In one instance, files with long names downloaded via the browser "can be exploited to cause memory corruption," according to Secunia. That could result in the host computer becoming vulnerable to arbitrary code execution -- a situation where intruders can remotely execute commands on the targeted machine.
Secunia notes that neither vulnerability has been patched by Apple.
Word of the problems is the latest black eye for Safari 3.1.
A number of users have complained that the browser functions poorly, or crashes altogether, on computers running Microsoft's Windows XP operating system.
"When I try to start Safari 3.1 in Windows XP, it crashes right away," said SakJosep, in a post currently on Apple's online support forum.
Such complaints are echoing across a Safari support forum thread on Apple's Web site.
Apple's also been hit with criticism for the way it launched the new browser last week. The company included it as a stealth update for users of its iTunes and QuickTime software. Mozilla CEO John Lilly likened the strategy to tactics used by hackers to insert malicious code into downloads.
"Apple has made it incredibly easy -- the default, even -- for users to install ride along software that they didn't ask for, and maybe didn't want," said Lilly, in a blog post. "This is wrong, and borders on malware distribution practices."
Safari competes with Mozilla's Firefox product in the Web browser market.
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