<PAGE>

                                                                   EXHIBIT 10.32
                                                                   -------------

                 NON-COMPETITION AND NON-SOLICITATION AGREEMENT
                 ----------------------------------------------

      This Agreement is made between Entrust Technologies Inc., a Maryland
corporation ("Entrust"), and David Thompson (the "Employee").

      WHEREAS, in order to reduce uncertainty regarding the Employee's continued
employment during the current transition period, Entrust has entered into the
Officer Retention Program and Agreement on the condition that the Employee
execute this Agreement; and

      WHEREAS, during the term of the Officer Retention Program, the Employee
will have access to and be instrumental in developing and implementing critical
aspects of Entrust's strategic business plan;

      WHEREAS, the Employee is an owner of capital stock or options to acquire
the capital stock of the Company and will otherwise personally benefit from the
Officer Retention Program and Agreement contemplated by this Agreement.

      NOW, THEREFORE, in consideration of (i) Entrust entering into the Officer
Retention Program and Agreement, (ii) the benefit to the Employee from the
transactions contemplated in the Officer Retention Program, (iii) the employment
or continued employment of the Employee by Entrust or any of its subsidiaries,
and (iv) the continued receipt and access to confidential, proprietary, and
trade secret information associated with the Employee's position with Entrust,
the Employee and Entrust agree as follows:

      1. Confidentiality. The Employee hereby acknowledges and reaffirms to the
         ----------------
same extent as if restated here in full the promises and obligations set forth
in the Intellectual Property and Confidentiality Agreement signed by the
Employee on or about October 11, 1999 and the Conflict of Interest Agreement
signed by the Employee on or about October 11, 1999.

      2. Non-Competition and Non-Solicitation. The Employee acknowledges and
         -------------------------------------
agrees that the nature of the Entrust confidential, proprietary, and trade
secret information to which the Employee has, and will continue to have, access
to derives value from the fact that it is not generally known and used by others
in the highly competitive, international industry in which Entrust competes. The
Employee further acknowledges and agrees that, even in complete good faith, it
would be impossible for the Employee to work in a similar capacity for a
competitor of Entrust without drawing upon and utilizing information gained
during employment with Entrust. Accordingly, at all times during the Employee's
employment with Entrust and for a period of one year after termination, for any
reason, of such employment, the Employee will not, directly or indirectly:

            (a) Engage in any business or enterprise (whether as owner, partner,
officer, director, employee, consultant, investor, lender or otherwise, except
as the holder of not more than 1 % of the outstanding stock of a company) that
directly or indirectly competes with Entrust's business or the business of any
of its subsidiaries anywhere in the United States, Canada or Europe, including
but not limited to any business or enterprise that develops, manufactures,
markets, or sells any product or service that competes with any product or
service developed, manufactured, marketed or sold, or planned to be developed,
manufactured, marketed

<PAGE>

or sold, by Entrust or any of its subsidiaries while the Employee was employed
by Entrust or any of its subsidiaries; or

            (b) Either alone or in association with others (i) solicit, or
facilitate any organization with which the Employee is associated in soliciting,
any employee of Entrust or any of its subsidiaries to leave the employ of
Entrust or any of its subsidiaries; (ii) solicit for employment, hire or engage
as an independent contractor, or facilitate any organization with which the
Employee is associated in soliciting for employment, hire or engagement as an
independent contractor, any person who was employed by Entrust or any of its
subsidiaries at any time during the term of the Employee's employment with
Entrust or any of its subsidiaries (provided, that this clause (ii) shall not
apply to any individual whose employment with Entrust or any of its subsidiaries
has been terminated for a period of one year or longer); or (iii) solicit
business from or perform services for any customer, supplier, licensee or
business relation of Entrust or any of its subsidiaries, induce or attempt to
induce, any such entity to cease doing business with Entrust or any of its
subsidiaries; or in any way interfere with the relationship between any such
entity and Entrust or any of its subsidiaries.

      3. Miscellaneous.
         --------------

            (a) Extension. If the Employee violates the provisions of Sections 1
                ----------
or 2, the Employee shall continue to be bound by the restrictions set forth in
Sections 1 and 2 until a period of one year has expired without any violation of
such provisions.

            (b) Not Employment Contract. The Employee acknowledges that this
                ------------------------
Non-Competition and Non-Solicitation Agreement does not constitute a contract of
employment and, except as set forth in the accompanying Officer Retention
Program agreement (to which this Agreement is ancillary), does not guarantee
that the Company or any of its subsidiaries will continue his/her employment for
any period of time or otherwise change the at-will nature of his/her employment.

            (c) Interpretation. If any restriction set forth in Sections 1 or 2
                ---------------
is found by any court of competent jurisdiction to be invalid, illegal, or
unenforceable, it shall be modified to the minimum extent necessary to render
the modified restriction valid, legal and enforceable. The parties intend that
the non-competition and non-solicitation provisions contained in this Agreement
shall be deemed to be a series of separate covenants, one for each and every
county of each and every state of the United States of America and each and
every political subdivision of each and every country outside the United States
of America where this provision is intended to be effective.

            (d) Severability. The invalidity or unenforceability of any
                -------------
provision of this Agreement shall not affect the validity or enforceability of
any other provision of this Agreement.

            (e) Waiver of Rights. No delay or omission by Entrust in exercising
                -----------------
any right under this Agreement will operate as a waiver of that or any other
right. A waiver or consent given by Entrust on any one occasion is effective
only in that instance and will not be construed as a bar to or waiver of any
right on any other occasion.

<PAGE>

            (f) Equitable Remedies. The restrictions contained in this Agreement
                -------------------
are necessary for the protection of the business and goodwill of Entrust and its
subsidiaries and are considered by the Employee to be reasonable for such
purpose. The Employee agrees that any breach of this Agreement is likely to
cause Entrust substantial and irrevocable damage and therefore, in the event of
any such breach, the Employee agrees that Entrust, in addition to such other
remedies which may be available, shall be entitled to specific performance and
other injunctive relief.

            (g) Governing Law. This Agreement shall be governed by and construed
                --------------
in accordance with the laws of the State of Texas. Any action, suit, or other
legal proceeding which is commenced to resolve any matter arising under or
relating to any provision of this Agreement shall be commenced only in a court
of the State of Texas (or, if appropriate, a federal court located within
Texas), and Entrust and the Employee each consents to the jurisdiction of such a
court.

            (h) Term. This Agreement shall be effective on March 6, 2001,
subject to the execution by the Employee of the Officer Retention Program and
Agreement. This Agreement shall expire March 6, 2002.

      THE EMPLOYEE ACKNOWLEDGES THAT HE/SHE HAS CAREFULLY READ THIS AGREEMENT
AND UNDERSTANDS AND AGREES TO ALL OF THE PROVISIONS IN THIS AGREEMENT.

                                        ENTRUST TECHNOLOGIES INC.


Date:    4/4/01                         By:  /s/ James A. Thomson
       ----------------------------        -------------------------------------

                                        EMPLOYEE:


Date:  April 9, 2001                      /s/ David L. Thompson
       ----------------------------     ----------------------------------------
                                        (Signature)