Exhibit 99.1

Zix Corporation Responds to Letter from Meldrum Asset Management

DALLAS, TX, October 29, 2012 — Zix Corporation, (Nasdaq: ZIXI) (“ZixCorp”), the leader in email encryption services, today issued a response to Meldrum Asset Management’s (“Meldrum”) request to call a special meeting of shareholders to, among other things, remove without cause three independent directors from the Company’s Board of Directors and install three directors selected by Meldrum:

“ZixCorp and its Board of Directors have a demonstrated track record of advancing the interests of the Company’s shareholders, customers, and employees. The Company is executing a strategy that has already delivered 15 consecutive quarters of record revenue growth and a year-to-date 31% increase in new sales.

“ZixCorp has, in the past, enjoyed a constructive dialogue with Meldrum. The Company is therefore disappointed by Meldrum’s abrupt pursuit of its own narrower interests, as opposed to the interests of ZixCorp’s other shareholders and constituencies. This includes Meldrum’s stated intent to replace three independent directors with two Meldrum principals and a Meldrum designee and thereby gain veto power over all Board decisions.”

ZixCorp also corrected Meldrum’s representation that the Company’s bylaws specify a seven-member Board of Directors. The Company’s bylaws authorize the Board to set the number of its members from time to time.

About Zix Corporation

Zix Corporation (“ZixCorp”) provides the only email encryption services designed with your most important relationships in mind. Many of the most influential companies and government organizations use the proven ZixCorp^® Email Encryption Services, including WellPoint, the SEC, and more than 1,500 hospitals and 1,800 financial institutions. ZixCorp Email Encryption Services are powered by ZixDirectory^®, the largest email encryption community in the world. The tens of millions of ZixDirectory members can feel secure knowing their most important relationships are protected. For more information, visit www.zixcorp.com.

Important Additional Information

Zix Corporation (“ZixCorp”), its directors and certain members of its management and employees may be deemed to be “participants” in the solicitation of proxies in connection with a possible special meeting of its shareholders under the rules of the Securities and Exchange Commission (“SEC”). Interests of persons who may be deemed to be participants in the solicitation will be included in ZixCorp’s proxy statement relating to any such special meeting to be filed with the SEC. Information concerning beneficial ownership of ZixCorp stock by its directors and certain executive officers is included in its proxy statement dated April 27, 2012 and subsequent statements of changes in beneficial ownership on file with the SEC. Shareholders will be able to obtain free copies of the proxy statement relating to the possible special meeting of shareholders and any other relevant documents filed by ZixCorp with the SEC through the SEC’s Web site at www.sec.gov or through ZixCorp’s Web site at www.zixcorp.com. Shareholders are advised to read the special meeting proxy statement, if and when it is available, because it will contain important information.

ZixCorp Contact Information

Perry Street Communications, Dallas

Jon Morgan (jmorgan@perryst.com)

Jen Habicht (jhabicht@perryst.com)

214-965-9955