This paper describes new protocols for implementation of some security services for cooperation of mutually suspicious users. Such services may be: secure user identification and authentication, disclosure protocol, certified mail, contract signing, decision protocol (coin flipping), secure computing and secure group communications (teleconferencing). Those special security services may be implemented in a computer network or in OSI system in principle in two ways. If a trusted third party is used, called “beacon” by Rabin, then it must perform special protocols, which assist two (or more) mutually suspicious users to exchange confidential information. Without the third party, two suspicious users may exchange such information by a special randomized protocol, described, for instance, by Even et al. or by protocols (Blum). In this paper some modifications of Rabin's protocols are suggested, so that new versions of protocols may be used to implement the same security services, but with better operational efficiency.