Hierarchical identity-based encryption and signature schemes

A computer-implemented encryption method for encrypting a message M for decryption with secret information of an intended recipient entity E in a hierarchical cryptographic schemer comprises (1) obtaining a variable value r ; (2) obtaining a first encryption of the message M , the first encryption being decryptable with a value g r , where g is a value of a predefined function on a value ê ( p 0 , p 1 ); ê :G 1 x G 1 †’G 2 is a non-degenerate bilinear mapping, where G 1 and G 2 are groups, and where ê, G 1 and G 2 are to be used for the decryption; p 0 , p 1 are elements of G 1 at least one of which depends on the ID of E's parent in the hierarchical cryptographic system; (3) obtaining a first ciphertext portion comprising a plurality of values each of which is an element of the group G 1 and is a linear expression of values of a form rF where each F is a predefined function of an ID of E and/or at least one parent of E, where at least one value F depends on the ID of at least one parent of E; and (4) generating a ciphertext formed using the first ciphertext portion and the first encryption of the message M .