The Yahoo blogging platform Tumblr has advised the public to "change your passwords everywhere - especially your high-security services like email, file storage and banking".
Security advisers have given similar warnings about the Heartbleed Bug.
It follows news that a product used to safeguard data could be compromised to allow eavesdropping.
OpenSSL is a popular cryptographic library used to digitally scramble sensitive data as it passes to and from computer servers so that only the service provider and the intended recipients can make sense of it.
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