This comes after Dutch certificate issuer DigiNotar was subject to a breach, leading to numerous bogus authentications being created.
According to Mozilla, it wants proof that other companies have protected their systems.
Kathleen Wilson, head of Mozilla's security certificate group, which has reserved the right to revoke certificates recognised by Firefox, explained that working with the browser was at its "sole discretion".
"We will take whatever steps are necessary to keep our users safe," she told wireless communication device users and others.
In other industry news, HTC recently lodged a fresh complaint against Apple with the US International Trade Commission, alleging that the firm used patents it bought from Google last week.
Apple's devices infringe patents involving Wi-Fi capability and processor communication technology, according to HTC.
This is the third complaint that HTC has filed against Apple.
Posted by Simon Jones
