A method for the secure data transmission between an arbitrary sender (S A) and an arbitrary addressee (S B), which are connected with each other via a computer network, wherein the computer network includes parties (MP i,, MP u, MP v, MP w, MP j), wherein the parties are disjoint subsets of independently addressable computer systems of the computer network, and a) a message (m 0) to be transmitted is split up into k ∈ N submessages (t p) by Secret Sharing, so that n ∈ N submessages (t p) are required to be able to therefrom reconstruct the message (m 0) to be transmitted, b) the submessages (t p) only are transmitted to independently addressable computer systems (S x) for switching via secure channels in different parties (MP u, MP v, MP w) to which a secure channel can be set up and which in the following also are referred to as acquaintances, and wherein into no party (MP u, MP v, MP w) more than one submessage (t p) can get, c) each independently, addressable computer systems for switching (S x) checks the submessage (t p) arriving from an acquaintance via a secure channel and adds an authenticity identifier (I Ap) to a correct submessage (t p), d1) when between, an independently addressable computer system for switching (S x) and the addressee (S B) no secure channel can be set up, the correct submessage (t p) together with the associated correct authenticity identifier (I Ap) is forwarded to another independently addressable computer system for switching (S xNew) in the same party (MP u, MP v, MP w) via a secure channel, wherein step d1) is again executed by this other independently addressable computer system for switching (S xNew) after checking the correctness, d2) when between an independently addressable computer system for switching (S x) and the addressee (S B) a secure channel can be set up, the correct submessage (t p) together with the associated correct authenticity identifier (I Ap) is transmitted to the addressee (S B) via this secure channel, e) the addressee (S B) checks all submessages (t p) which it has received via secure channels together with the associated authenticity identifiers (I Ap) from independently addressable computer systems for switching (S x) and stores the same together with a unique identification of the party (MP u, MP v, MP w) from which it has received the same, f) when the addressee (S B) has correctly received at least n submessages (t p) together with matching associated authenticity identifiers (I Ap) from at least n different parties (MP u, MP v, MP w), it reconstructs the message (m 0) from the submessages (t p). a) a message (m 0) to be transmitted is split up into k ∈ N submessages (t p) by Secret Sharing, so that n ∈ N submessages (t p) are required to be able to therefrom reconstruct the message (m 0) to be transmitted, b) the submessages (t p) only are transmitted to independently addressable computer systems (S x) for switching via secure channels in different parties (MP u, MP v, MP w) to which a secure channel can be set up and which in the following also are referred to as acquaintances, and wherein into no party (MP u, MP v, MP w) more than one submessage (t p) can get, c) each independently, addressable computer systems for switching (S x) checks the submessage (t p) arriving from an acquaintance via a secure channel and adds an authenticity identifier (I Ap) to a correct submessage (t p), d1) when between, an independently addressable computer system for switching (S x) and the addressee (S B) no secure channel can be set up, the correct submessage (t p) together with the associated correct authenticity identifier (I Ap) is forwarded to another independently addressable computer system for switching (S xNew) in the same party (MP u, MP v, MP w) via a secure channel, wherein step d1) is again executed by this other independently addressable computer system for switching (S xNew) after checking the correctness, d2) when between an independently addressable computer system for switching (S x) and the addressee (S B) a secure channel can be set up, the correct submessage (t p) together with the associated correct authenticity identifier (I Ap) is transmitted to the addressee (S B) via this secure channel, e) the addressee (S B) checks all submessages (t p) which it has received via secure channels together with the associated authenticity identifiers (I Ap) from independently addressable computer systems for switching (S x) and stores the same together with a unique identification of the party (MP u, MP v, MP w) from which it has received the same, f) when the addressee (S B) has correctly received at least n submessages (t p) together with matching associated authenticity identifiers (I Ap) from at least n different parties (MP u, MP v, MP w), it reconstructs the message (m 0) from the submessages (t p).