At block 550, a third secret share may be generated by application of an XOR operation to the third, fourth, and first secret segments. The third secret share may be formed of a header and share encoded data and the XOR operation may be used to generate the share encoded data. The secret segments used in the XOR operation may be based on the vertices incident to the face of a tetrahedron corresponding to the third secret share. The XOR operation may be a bitwise XOR operation including a first bitwise XOR operation of the third secret segment with the fourth secret segment and a second bitwise XOR operation of the result of the first bitwise XOR operation and the first secret segment.

At block 560, a fourth secret share may be generated by application of an XOR operation to the fourth, first, and second secret segments. The fourth secret share may be formed of a header and share encoded data and the XOR operation may be used to generate the share encoded data. The secret segments used in the XOR operation may be based on the vertices incident to the face of a tetrahedron corresponding to the fourth secret share. The XOR operation may be a bitwise XOR operation including a first bitwise XOR operation of the fourth secret segment with the first secret segment and a second bitwise XOR operation of the result of the first bitwise XOR operation and the second secret segment.

At block 570, a share identifier may be assigned to the first, second, third, or fourth secret shares to indicate an order of generation of the first, second, third, and fourth secret shares. The share identifier may indicate the given face of the tetrahedron represented by the secret share. The share identifier may form part of the header of the secret share. The share header is described in more detail with respect to FIGS. 10a and 10b.

At block 575, a header of the first, second, third, and fourth secret shares may be written, respectively indicating the share identifier and the amount of the sufficient information added to the secret. The amount of sufficient information written to the header may indicate the number of zeroes added to the secret at block 515. The share identifier may be the identifier assigned at block 570. The share header is described in more detail with respect to FIGS. 10a and 10b.

At block 580, the first, second, third, or fourth secret shares may be transmitted to respective recipients. In some examples, the secret shares may be transmitted to different recipients through different transmission media.

Although FIG. 5 discloses a particular number of operations related to method 500, method 500 may be executed with greater or fewer operations than those depicted in FIG. 5. In addition, although FIG. 5 discloses a certain order of operations to be taken with respect to method 500, the operations comprising method 500 may be completed in any suitable order.

FIG. 6 illustrates a bitwise XOR calculation to decode secret segments from secret shares, according to examples of the present disclosure. The tetrahedron model described with respect to FIG. 1 may be used to decode a secret from secret shares. Specifically, as described in further detail with respect to FIGS. 6-8, a secret segment is reconstructed from the three shares represented by the faces incident to the vertex of the secret.

The relationship between a given secret segment with three secret shares is indicated in table 600. Each row of table 600 indicates the various data elements that are involved in computing a secret segment. A given vertex in tetrahedron 100 (shown in FIG. 1) has three faces incident to the given vertex. The three secret shares may be involved in the XOR operation used to generate the secret segment and “circle+” indicates bitwise XOR operation. In particular, secret segment 1 is calculated based on secret share 1, secret share 3 and secret share 4 (e.g., secret share 1 XOR secret share 3 XOR secret share 4); secret segment 2 is calculated based on secret share 1, secret share 2 and secret share 4 (e.g., secret share 1 XOR secret share 2 XOR secret share 4); secret segment 3 is calculated based on secret share 1, secret share 2 and secret share 3 (e.g., secret share 1 XOR secret share 2 XOR secret share 3); and secret segment 4 is calculated based on secret share 2, secret share 3 and secret share 4 (e.g., secret share 2 XOR secret share 3 XOR secret share 4).

A secret may then be recreated from the four secret segments. Secret segment 1, secret segment 2, secret segment 3, and secret segment 4 may be combined to recreate the complete secret. For example, secret segment 1 may be “AB,” secret segment 2 may be “CD,” secret segment 3 may be “EF,” and secret segment 4 may be “GH.” The secret may be created by combining, or rearranging according to a predetermined order, secret segment 1, secret segment 2, secret segment 3, and secret segment 4 to decode the complete secret as “ABCEDFGH.”

FIG. 7 illustrates a system 700 for decoding four secret shares to recreate a secret, according to examples of the present disclosure. Four players 750a-750d may provide four encoded secret shares to secret sharing system 720. A given secret share may be of size n/4-bytes, where “n” is the number of bytes of the secret. For example, the secret may have a size of eight bytes and a given secret share may have a size of two bytes, without taking into account any header.

Secret sharing system 720 may include secret share decoding circuit 760 and data aggregating circuit 770. Secret sharing system 720 may be a trust platform implemented in any suitable combination of analog and digital circuitry, such as a suitable microprocessor, microcontroller, control board, or other computing device having input and output interfaces for communicating with other devices, as well as memory or other storage for program logic/instructions that secret sharing system 720 executes to send and receive signals and process data. Secret share decoding circuit 760 may decode the four secret shares in to four secret segments as described with respect to FIGS. 6 and 8-9. For example, the four secret shares may be decoded as secret segment 1: “AB,” secret segment 2: “CD,” secret segment 3: “EF,” and secret segment 4: “GH.” Data aggregating circuit 770 may combine the four secrets to recreate the secret as described with respect to FIGS. 6 and 8-9. For example, data aggregating circuit 770 may combine secret segment 1, secret segment 2, secret segment 3, and secret segment 4 to recreate the secret “ABCDEFGH.” Secret sharing system 720 may distribute the complete secret to secret recipient 710. Secret recipient 710 may be any other system which may use the secret.

FIG. 8 illustrates a method performed for decoding secret shares to recreate the secret, according to examples of the present disclosure. Method 800