields of clinical, sports and exercise medicine and the coordination of the Committee is handled by the Cycling Anti-Doping Foundation (CADF), the independent body mandated by the UCI to carry out anti-doping in the sport."
Britain's anti-doping agency UKAD said it had written to its athletes to warn their data may be at risk in the attack on WADA's anti-doping administration and management system (ADAMS) via an International Olympic Committee-created account for last month's Rio Games.
"UKAD strongly condemns actions of this nature and we are appalled that five members of Team GB have had their private data published illegally online," it said.
"Not only does it undermine our work and the protection of clean sport but it is grossly unfair to the athletes whose personal data has been put at risk."
