Bain Capital agreed to buy Blue Coat Systems Inc., a provider of Internet security software, for $2.4 billion from private equity firm Thoma Bravo.

Bain is paying all cash, according to a statement Tuesday from Sunnyvale, California-based Blue Coat. The company expects the transaction to be completed in the first half of 2015.

Investment firms are seeking to profit as companies turn to Internet security providers to protect against a growing threat of cyber attacks.

The recent attack on Sony Pictures, the movie studio of Sony Corp. (NYSE: SNE), which resulted in the illegal downloading of millions of copies of Sony movies, including “Fury,” served as a wakeup call for many companies. Investors are taking notice. For more, see Hacked Sony Movies Highlight Opportunities for Buyers of Cybersecurity Firms.  

Passport Capital, a hedge fund run by John Burbank, told investors last year that one of its key investment themes is cyber security, after a wave of attacks targeted Home Depot Inc., JPMorgan Chase & Co. and Sears Holdings Corp.’s Kmart discount chain.

Private equity investment in Internet services companies has almost doubled to $115 billion in the past three years, from $60 billion in the previous three-year period, according to data compiled by Bloomberg.

Thoma Bravo acquired Blue Coat Systems in 2012, taking it private in a $1.3 billion transaction. Founded in 1996, the company makes software to increase Web security and run faster video applications.

One of Blue Coat’s biggest technologies is Web gateways, which are devices through which companies funnel their Internet traffic to scan for hacking threats. The appliances, which are also used to authenticate users accessing corporate networks and manage the sending of encrypted data traffic, are part of a segment of the security industry expected to grow 8 percent this year to $2.5 billion, according to Gartner Inc.

Bain, which oversees about $80 billion, invests across private equity, venture and credit markets. The firm, which former U.S. presidential candidate Mitt Romney left in 1999, finished raising $7.3 billion last year for its 11th main buyout fund.

Goldman Sachs Group Inc. and law firm Wilson Sonsini Goodrich & Rosati advised Blue Coat. Bainreceived advice from Jefferies Group LLC, Ropes & Gray LLP and PwC LLP.

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