Over the years the Internet has established itself to be the most widely accepted form of communication. On the other hand, it has also proved itself to be an extremely insecure network. An issue is whether the insecure nature of the Internet creates a lack of trust or reluctance on the part of individuals and businesses to use Electronic Signatures, and in particular, Digital Signatures? This paper attempts to answer this question by examining two issues. First, how secure is the process of issuance of Digital Signature Certificates (DSCs)/key pairs by a Certification Authority (CA)? Second, what are the security issues associated with the storage of DSCs/key pairs? It is shown in the paper that the issuing of DSCs/key pairs by the CA's to their subscribers is a fairly secure process. However, the storing of DSCs/key pairs is a major security issue. It is suggested that legislation should make it mandatory for CAs to issue DSCs/key pairs on portable information storage devices. It is further suggested that CAs issue DSCs/key pairs on secure and user friendly portable information storage devices such as the flash disk. Finally, it is argued that, though the security of the DSCs/key pairs stored on flash disks can be further enhanced through the use of biometrics, legislation should tread carefully when laying down any rules or guidelines in this regard because of the privacy and sensitivity issues associated with the use of biometrics.