Document:

<PAGE>

                                                                    EXHIBIT 10.2

                         PILOT NETWORK SERVICES, INC.

                        COMMON STOCK PURCHASE AGREEMENT

                               December 28, 1999
<PAGE>

                               TABLE OF CONTENTS

<TABLE>
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                                                                            Page
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<S>                                                                         <C>
1.   PURCHASE AND SALE OF COMMON STOCK...................................      1
     1.1   Sale and Issuance of Common Stock.............................      1
     1.2   Closing; Delivery.............................................      1

2.   REPRESENTATIONS AND WARRANTIES OF THE COMPANY.......................      1
     2.1   Organization, Good Standing and Qualification.................      1
     2.2   Authorization.................................................      1
     2.3   Valid Authorization and Issuance of Shares....................      2
     2.4   Litigation....................................................      2
     2.5   Compliance with Other Instruments.............................      2
     2.6   Rights of Registration and Voting Rights......................      3
     2.7   Financial Statements..........................................      3
     2.8   Corporate Documents...........................................      3
     2.9   Capitalization................................................      3
     2.10  No Material Adverse Change....................................      4
     2.11  Real Property.................................................      4
     2.12  Insurance.....................................................      4
     2.13  Intellectual Property.........................................      4
     2.14  Consents......................................................      4
     2.15  Labor Agreements and Actions..................................      4
     2.16  Disclosure....................................................      5
     2.17  Securities Filings............................................      5
     2.18  Year 2000 Compliance..........................................      5

3.   REPRESENTATIONS AND WARRANTIES OF THE PURCHASER.....................      5
     3.1   Authorization.................................................      6
     3.2   Purchase Entirely for Own Account.............................      6
     3.3   Disclosure of Information.....................................      6
     3.4   Restricted Securities.........................................      6
     3.5   Legends.......................................................      6
     3.6   Accredited Investor...........................................      7
</TABLE>

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                               TABLE OF CONTENTS
                                  (continued)

<TABLE>
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4.   CONDITIONS OF THE PURCHASER'S OBLIGATIONS AT CLOSING................      7
     4.1   Representations and Warranties................................      7
     4.2   Qualifications................................................      7
     4.3   Warrant.......................................................      7
     4.4   Strategic Business Relationship Agreement.....................      7
     4.5   Escrow Agreement..............................................      7
     4.6   Opinion.......................................................      7

5.   CONDITIONS OF THE COMPANY'S OBLIGATIONS AT CLOSING..................      7
     5.1   Representations and Warranties................................      7
     5.2   Qualifications................................................      7

6.   COVENANTS OF THE COMPANY............................................      8
     6.1   Nomination of Director........................................      8
     6.2   Amendment to Existing Investors' Rights Agreement.............      8

7.   MISCELLANEOUS.......................................................      8
     7.1   Survival of Warranties........................................      8
     7.2   Transfer; Successors and Assigns..............................      8
     7.3   Governing Law.................................................      9
     7.4   Counterparts..................................................      9
     7.5   Titles and Subtitles..........................................      9
     7.6   Notices.......................................................      9
     7.7   Fees and Expenses.............................................      9
     7.8   Amendments and Waivers........................................      9
     7.9   Severability..................................................      9
     7.10  Delays or Omissions...........................................      9
     7.11  Entire Agreement..............................................     10
     7.12  Corporate Securities Law......................................     10
     7.13  Confidentiality...............................................     10
</TABLE>

EXHIBIT A  FORM OF WARRANT

EXHIBIT B  FORM OF ESCROW AGREEMENT

                                     -ii-
<PAGE>

                         PILOT NETWORK SERVICES, INC.

                        COMMON STOCK PURCHASE AGREEMENT
                        -------------------------------

     This Common Stock Purchase Agreement (the "Agreement") is made as of the
                                                ---------
28th day of December, 1999 by and between Pilot Network Services, Inc., a
Delaware corporation (the "Company") and Primus Telecommunications Group,
                           -------
Incorporated (the "Purchaser").
                   ---------

     The parties hereby agree as follows:

     1.   Purchase and Sale of Common Stock.
          ---------------------------------

          1.1  Sale and Issuance of Common Stock.  Subject to the terms and
               ---------------------------------
conditions of this Agreement, the Purchaser agrees to purchase at the Closing
and the Company agrees to sell and issue to the Purchaser at the Closing,
919,540 shares of Common Stock at a purchase price of $16.3125 per share, for an
aggregate purchase price of $14,999,996.25. The shares of Common Stock issued to
the Purchaser pursuant to this Agreement shall be hereinafter referred to as the
"Shares."
 ------

          1.2  Closing; Delivery.
               -----------------

               (a)  The purchase and sale of the Shares shall take place at the
offices of Orrick, Herrington & Sutcliffe LLP, San Francisco, California, at
10:00 a.m., on December 28, 1999 (which time and place are designated as the
"Closing").
 -------

               (b)  At the Closing, the Company shall deliver to the Purchaser a
certificate representing the Common Stock and the Warrant (as defined herein)
being purchased hereby against payment of the purchase price therefor by a check
payable to the Company. The stock certificate, the Warrant and the check shall
be delivered to the escrow holder pursuant to the Escrow Agreement in the form
of Exhibit B hereto (the "Escrow Agreement").
                          ----------------

     2.   Representations and Warranties of the Company.  The Company hereby
          ---------------------------------------------
represents and warrants to the Purchaser that:

          2.1  Organization, Good Standing and Qualification.  The Company is a
               ---------------------------------------------
corporation duly organized, validly existing and in good standing under the laws
of the State of Delaware and has all requisite corporate power and authority to
carry on its business and enter into the Agreements (as defined below).  The
Company is duly qualified to transact business and is in good standing in each
jurisdiction in which the failure so to qualify would have a material adverse
effect on its business or properties.

          2.2  Authorization.  All corporate action on the part of the Company,
               -------------
its officers, directors and stockholders necessary for the authorization,
execution and delivery of this Agreement, the Warrant in the form attached
hereto as Exhibit A (the "Warrant"), the Escrow Agreement and Strategic Business
          ---------       -------
Relationship Agreement to be entered into between the Company and the Purchaser
(the "Strategic Business Relationship Agreement" and, collectively
      -----------------------------------------
<PAGE>

with this Agreement, the Escrow Agreement and the Warrant, the "Agreements") and
                                                                ----------
the performance of all obligations of the Company hereunder and thereunder has
been taken prior to the Closing. The Agreements, when executed and delivered by
the Company, shall constitute valid and legally binding obligations of the
Company, enforceable against the Company in accordance with their terms, except
as limited by applicable bankruptcy, insolvency, reorganization, moratorium,
fraudulent conveyance, and other laws of general application affecting
enforcement of creditors' rights generally, as limited by laws relating to the
availability of specific performance, injunctive relief, or other equitable
remedies.

          2.3  Valid Authorization and Issuance of Shares.  The Shares that are
               ------------------------------------------
being issued to the Purchaser hereunder have been duly authorized for issuance
and, when issued, sold and delivered in accordance with the terms hereof for the
consideration expressed herein, will be duly and validly issued, fully paid and
nonassessable and free of restrictions on transfer other than applicable state
and federal securities laws.  Based in part upon the representations of the
Purchaser in this Agreement and subject to the filing of any applicable notices
under federal and state securities laws, the Shares will be issued in compliance
with all applicable federal and state securities laws.

          2.4  Litigation.  There is no action, suit, proceeding or
               ----------
investigation pending or, to the Company's knowledge, currently threatened
against the Company or any of its subsidiaries that questions the validity of
the Agreements or the right of the Company to enter into them, or to consummate
the transactions contemplated hereby or thereby, or that might result, either
individually or in the aggregate, in any material adverse changes in the assets,
condition or affairs of the Company, financially or otherwise, or any change in
the current equity ownership of the Company, nor is the Company aware that there
is any basis for the foregoing.  Neither the Company nor any of its subsidiaries
is a party or subject to the provisions of any order, writ, injunction, judgment
or decree of any court or government agency or instrumentality.  There is no
action, suit, proceeding or investigation by the Company or any of its
subsidiaries currently pending or which the Company or any of its subsidiaries
intends to initiate.

          2.5  Compliance with Other Instruments.  Neither the Company nor any
               ---------------------------------
of its subsidiaries is in violation or default of any provisions of (i) their
respective charters or bylaws (or similar applicable organizational documents),
(ii) any instrument, judgment, order, writ, decree, agreement (written or oral)
or contract to which any of them is a party or by which any of them is bound or
(iii) any federal or state statute, rule or regulation, except in the case of
clause (ii) or (iii) above, where any such violation or default would not be
material or have a material adverse effect on the Company.  The execution,
delivery and performance of the Agreements by the Company and the consummation
by the Company of the transactions contemplated hereby or thereby (1) will not
be an event which results in the creation of any lien, charge or encumbrance
upon any assets of the Company or any of its subsidiaries and (2) will not
result in any violation or be in conflict with or constitute, with or without
the passage of time and giving of notice, a default under (a) the Company's
charter or bylaws, (b) any instrument, judgment, order, writ, decree, agreement
(written or oral) or contract or (c) any federal or state statute, rule or
regulation, except in the case of clause (b) or (c) above, where any such
violation, conflict or default would not be material or have a material adverse
effect on the Company.

                                      -2-
<PAGE>

          2.6   Rights of Registration and Voting Rights.  Except as provided in
                ----------------------------------------
that certain Amended and Restated Investors' Rights Agreement, dated as of March
31, 1997, among the Company and the investors listed on Schedule I thereto, as
amended by that certain Amendment to Investors' Rights Agreement dated as of
December 22, 1997 and that certain Second Amendment to Investors' Rights
Agreement dated February 26, 1998, including the obligation of the Company to
amend such agreement to grant registration rights to Greyrock Capital (the
"Existing Investors' Rights Agreement"), the Company has not granted or agreed
 ------------------------------------
to grant any registration rights, including piggyback rights, to any person or
entity.  To the Company's knowledge, no stockholder of the Company has entered
into any agreements with respect to the voting of capital shares of the Company.

          2.7   Financial Statements.  The Company has made available to the
                --------------------
Purchaser its audited financial statements (including balance sheet, income
statement and statement of cash flows) for the fiscal year ended March 31, 1999
included in the Company's Annual Report on Form 10-K for such year and the
unaudited financial statements for the quarters ended June 30, 1999 and
September 30, 1999 included in the Company's Quarterly Reports on Form 10-Q for
such quarters (collectively, the "Financial Statements").  The Financial
                                  --------------------
Statements have been prepared in accordance with generally accepted accounting
principles applied on a consistent basis throughout the periods indicated. The
Financial Statements fairly present the financial condition and operating
results of the Company as of the dates, and for the periods, indicated therein,
subject, in the case of the unaudited financial statements, to normal year-end
audit adjustments. Except as set forth in the Financial Statements, the Company
(i) has no material liabilities, contingent or otherwise, other than (a)
liabilities incurred in the ordinary course of business subsequent to September
30, 1999 and (b) obligations under contracts and commitments incurred in the
ordinary course of business and not required under generally accepted accounting
principles to be reflected in the Financial Statements, which, in both cases,
individually or in the aggregate are not material to the financial condition or
operating results of the Company and (ii) has not entered into any material
transaction other than transactions in the ordinary course of business or which
are not material to the Company, other than the transaction with Greyrock
Capital, a description of which has been provided to the Purchaser. The net
operating loss carryforwards of the Company are accurately described in the
Financial Statements.

          2.8   Corporate Documents. The Restated Certificate of Incorporation
                -------------------
and Bylaws of the Company are in the form provided by the Company to the
Purchaser. Such documents are in full force and effect and have not since been
amended.

          2.9   Capitalization.  The authorized and outstanding capital of the
                --------------
Company as of September 30, 1999 is as set forth on Schedule 2.9 hereto.  There
have been no changes to such capitalization since such date except for the
exercise of options by option holders, the exercise or conversion of warrants to
purchase 75,000 shares of Common Stock of the Company by warrant holders and the
issuance of warrants to purchase 121,212 shares of Common Stock of the Company
to Greyrock Capital for $8.25 per share.

          2.10  No Material Adverse Change.  Since September 30, 1999, there has
                --------------------------
not been any change in the assets, liabilities, financial condition or operating
results of the Company

                                      -3-
<PAGE>

from that reflected in the Financial Statements, except changes in the ordinary
course of business that have not been, in the aggregate, materially adverse.

          2.11  Real Property. The Company does not own any real property.  With
                -------------
respect to the real property it leases, the Company is in compliance with such
leases and, to its knowledge, holds a valid leasehold interest free of any
liens, claims or encumbrances.

          2.12  Insurance.  The Company has in full force and effect fire,
                ---------
casualty and liability insurance policies, with extended coverage on its
properties in such amounts as are customarily maintained by persons engaged in
similar businesses and owning similar properties in the same general areas in
which the Company operates.

          2.13  Intellectual Property.  The Company owns or possesses sufficient
                ---------------------
legal rights to all patents, trademarks, service marks, tradenames, copyrights,
trade secrets, source or object code, licenses, information and proprietary
rights and processes necessary for its business without any conflict with, or
infringement of, the rights of others. The Company has not received any
communications alleging that the Company has violated or, by conducting its
business, would violate any of the patents, trademarks, service marks,
tradenames, copyrights, trade secrets, source or object code, or other
proprietary rights or processes of any other person or entity and, to the
Company's knowledge, it is not in violation of any of the foregoing rights with
respect to any third party. The Company is not aware that any of its employees
is obligated under any contract (including licenses, covenants or commitments of
any nature) or other agreement, or subject to any judgment, decree or order of
any court or administrative agency, that would interfere with the use of such
employee's best efforts to promote the interest of the Company or that would
conflict with the Company's business.

          2.14  Consents.  No consent, approval, order or authorization of, or
                --------
registration, qualification, designation, declaration or filing with, any third
party or any federal, state or local governmental authority on the part of the
Company is required in connection with the consummation of the transactions
contemplated by this Agreement, except for filings that may be required under
applicable securities laws and compliance with the Hart-Scott-Rodino Antitrust
Improvements Act of 1976 in connection with the exercise of the Warrant under
certain circumstances.

          2.15  Labor Agreements and Actions.  The Company is not bound by or
                ----------------------------
subject to (and none of its assets or properties is bound by or subject to) any
written or oral, express or implied, contract, commitment or arrangement with
any labor union, and no labor union has requested or, to the knowledge of the
Company, has sought to represent any of the employees, representatives or agents
of the Company.  There is no strike or other labor dispute involving the Company
pending, or to the knowledge of the Company threatened, which could have a
material adverse effect on the assets, properties, financial condition,
operating results, or business of the Company, nor is the Company aware of any
labor organization activity involving its employees. The employment of each
officer and employee of the Company is terminable at the will of the Company.
The Company has complied in all material respects with all applicable state and
federal equal employment opportunity laws and with other laws related to
employment.

                                      -4-
<PAGE>

          2.16  Disclosure.  No representation or warranty of the Company
                ----------
contained in this Agreement and the exhibits and schedules attached hereto, any
certificate furnished or to be furnished to the Purchaser at the Closing, or any
other information regarding the Company provided by the Company to the Purchaser
contains any untrue statement of a material fact or omits to state a material
fact necessary in order to make the statements contained herein or therein not
misleading in light of the circumstances under which they were made.

          2.17  Securities Filings.  The Company has made available to the
                ------------------
Purchaser each registration statement, report, proxy statement or information
statement and all exhibits thereto (collectively, the "Company Reports")
                                                       ---------------
prepared by it since the effective date of the Company's initial registration
statement, each in the form (including exhibits and any amendments thereto)
filed with the Securities and Exchange Commission (the "SEC").  The Company
                                                        ---
Reports were filed with the SEC in a timely manner and constitute all forms,
reports and documents required to be filed by the Company pursuant to the
Securities Exchange Act of 1934, as amended, and the rules and regulations
promulgated thereunder (the "Securities Laws").  As of their respective dates,
                             ---------------
the Company Reports (a) complied as to form in all material respects with the
applicable requirements of the Securities Laws and (b) did not contain any
untrue statement of a material fact or omit to state a material fact required to
be stated therein or necessary to make the statements made therein, in light of
the circumstances under which they were made, not misleading. There is no
unresolved violation asserted by any governmental authority with respect to any
of the Company Reports.

          2.18  Year 2000 Compliance. The Company has (a) conducted a review and
                --------------------
assessment of all areas within its business and operations (including those
affected by suppliers and vendors) that could be adversely affected by the risk
that computer applications used by the Company (or its suppliers and vendors)
may be unable to recognize and perform properly date-sensitive functions
involving any date after December 31, 1999 (the "Year 2000 Problem") and (b)
                                                 -----------------
developed and implemented a plan for addressing the Year 2000 Problem on a
timely basis. All computer applications that are necessary to the Company's
business and operations (including, to the Company's knowledge, the computer
applications of the Company's suppliers and vendors) will be Year 2000 compliant
by being able to perform properly on a timely basis date-sensitive functions for
all dates after December 31, 1999, except to the extent that a failure to do so
could not reasonably be expected to have a material adverse effect on the
Company. The Company will promptly notify the Purchaser in the event the Company
discovers or determines that any computer application (including those of its
suppliers and vendors) that is necessary to its business and operations will not
be Year 2000 compliant on a timely basis. The Company will cooperate fully with
the Purchaser in connection with any due diligence review that the Purchaser may
conduct in determining whether the Company has a Year 2000 Problem.

     3.   Representations and Warranties of the Purchaser.  The Purchaser hereby
          -----------------------------------------------
represents and warrants to the Company that:

          3.1   Authorization.  The Purchaser has full power and authority to
                -------------
enter into this Agreement.  The Agreements, when executed and delivered by the
Purchaser, will constitute valid and legally binding obligations of the
Purchaser, enforceable in accordance with their

                                      -5-
<PAGE>

terms, except as limited by applicable bankruptcy, insolvency, reorganization,
moratorium, fraudulent conveyance, and any other laws of general application
affecting enforcement of creditors' rights generally, and as limited by laws
relating to the availability of a specific performance, injunctive relief, or
other equitable remedies.

          3.2  Purchase Entirely for Own Account.  This Agreement is made with
               ---------------------------------
the Purchaser in reliance upon the Purchaser's representation to the Company,
which by the Purchaser's execution of this Agreement, the Purchaser hereby
confirms, that the Shares to be acquired by the Purchaser will be acquired for
investment for the Purchaser's own account, not as a nominee or agent, and not
with a view to the resale or distribution of any part thereof except in
accordance with the restrictions on transfer set forth in any legends thereon,
this Agreement and in accordance with the Existing Investors' Rights Agreement.
By executing this Agreement, the Purchaser further represents that the Purchaser
does not presently have any contract, undertaking, agreement or arrangement with
any person to sell, transfer or grant participations to such person or to any
third person, with respect to any of the Shares. The Purchaser has not been
formed for the specific purpose of acquiring the Shares.

          3.3  Disclosure of Information.  The Purchaser has had an opportunity
               -------------------------
to discuss the Company's business, management, financial affairs and the terms
and conditions of the offering of the Shares with the Company's management and
has had an opportunity to review the Company's facilities.

          3.4  Restricted Securities.  The Purchaser understands that the Shares
               ---------------------
have not been registered under the Securities Act of 1933 (the "Securities
                                                                ----------
Act"), by reason of a specific exemption from the registration provisions of the
---
Securities Act which depends upon, among other things, the bona fide nature of
the investment intent and the accuracy of the Purchaser's representations as
expressed herein. The Purchaser understands that the Shares are "restricted
securities" under applicable U.S. federal and state securities laws and that,
pursuant to these laws, the Purchaser must hold the Shares indefinitely unless
they are registered with the Securities and Exchange Commission and qualified by
state authorities, or an exemption from such registration and qualification
requirements is available. The Purchaser further acknowledges that if an
exemption from registration or qualification is available, it may be conditioned
on various requirements including, but not limited to, the time and manner of
sale, the holding period for the Shares, and on requirements relating to the
Company which are outside of the Purchaser's control, and which the Company is
under no obligation and may not be able to satisfy.

          3.5  Legends.  The Purchaser understands that the Shares and any
               -------
securities issued in respect of or exchange for the Shares may bear one or all
of the following legends:

               (a)  "THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AND HAVE BEEN ACQUIRED FOR
INVESTMENT AND NOT WITH A VIEW TO, OR IN CONNECTION WITH, THE SALE OR
DISTRIBUTION THEREOF.  NO SUCH SALE OR DISTRIBUTION MAY BE EFFECTED WITHOUT AN
EFFECTIVE REGISTRATION

                                      -6-
<PAGE>

STATEMENT RELATED THERETO OR AN OPINION OF COUNSEL IN A FORM SATISFACTORY TO THE
COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED UNDER THE SECURITIES ACT OF
1933."

               (b)  Any legend set forth in the other Agreements.

               (c)  Any legend required by the Blue Sky laws of any state to the
extent such laws are applicable to the shares represented by the certificate so
legended.

          3.6  Accredited Investor.  The Purchaser is an accredited investor as
               -------------------
defined in Rule 501(a) of Regulation D promulgated under the Securities Act.

     4.   Conditions of the Purchaser's Obligations at Closing.  The obligations
          ----------------------------------------------------
of the Purchaser to the Company under this Agreement are subject to the
fulfillment, on or before the Closing, of each of the following conditions,
unless otherwise waived:

          4.1  Representations and Warranties.  The representations and
               ------------------------------
warranties of the Company contained in Section 2 shall be true and correct on
and as of the Closing.

          4.2  Qualifications.  All authorizations, approvals or permits, if
               --------------
any, of any governmental authority or regulatory body of the United States or of
any state that are required in connection with the lawful issuance and sale of
the Shares pursuant to this Agreement shall be obtained and effective as of the
Closing.

          4.3  Warrant.  The Company shall have executed and delivered to the
               -------
Purchaser the Warrant in substantially the form attached as Exhibit A.
                                                            ---------

          4.4  Strategic Business Relationship Agreement. The Company and the
               -----------------------------------------
Purchaser shall have executed and delivered a Strategic Business Relationship
Agreement in a form agreed to by the Company and the Purchaser.

          4.5  Escrow Agreement.  The Company and the Purchaser shall have
               ----------------
entered into the Escrow Agreement substantially in the form of Exhibit B hereto.

          4.6  Opinion.  The Company shall have delivered to the Purchaser an
               -------
opinion of Orrick, Herrington & Sutcliffe LLP in a form agreed to by the
Purchaser and its counsel.

     5.   Conditions of the Company's Obligations at Closing.  The obligations
          --------------------------------------------------
of the Company to the Purchaser under this Agreement are subject to the
fulfillment, on or before the Closing, of each of the following conditions,
unless otherwise waived:

          5.1  Representations and Warranties.  The representations and
               ------------------------------
warranties of the Purchaser contained in Section 3 shall be true and correct on
and as of the Closing.

          5.2  Qualifications.  All authorizations, approvals or permits, if
               --------------
any, of any governmental authority or regulatory body of the United States or of
any state that are required in

                                      -7-
<PAGE>

connection with the lawful issuance and sale of the Shares pursuant to this
Agreement shall be obtained and effective as of the Closing.

     6.   Covenants of the Company.
          ------------------------

          6.1  Nomination of Director.
               ----------------------

               (a)  Effective as of the date of this Agreement, the Company will
cause K. Paul Singh to be elected a member of the Board of Directors of the
Company as a "Class II" director.

               (b)  At the annual meeting of stockholders of the Company to be
held in the year 2000, the Company and the Company's Board of Directors will
nominate and recommend to the Company's stockholders K. Paul Singh to serve on
the Board of Directors of the Company as a "Class II" director. The Company also
shall use its reasonable efforts to solicit from the stockholders of the Company
eligible to vote in the election of directors at such meeting a proxy to vote
for K. Paul Singh.

          6.2  Amendment to Existing Investors' Rights Agreement.  The Company
               -------------------------------------------------
agrees to use its best efforts to obtain by January 31, 2000 the requisite
consent of the holders of registrable stock under the Existing Investors' Rights
Agreement and Grayrock Capital necessary to amend such agreement (a) to grant to
the Purchaser demand registration rights with respect to the Shares and the
shares of Common Stock issuable upon exercise of the Warrant (the "Warrant
                                                                   -------
Shares") beginning six months after the date hereof and (b) to grant piggyback
------
registration rights to the Purchaser with respect to the Shares and the Warrant
Shares on the same terms and conditions as are generally applicable to the other
holders of registrable stock thereunder; provided, however, that the Purchaser
will have the right to demand a registration if the Purchaser proposes to
register at least 50% of the Shares or all of the Warrant Shares. If the Company
is unable to so amend the Existing Investors' Rights Agreement, the Company
shall enter into a registration rights agreement with the Purchaser in a form
reasonably acceptable to the Purchaser.

     7.   Miscellaneous.
          -------------

          7.1  Survival of Warranties.  Unless otherwise set forth in this
               ----------------------
Agreement, the warranties, representations and covenants of the Company and the
Purchaser contained in or made pursuant to this Agreement shall survive the
execution and delivery of this Agreement and the Closing.

          7.2  Transfer; Successors and Assigns.  The terms and conditions of
               --------------------------------
this Agreement shall inure to the benefit of and be binding upon the respective
successors and assigns of the parties.  Nothing in this Agreement, express or
implied, is intended to confer upon any party other than the parties hereto or
their respective successors and assigns any rights, remedies, obligations, or
liabilities under or by reason of this Agreement, except as expressly provided
in this Agreement.

                                      -8-
<PAGE>

          7.3   Governing Law.  This Agreement and all acts and transactions
                -------------
pursuant hereto and the rights and obligations of the parties hereto shall be
governed, construed and interpreted in accordance with the laws of the State of
Delaware, without giving effect to principles of conflicts of law.

          7.4   Counterparts.  This Agreement may be executed in counterparts,
                ------------
each of which shall be deemed an original and all of which together shall
constitute one instrument.

          7.5   Titles and Subtitles.  The titles and subtitles used in this
                --------------------
Agreement are used for convenience only and are not to be considered in
construing or interpreting this Agreement.

          7.6   Notices. Any notice required or permitted by this Agreement
                -------
shall be in writing and shall be deemed sufficient (i) upon delivery, when
delivered personally or sent by facsimile, (ii) on the next business day after
dispatch when delivered by overnight courier or sent by telegram, or (iii) on
the fifth business day after being deposited in the U.S. mail, as certified or
registered mail, with postage prepaid, addressed (a) if to the Company, to 1080
Marina Village Parkway, Alameda, California 94501, Attn: Chief Financial
Officer, facsimile number (510) 433-7811, with a copy to Orrick, Herrington &
Sutcliffe LLP, 400 Sansome Street, San Francisco, California 94111, Attn: Peter
Lillevand, Esq., facsimile number (415) 773-5759 or (b) if to the Purchaser, to
1700 Old Meadow Road, Third Floor, McLean, Virginia 22102, Attn: David P.
Slotkin, Esq., Deputy General Counsel, with a copy to Hogan & Hartson L.L.P.,
Columbia Square, 555 Thirteenth Street, N.W., Washington, D.C. 20004, Attn:
David W. Bonser, Esq., or such other addresses as either party may from time to
time specify in writing.

          7.7   Fees and Expenses.  Each party shall pay its own fees and
                -----------------
expenses incurred with respect to this Agreement and the transactions
contemplated hereby, except for any registration expenses payable by the Company
under the Existing Investors' Rights Agreement, as amended as contemplated
hereby.

          7.8   Amendments and Waivers.  Any term of this Agreement may be
                ----------------------
amended or waived only with the written consent of the Company and the
Purchaser.

          7.9   Severability.  If one or more provisions of this Agreement are
                ------------
held to be unenforceable under applicable law, the parties agree to renegotiate
such provision in good faith. In the event that the parties cannot reach a
mutually agreeable and enforceable replacement for such provision, then (a) such
provision shall be excluded from this Agreement, (b) the balance of the
Agreement shall be interpreted as if such provision were so excluded and (c) the
balance of the Agreement shall be enforceable in accordance with its terms.

          7.10  Delays or Omissions. No delay or omission to exercise any right,
                -------------------
power or remedy accruing to any party under this Agreement, upon any breach or
default of any other party under this Agreement, shall impair any such right,
power or remedy of such non-breaching or non-defaulting party nor shall it be
construed to be a waiver of any such breach or default, or an acquiescence
therein, or of or in any similar breach or default thereafter occurring; nor
shall any waiver of any single breach or default be deemed a waiver of any other
breach or default

                                      -9-
<PAGE>

theretofore or thereafter occurring. Any waiver, permit, consent or approval of
any kind or character on the part of any party of any breach or default under
this Agreement, or any waiver on the part of any party of any provisions or
conditions of this Agreement, must be in writing and shall be effective only to
the extent specifically set forth in such writing. All remedies, either under
this Agreement or by law or otherwise afforded to any party, shall be cumulative
and not alternative.

          7.11  Entire Agreement.  This Agreement and the documents referred to
                ----------------
herein constitute the entire agreement between the parties hereto pertaining to
the subject matter hereof, and any and all other written or oral agreements
relating to the subject matter hereof existing between the parties hereto are
expressly canceled.

          7.12  Corporate Securities Law.  THE SALE OF THE SECURITIES WHICH ARE
                ------------------------
THE SUBJECT OF THIS AGREEMENT HAS NOT BEEN QUALIFIED WITH THE COMMISSIONER OF
CORPORATIONS OF THE STATE OF CALIFORNIA AND THE ISSUANCE OF THE SECURITIES OR
THE PAYMENT OR RECEIPT OF ANY PART OF THE CONSIDERATION THEREFOR PRIOR TO THE
QUALIFICATION IS UNLAWFUL, UNLESS THE SALE OF SECURITIES IS EXEMPT FROM THE
QUALIFICATION BY SECTION 25100, 25102 OR 25105 OF THE CALIFORNIA CORPORATIONS
CODE.  THE RIGHTS OF ALL PARTIES TO THIS AGREEMENT ARE EXPRESSLY CONDITIONED
UPON THE QUALIFICATION BEING OBTAINED UNLESS THE SALE IS SO EXEMPT.

          7.13  Confidentiality.  Each party hereto agrees that, except with the
                ---------------
prior written permission of the other party, it shall at all times keep
confidential and not divulge, furnish or make accessible to anyone any
confidential information, knowledge or data concerning or relating to the
business or financial affairs of the other parties to which such party has been
or shall become privy by reason of this Agreement, discussions or negotiations
relating to this Agreement, the performance of its obligations hereunder or the
ownership of Shares purchased hereunder. The provisions of this Section 7.13
shall be in addition to, and not in substitution for, the provisions of any
separate nondisclosure agreement executed by the parties hereto with respect to
the transactions contemplated hereby. The provisions of this Section 7.13 shall
not apply to any information that (a) is or becomes a part of the public domain
through no act or omission of the receiving party; (b) was in the receiving
party's lawful possession prior to any disclosure by the other party and had not
been obtained by the receiving party either directly or indirectly from the
disclosing party, as demonstrated by files in existence at the time of
disclosure; (c) is furnished by the disclosing party to a third party without
restrictions similar to those contained in this Agreement; (d) is lawfully
disclosed to the receiving party by a third party without, to the knowledge of
the receiving party, restriction on disclosure; (e) is independently developed
by the receiving party without reference to confidential information received
under this Agreement; or (f) is compelled by law or legal process to be
disclosed, provided that the receiving party has complied with Section 5(a) of
the Mutual Non-Disclosure Agreement dated November 1, 1999 by and between the
Company and the Purchaser.

                           [Signature Pages Follow]

                                      -10-
<PAGE>

     The parties have executed this Agreement as of the date first written
above.

                                   COMPANY:

                                   Pilot Network Services, Inc.

                                   By:  /s/ William C. Leetham
                                        ----------------------------------------

                                   Name: William C. Leetham
                                         ---------------------------------------
                                              (print)
                                   Title: Chief Financial Officer
                                          --------------------------------------

                                   PURCHASER:

                                   Primus Telecommunications Group,
                                   Incorporated

                                   By: /s/ Neil L. Hazard
                                       -----------------------------------------

                                   Name: Neil L. Hazard
                                         ---------------------------------------
                                              (print)
                                   Title: Chief Financial Officer
                                          --------------------------------------

<PAGE>

                                   EXHIBIT A
                                   ---------

                                FORM OF WARRANT
<PAGE>

                                   EXHIBIT B
                                   ---------

                           FORM OF ESCROW AGREEMENT<PAGE>

                                                                    EXHIBIT 10.3

     THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE SOLD, PLEDGED, OR
OTHERWISE TRANSFERRED WITHOUT AN EFFECTIVE REGISTRATION THEREOF UNDER SUCH ACT
OR PURSUANT TO RULE 144 OR AN OPINION OF COUNSEL, WHICH MAY BE IN-HOUSE COUNSEL,
IN A FORM REASONABLY SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT
REQUIRED.

                      ___________________________________

                           WARRANT TO PURCHASE STOCK

Warrant to Purchase 200,000 Shares    Issue Date:              December 28, 1999
of the Common Stock of Pilot          Expiration Date:         December 28, 2002
Network Services, Inc.                Initial Exercise Price:  $25.00 per share

     FOR VALUE RECEIVED, PILOT NETWORK SERVICES, INC., a Delaware corporation
(the "Company"), hereby certifies that PRIMUS TELECOMMUNICATIONS GROUP,
      -------
INCORPORATED ("Holder") is entitled to purchase the number of fully paid and
               ------
non-assessable shares of common stock (the "Shares") of the Company at the
                                            ------
initial exercise price per Share (the "Warrant Price") all as set forth above
                                       -------------
and as adjusted pursuant to Article 2 of this Warrant, subject to the provisions
and upon the terms and conditions set forth in this Warrant.

ARTICLE 1.  EXERCISE.

     1.1  Method of Exercise.  This Warrant is exercisable, in whole or in part,
at any time and from time to time on or before the Expiration Date set forth
above; provided, however, that this Warrant may not be exercised until all
applicable requirements, if any, of the Hart-Scott-Rodino Antitrust Improvements
Act of 1976, as amended (the "HSR Act"), have been satisfied.  The Company
                              -------
agrees to file and cooperate with Holder in filing all documents required to
comply with the HSR Act.  Holder may exercise this Warrant by delivering a duly
executed Notice of Exercise in substantially the form attached as Appendix 1 to
the principal office of the Company.  Holder shall also deliver to the Company a
wire transfer or certified check for the aggregate Warrant Price for the Shares
being purchased.

     1.2  Delivery of Certificate and New Warrant. Promptly after Holder
exercises this Warrant, the Company shall deliver at its expense to Holder
certificates for the Shares acquired and, if this Warrant has not been fully
exercised and has not expired, a new Warrant representing the Shares not so
acquired.

     1.3  Replacement of Warrants. On receipt of evidence reasonably
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant and, in the case of loss, theft or destruction, on delivery of an
indemnity agreement reasonably satisfactory in form and amount to the Company
or, in the case of mutilation, on surrender and cancellation of this
<PAGE>

Warrant, the Company shall execute and deliver, in lieu of this Warrant, a new
warrant of like tenor.

     1.4  Fractional Shares.  No fractional Shares shall be issuable upon
exercise of the Warrant and the number of Shares to be issued shall be rounded
down to the nearest whole Share.  If a fractional share interest arises upon any
exercise of the Warrant, the Company shall eliminate such fractional share
interest by paying Holder an amount computed by multiplying the fractional
interest by the fair market value of a full Share.

ARTICLE 2.  ADJUSTMENTS TO THE SHARES.

     2.1  Stock Dividends, Splits, Etc.  If the Company declares or pays a
dividend on its common stock payable in common stock or other securities,
combines its outstanding shares of common stock, makes a distribution of capital
stock to holders of its common stock or subdivides the outstanding common stock
into a greater amount of common stock, then the number of shares for which this
Warrant may be exercised shall be proportionately adjusted such that, upon
exercise of this Warrant, Holder shall receive a proportionate number of
securities to which Holder would have been entitled had Holder owned the Shares
of record as of the date the applicable event occurred, and the per share
Warrant Price shall be adjusted so that the aggregate Warrant Price remains the
same.

     2.2  Reclassification.  Upon any reclassification that results in a change
of the number and/or class of the securities issuable upon exercise of this
Warrant, Holder shall be entitled to receive, upon exercise of this Warrant, the
number and kind of securities and property that Holder would have received for
the Shares if this Warrant had been exercised immediately before such
reclassification. The Company shall promptly issue to Holder a new Warrant for
such new securities or other property. The new Warrant shall provide for
adjustments which shall be as nearly equivalent as may be practicable to the
adjustments provided for in this Article 2 including, without limitation,
adjustments to the Warrant Price and the number of securities or property
issuable upon exercise of the new Warrant. The provisions of this Section 2.2
shall similarly apply to successive reclassifications.

     2.3  Adjustments for Business Combinations, Etc.  Upon a merger or
consolidation of the Company with or into, or a transfer of all or substantially
all of the assets of the Company to, another entity (a "Consolidation Event"),
                                                        -------------------
then the Holder shall be entitled to receive upon such transfer, merger or
consolidation becoming effective, and upon payment of the Warrant Price, the
number of shares or other securities or property of the Company or of the
successor corporation resulting from such merger or consolidation, which would
have been received by the Holder for the shares of stock subject to this Warrant
had this Warrant been exercised immediately prior to such transfer, merger or
consolidation becoming effective or to the applicable record date thereof, as
the case may be. The Company shall not effect any Consolidation Event unless the
resulting successor or acquiring entity (if not the Company) assumes by written
instrument the obligation to deliver to the Holder such shares of stock and/or
other securities as the Holder is entitled to receive had this Warrant been
exercised in accordance with the foregoing. Such successor shall promptly issue
to Holder a new Warrant for such new securities or other property. The new
Warrant shall provide for adjustments which shall be as nearly equivalent as may
be practicable to the adjustments provided for in this Article 2

                                       2
<PAGE>

including, without limitation, adjustments to the Warrant Price and the number
of securities or property issuable upon exercise of the new Warrant. The
provisions of this Section 2.3 shall similarly apply to successive
reclassifications, exchanges, substitutions, or other events.

     2.4  No Impairment.  The Company shall not, by amendment of its Certificate
of Incorporation or through a reorganization, transfer of assets, consolidation,
merger, dissolution, issue or sale of securities or any other voluntary action,
avoid or seek to avoid the observance or performance of any of the terms to be
observed or performed under this Warrant by the Company, but shall at all times
in good faith assist in carrying out of all the provisions of this Article 2 and
in taking all such action as may be necessary or appropriate to protect Holder's
rights under this Article against impairment.

     2.5  Certificate as to Adjustments.  Upon each adjustment of the Warrant
Price, the Company shall promptly compute such adjustment and furnish Holder
with a certificate of its Chief Financial Officer setting forth such adjustment
and the facts upon which such adjustment is based.  The Company shall, upon
written request, furnish Holder a certificate setting forth the Warrant Price in
effect upon the date thereof and the series of adjustments leading to such
Warrant Price.

ARTICLE 3.  REPRESENTATIONS AND COVENANTS OF THE COMPANY.

     3.1  Validly Issued Shares.  The Company hereby represents and warrants to
the Holder that the Shares that may be issued upon the exercise of the purchase
right represented by this Warrant shall, upon issuance, be duly authorized,
validly issued, fully paid and non-assessable, and free of any liens and
encumbrances except for restrictions on transfer provided for herein or under
applicable federal and state securities laws.

     3.2  Valid Authorization.  The Company hereby represents and warrants to
the Holder that the execution and delivery of this Warrant by the Company have
been duly authorized by all necessary corporate action on the part of the
Company and no additional consent or approval by any third party or governmental
authority is required for the execution and delivery by the Company of this
Warrant, other than those required under the HSR Act under certain
circumstances.

     3.3  Notice of Certain Events.  If the Company proposes at any time (a) to
declare any dividend or distribution upon its common stock, whether in cash,
property, stock, or other securities (other than a regular cash dividend); (b)
to offer for subscription pro rata to the holders of common stock any additional
shares of stock of any class or series or other rights; (c) to effect any
reclassification or recapitalization of common stock; or (d) to merge or
consolidate with or into any other corporation, or sell or convey all or
substantially all of its assets, or to liquidate, dissolve or wind up; then, in
connection with each such event, the Company shall give Holder (1) at least 10
business days prior written notice of the date on which a record will be taken
for such dividend, distribution, or subscription rights (and specifying the date
on which the holders of common stock will be entitled thereto) or for
determining rights to vote, if any, in respect of the matters referred to in (c)
and (d) above; and (2) in the case of the matters referred to in (c) and (d)
above, the same notice that is provided to stockholders of the Company including
when the same will take place (and specifying the date on which the holders of
common stock will be

                                       3
<PAGE>

entitled to exchange their common stock for securities or other property
deliverable upon the occurrence of such event).

     3.4  Reservation of Shares.  The Company shall at all times reserve for
issuance pursuant to this Warrant such number of shares of Common Stock as are
issuable upon exercise of this Warrant.

     3.5  Periodic Reports.  The Company shall continue to file with the
Securities and Exchange Commission all periodic reports required under the
Securities Exchange Act of 1934 during the term of this Warrant; provided,
however, that such obligation may terminate in the event of a merger or
consolidation of the Company in which the Company is not the surviving entity,
the acquisition of substantially all of the voting stock of the Company by a
single entity or group of related entities or a sale of all or substantially all
of the assets of the Company.

     3.6  NASDAQ Listing.  (a) The Company will cause the shares of Common Stock
issuable upon exercise of this Warrant to be listed for trading on the NASDAQ
National Market System.

          (b)  The Company will use its best efforts to cause its common stock
to remain listed for trading on the NASDAQ National Market System or the New
York Stock Exchange; provided, however, that such obligation may terminate in
the event of or merger or consolidation of the Company in which the Company is
not the surviving entity, the acquisition of substantially all of the voting
stock of the Company by a single entity or group of related entities or a sale
of all or substantially all of the assets of the Company.

     3.7  Registration Rights.  The Company agrees to use its best efforts to
obtain by January 31, 2000 the requisite consent of the holders of registrable
stock under that certain Amended and Restated Investors' Rights Agreement, dated
as of March 31, 1997, among the Company and the investors listed on Schedule I
thereto, as amended by that certain Amendment to Investors' Rights Agreement
dated as of December 22, 1997 and that certain Second Amendment to Investors'
Rights Agreement dated February 26, 1998, including the obligation of the
Company to amend such agreement to grant registration rights to Greyrock Capital
(the "Existing Investors' Rights Agreement"), necessary to amend such agreement
      ------------------------------------
(a) to grant to the Holder demand registration rights with respect to the Shares
beginning six months after the date hereof and (b) to grant piggyback
registration rights to the Holder with respect to the Shares on the same terms
and conditions as are generally applicable to the other holders of registrable
stock thereunder; provided, however, that the Holder will have the right to
demand a registration if the Holder proposes to register all of the Shares. If
the Company is unable to so amend the Existing Investors' Rights Agreement, the
Company shall enter into a registration rights agreement with the Holder in a
form reasonably acceptable to the Holder.

ARTICLE 4.  MISCELLANEOUS.

     4.1  This Warrant and the Shares shall be imprinted with a legend in
substantially the following form:

     THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
AMENDED, AND MAY NOT BE SOLD, PLEDGED OR OTHERWISE

                                       4
<PAGE>

TRANSFERRED WITHOUT AN EFFECTIVE REGISTRATION THEREOF UNDER SUCH ACT OR PURSUANT
TO RULE 144 OR AN OPINION OF COUNSEL, WHICH MAY BE IN-HOUSE COUNSEL, IN A FORM
REASONABLY SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED.

     4.2  Compliance with Securities Laws on Transfer.  This Warrant and the
Shares issuable upon exercise of this Warrant may not be transferred or assigned
in whole or in part without compliance with applicable federal and state
securities laws (including, without limitation, the delivery of investment
representation letters and legal opinions satisfactory to the Company, if
requested by the Company). The Company shall not require Holder to provide an
opinion of counsel if the transfer is to an affiliate of Holder or if there is
no material question as to the availability of current information as referenced
in Rule 144(c), Holder represents that it has complied with Rule 144(d) and (e),
the selling broker represents that it has complied with Rule 144(f), and the
Company is provided with a copy of Holder's notice of proposed sale.

     4.3  Transfer Procedure.  Subject to the provisions of Sections 4.1 and
4.2, Holder may transfer all or part of this Warrant by giving the Company
notice of the portion of the Warrant being transferred setting forth the name,
address and taxpayer identification number of the transferee and surrendering
this Warrant to the Company for reissuance to the transferee (and Holder if
applicable).

     4.4  Notices.  Any notice required or permitted by this Warrant shall be in
writing and shall be deemed sufficient (i) upon delivery, when delivered
personally or sent by facsimile, (ii) on the next business day after dispatch
when delivered by overnight courier or sent by telegram, or (iii) on the fifth
business day after being deposited in the U.S. mail, as certified or registered
mail, with postage prepaid, addressed (a) if to the Company, to 1080 Marina
Village Parkway, Alameda, California  94501, Attn:  Chief Financial Officer,
facsimile number (510) 433-7811, with a copy to Orrick, Herrington & Sutcliffe
LLP, 400 Sansome Street, San Francisco, California  94111, Attn:  Peter
Lillevand, Esq., facsimile number (415) 773-5759 or (b) if to the Holder, to
1700 Old Meadow Road, Third Floor, McLean, Virginia  22102, Attn:  David P.
Slotkin, Esq., Deputy General Counsel, with a copy to Hogan & Hartson L.L.P.,
Columbia Square, 555 Thirteenth Street, N.W., Washington, D.C. 20004, Attn:
David W. Bonser, Esq., or such other addresses as either party may from time to
time specify in writing.

     4.5  Waiver.  This Warrant and any term hereof may be changed, waived,
discharged or terminated only by an instrument in writing signed by the party
against which enforcement of such change, waiver, discharge or termination is
sought.

     4.6  Governing Law.  This Warrant shall be governed by and construed in
accordance with the laws of the State of Delaware, without giving effect to its
principles regarding conflicts of law.

                                    PILOT NETWORK SERVICES, INC.

                                    By  /s/ William C. Leetham
                                        --------------------------------------
                                        Name:  William C. Leetham
                                        Title: Chief Financial Officer

                                       5
<PAGE>

                                  APPENDIX 1

                              NOTICE OF EXERCISE
                              ------------------

     1.   The undersigned hereby elects to purchase _________________ shares of
the Common Stock of Pilot Network Services, Inc. pursuant to the terms of the
attached Warrant, and tenders herewith payment of the purchase price of such
shares in full.

     2.   Please issue a certificate or certificates representing said shares in
the name of the undersigned or in such other name as is specified below:

                    ___________________________
                                   (NAME)

                    ___________________________
                    ___________________________
                    ___________________________
                                (ADDRESS)

     3.   The undersigned represents it is acquiring the shares solely for its
own account and not as a nominee for any other party and not with a view toward
the resale or distribution thereof except in compliance with applicable
securities laws.

     ___________________________
     (Signature)

     ___________________________
     (Date)

                                       6

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