Certification path validation is a complex task that implies high computational cost. In this process is necessary to verify the binding between the owner ofthe certificate and his public key. In SET protocol, the customer and merchant require to verify the certification path of their certificates to trust each other. The customer and merchant carry out several cryptographic operations to complete SET protocol including the authentication process. Because mobile devices are limited in terms of processing and storage capacities, it is relevant to reduce the computational cost required by the cryptographic operations. In this paper, we apply TRUTHC (TrustRelationship Using Two Hash Chains) to reduce thecomputational cost of cryptographic operations carried out by the customer and merchant to complete the certification path validation. In addition, we compare the results using RSA and ECDSA protocols, with a typical PKI.