Delay Tolerant Network (DTN) enables communication in opportunistic networks where disruptive links result into intermittent connectivity. Routing protocols in such opportunistic environments mainly rely on broadcast/multicast communication in order to maximize the chances of packet delivery to destination node. Lack of end-to-end path and the essential requirement of store-carry-forward decision of packets by intermediate nodes, pose a serious threat to security and privacy concerns in DTNs. This article proposes a novel approach for secure and private communication in DTNs by hiding the identity of nodes using pseudonyms. The approach is based on Privacy by Architecture (PbA) where minimal identifying information of a user is sent to a certificate authority (CA) while requesting for a certificate. The novel PbA based scheme is composed of a set of protocols to address the aforementioned challenges; the Pseudonym Credential and Pseudonym Identity/Certificate Issuance protocols. The proposed approach is validated using formal modeling in CasperFDR which is the state-of-the art compiler for performance analysis of security protocols. To strengthen our claim, an information theoretic quantification method is employed to measure the Degree of Anonymity (DoA) of the approach. The approach performs efficiently and requires no end-to-end connectivity for messages exchange between the user and the certificate authority, thus making it an ideal choice for ensuring security and privacy in DTNs. Results show that the proposed approach guards against privacy attacks and delivers a high degree of anonymity even in the presence of compromised nodes in the network.