Secret-sharing encoding and decoding using exclusive or operations
A system and method for a secret-sharing encoding and decoding using exclusive OR (XOR) operations. A first apparatus includes a data splitting circuit to receive a secret and generate first, second, third, and fourth secret segments based on the secret and a secret share encoding circuit to generate first, second, third, and fourth secret shares by application of XOR operations to the first, second, third, and fourth secret segments. A second apparatus includes a secret share decoding circuit to receive first, second, third, and fourth secret shares and generate first, second, third, and fourth secret segments by application of an XOR operation to share encoded data of the first, second, third, and fourth secret shares, and a data aggregating circuit to: receive the first, second, third, and fourth secret segments; and recreate a secret by combining the first, second, third, and fourth secret segments.
1 . An apparatus, comprising:
a data splitting circuit to:
receive a secret; and
generate a first secret segment, a second secret segment, a third secret segment, and a fourth secret segment based on the secret; and
a secret share encoding circuit to:
generate a first secret share by application of an exclusive OR (XOR) operation to the first, second, and third secret segments;
generate a second secret share by application of the XOR operation to the second, third, and fourth secret segments;
generate a third secret share by application of the XOR operation to the third, fourth, and first secret segments; and
generate a fourth secret share by application of the XOR operation to the fourth, first, and second secret segments; and
the data splitting circuit further to:
transmit the first, second, third, and fourth secret shares to a second apparatus for a secret sharing.
2 . The apparatus of claim 1 , wherein the data splitting circuit is to:
add sufficient information to the secret such that the secret is divisible by four; and
write to a header of at least one of the first, second, third, and fourth secret shares indicating the sufficient information added to the secret.
3 . The apparatus of claim 1 , wherein the secret share encoding circuit is to assign a share identifier to the first, second, third, and fourth secret shares to indicate an order of generation of the first, second, third, and fourth secret shares; and
the data splitting circuit is to write to a header of the first, second, third, and fourth secret shares indicating share identifier.
4 . The apparatus of claim 1 , wherein generation of the first, second, third, and fourth secret segments comprises generation of the first, second, third, and fourth secret segments in a predetermined order.
5 . The apparatus of claim 1 , wherein generation of the first secret share includes:
application of a first bitwise XOR of the first secret segment with the second secret segment; and
application of a second bitwise XOR of a result of the first bitwise XOR with the third secret segment.
6 . An apparatus, comprising:
a secret share decoding circuit to:
receive a first secret share, a second secret share, a third secret share, and a fourth secret share;
generate a first secret segment by application of an exclusive OR (XOR) operation to share encoded data of the first, third, and fourth secret shares;
generate a second secret segment by application of the XOR operation to share encoded data of the first, second, and fourth secret shares;
generate a third secret segment by application of the XOR operation to first, share encoded data of the first, second and third secret shares; and
generate a fourth secret segment by application of the XOR operation to share encoded data of the second, third, and fourth secret shares; and
a data aggregating circuit to:
receive the first, second, third, and fourth secret segments; and
recreate a secret by combining the first, second, third, and fourth secret segments.
7 . The apparatus of claim 6 , wherein the data aggregating circuit is to truncate the secret to remove sufficient information added to the secret based on a secret length field in a header of at least one of the first, second, third, or fourth secret share.
8 . The apparatus of claim 6 , wherein the data aggregating circuit is to recreate the secret by combining the first, second, third, and fourth secret segments based on a share identifier.
9 . The apparatus of claim 6 , wherein the first, second, third, and fourth secret share are received from at least two different transmission media sources.
10 . The apparatus of claim 6 , wherein generation of the first secret segment includes:
application of a first bitwise XOR of share encoded data of the first secret share with share encoded data of the third secret share; and
application of a second bitwise XOR of a result of a first bitwise XOR with share encoded data of the fourth secret share.
11 . The apparatus of claim 6 , comprising:
transmitting the recreated secret.
12 . A method comprising:
receiving a secret;
generating a first secret segment, a second secret segment, a third secret segment, and a fourth secret segment based on the secret;
generating a first secret share by application of an exclusive OR (XOR) operation to the first, second, and third secret segments;
generating a second secret share by application of the XOR operation to the second, third, and fourth secret segments;
generating a third secret share by application of the XOR operation to the third, fourth, and first secret segments;
generating a fourth secret share by application of the XOR operation to the fourth, first, and second secret segments; and
transmitting the first, second, third, and fourth secret shares for a secret sharing.
13 . The method of claim 12 , comprising:
adding sufficient information to the secret such that the secret is divisible by four; and
writing to a header of at least one of the first, second, third, and fourth secret shares indicating the sufficient information added to the secret.
14 . The method of claim 12 , comprising:
assigning a share identifier to the first, second, third, and fourth secret shares to indicate an order of generation of the first, second, third, and fourth secret shares; and
writing to a header of the first, second, third, and fourth secret shares indicating the share identifier.
15 . The method of claim 12 , wherein generation of the first, second, third, and fourth secret segments comprises generation of the first, second, third, and fourth secret segments in a predetermined order.
16 . The method of claim 12 , wherein generation of the first secret share includes:
application of a first bitwise XOR of the first secret segment with the second secret segment; and
application of a second bitwise XOR of a result of the first bitwise XOR with the third secret segment.
17 . A method, comprising:
receiving a first secret share, a second secret share, a third secret share, and a fourth secret share;
generating a first secret segment by application of an exclusive OR (XOR) operation to share encoded data from the first, third, and fourth secret shares;
generating a second secret segment by application of the XOR operation to share encoded data from the first, second, and fourth secret shares;
generating a third secret segment by application of the XOR operation to share encoded data from the first, second, and third secret shares;
generating a fourth secret segment by application of the XOR operation to share encoded data from the second, third, and fourth secret shares; and
recreating a secret by combining the first, second, third, and fourth secret segments.
18 . The method of claim 17 , comprising:
truncating the secret to remove sufficient information added to the secret based on a secret length field in a header of at least one of the first, second, third, or fourth secret share.
19 . The method of claim 17 , comprising:
recreating the secret by combining the first, second, third, and fourth secret segments based on a share identifier.
20 . The method of claim 17 , comprising receiving the first, second, third, and fourth secret share from at least two different transmission media sources.
21 . The method of claim 17 , wherein generation of the first secret segment includes:
application of a first bitwise XOR of share encoded data of the first secret share with share encoded data of the third secret share; and
application of a second bitwise XOR of the result of a first bitwise XOR with share encoded data of the fourth secret share.