Zix (ZIXI) 10-Q 2012 Q3 Quarterly report

EXHIBIT 32.1

CERTIFICATION OF CEO AND CFO PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

November 7, 2012

Securities and Exchange Commission

450 Fifth Street, N.W.

Washington, D.C. 20549

Ladies and Gentlemen:

The certifications set forth below are being submitted in connection with the Quarterly Report on Form 10-Q (the “Report”) of Zix Corporation for the purpose of complying with Rule 13a-14(b) or Rule 15d-14(b) of the Securities Exchange Act of 1934 (the “Exchange Act”) and Section 1350 of Chapter 63 of Title 18 of the United States Code.

Richard D. Spurr, the chief executive officer, and Michael W. English, the chief financial officer of Zix Corporation, each certifies that to the best of his knowledge and in their respective capacities as an officer of Zix Corporation:

1. the Report fully complies with the requirements of Section 13(a) or 15(d) of the Exchange Act; and

2. the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of Zix Corporation.

/s/ RICHARD D. SPURR

Name: Richard D. Spurr

Title: President and Chief Executive Officer

/s/ MICHAEL W. ENGLISH

Name: Michael W. English

Title: Chief Financial Officer