Computer software and computer programs for encryption, computation of cryptographic objects, verification of cryptographic objects for use in computer servers, networks, Internet, wireless Internet, intranets and extranets; computer hardware; computer interface circuit board for data encryption and integrity assessment; computer network apparatus, namely network data encryption or integrity protection hardware and software; computer wired and wireless networks; computer software and hardware for methodology and framework protection; computer software for facilitating electronic commerce transaction and computer hardware for allowing users to perform electronic business transactions via a global computer network; computer software with a certification authorization engine for creating digital certificates over the wired and wireless Internet; computer hardware and software for facilitating secure electronic payments over the Internet; computer hardware and software key management server for secure cryptographic processing; computer software for creating a virtual secure private network environment; computer software for performing cryptographic operations, namely encryption, decryption, computation of cryptographic objects, verification of cryptographic objects, generating digital signature and signature verification and key generation and recovery; computer system comprising hardware and software for data confidentiality and integrity protection and encryption; computer software for secure e-mail and electronic transmissions; computer software for secure access to wired and wireless networks and connecting wired and wireless networks