A method for anonymously carrying out multiphase transactions over a distributed computer network that comprises a computer of a trusted authority, a user's computer, and servers of one or more service providers, wherein each of said computers/servers in said network comprises dedicated software that contains information, including a one-way function, and instructions necessary to execute said method, wherein said method is carried out as follows: a. the user's computer acts on behalf of the user to establish contact with the computer of the trusted authority; b. said computer of said trusted authority provides said user's computer with either: i. a secret random number; or ii. a hard to produce evidence; c. a transaction is started on behalf of the user by said user's computer which locally produces a unique pseudonym for each server of said one or more service provider that will be involved in the transaction, wherein said pseudonym is the output of said one-way function included on it's dedicated software which receives as an input either: i. said secret random number and the corresponding IP address of said server of said service provider; or ii. a commitment to produce said hard to produce evidence and said corresponding IP address of said server of said service provider; d. said user's computer uses said pseudonyms to communicate anonymously with said servers of said service providers; e. said user's computer initiates the carrying out of said transaction on behalf of the user by sending a resolve message based on either: i. said secret random number XOR said IP address of said server of said service provider; or ii. said commitment to produce said hard to produce evidence to each of said servers; f. said transaction is completed when: i. each of said servers of said service providers sends said secret random number revealed from said resolve message sent to it by said user's computer in step e.i. to said computer of said trusted authority, which confirms to each of said servers that the same user has interacted with each of them; or ii. said user's computer provides to each of said servers a computationally secure Interactive Zero Knowledge Proof ZKP, that proves that said user is the same anonymous identity that knows said evidence in said resolve message sent by said user's computer in step e.ii. a. the user's computer acts on behalf of the user to establish contact with the computer of the trusted authority; b. said computer of said trusted authority provides said user's computer with either: i. a secret random number; or ii. a hard to produce evidence; i. a secret random number; or ii. a hard to produce evidence; c. a transaction is started on behalf of the user by said user's computer which locally produces a unique pseudonym for each server of said one or more service provider that will be involved in the transaction, wherein said pseudonym is the output of said one-way function included on it's dedicated software which receives as an input either: i. said secret random number and the corresponding IP address of said server of said service provider; or ii. a commitment to produce said hard to produce evidence and said corresponding IP address of said server of said service provider; i. said secret random number and the corresponding IP address of said server of said service provider; or ii. a commitment to produce said hard to produce evidence and said corresponding IP address of said server of said service provider; d. said user's computer uses said pseudonyms to communicate anonymously with said servers of said service providers; e. said user's computer initiates the carrying out of said transaction on behalf of the user by sending a resolve message based on either: i. said secret random number XOR said IP address of said server of said service provider; or ii. said commitment to produce said hard to produce evidence to each of said servers; i. said secret random number XOR said IP address of said server of said service provider; or ii. said commitment to produce said hard to produce evidence to each of said servers; f. said transaction is completed when: i. each of said servers of said service providers sends said secret random number revealed from said resolve message sent to it by said user's computer in step e.i. to said computer of said trusted authority, which confirms to each of said servers that the same user has interacted with each of them; or ii. said user's computer provides to each of said servers a computationally secure Interactive Zero Knowledge Proof ZKP, that proves that said user is the same anonymous identity that knows said evidence in said resolve message sent by said user's computer in step e.ii. i. each of said servers of said service providers sends said secret random number revealed from said resolve message sent to it by said user's computer in step e.i. to said computer of said trusted authority, which confirms to each of said servers that the same user has interacted with each of them; or ii. said user's computer provides to each of said servers a computationally secure Interactive Zero Knowledge Proof ZKP, that proves that said user is the same anonymous identity that knows said evidence in said resolve message sent by said user's computer in step e.ii.