As a condition of the issuance of any permit to perform work or other operations upon state right-of-way pursuant to Parts 125, 126, 129, 131 and 134 of this Title, permittees are required to furnish proof that is duly subscribed by an insurance carrier, that compensation for all employees has been secured as required by section 57 of the Workers’ Compensation Law of the State of New York, or that the person or persons performing such work are exempted from the requirements of that law.