Modulation-agnostic transformations using unitary braid divisional multiplexing (UBDM)
A method for implementing a fast UBDM transform includes receiving a first, input vector via a processor, and partitioning the first vector to produce a magnitude vector and a sign vector. A second vector, including a modified magnitude vector and a modified sign vector, is generated by: applying a permutation to the magnitude vector to produce the modified magnitude vector, converting the sign vector, based on an algorithm, into an intermediate sign vector, and applying nonlinear layers to the intermediate sign vector. Each nonlinear layer includes a permutation, an S-box transformation, a diffusive linear operation and/or an Xor operation. Multiple linear layers are applied to the second vector to produce a third vector, the third vector being a transformed version of the first vector. A first signal representing the third vector is sent to at least one transmitter for transmission of a second signal representing the transformed data vector.
1. A method, comprising:
receiving, via a processor, a first vector;
partitioning the first vector, via the processor, to produce a magnitude vector and a sign vector;
generating a second vector, via the processor, including a modified magnitude vector and a modified sign vector, by:
applying a permutation to the magnitude vector to produce the modified magnitude vector,
converting the sign vector, based on an algorithm, into an intermediate sign vector, and
applying a plurality of nonlinear layers to the intermediate sign vector, each nonlinear layer from the plurality of nonlinear layers including at least one of a permutation, an S-box transformation, a diffusive linear operation, or an Xor operation, to produce the modified sign vector;
applying, via the processor, a plurality of linear layers to the second vector to produce a third vector, the third vector being a transformed version of the first vector; and
sending a first signal representing the third vector to at least one transmitter for transmission of a second signal representing the transformed data vector from the at least one transmitter to at least one receiver.
2. The method of claim 1 , wherein the converting the sign vector is based on an initialization vector.
3. The method of claim 1 , further comprising selecting the algorithm based on an encryption mode of operation of the processor.
4. The method of claim 1 , wherein the algorithm includes an Xor operation, and an encryption mode of operation of the processor is a cipher block chaining (CBC) mode.
5. The method of claim 1 , wherein the algorithm includes an Xor operation, and an encryption mode of operation of the processor is an electronic code book (ECB) mode.
6. The method of claim 1 , wherein a number of nonlinear layers in the plurality of nonlinear layers equals a number of linear layers in the plurality of linear layers.
7. The method of claim 1 , wherein a number of nonlinear layers in the plurality of nonlinear layers is different from a number of linear layers in the plurality of linear layers.
8. The method of claim 1 , wherein at least one of a number of linear layers (“L”) in the plurality of linear layers or a number of nonlinear layers (“Q”) in the plurality of nonlinear layers is equal to [log 2 (N)].
9. The method of claim 1 , wherein at least one of a number of nonlinear layers in the plurality of nonlinear layers or a number of linear layers in the plurality of linear layers is based on a performance constraint.
10. The method of claim 1 , wherein at least one of a number of nonlinear layers in the plurality of nonlinear layers or a number of linear layers in the plurality of linear layers is based on a security constraint.
11. The method of claim 1 , wherein the permutation applied to the magnitude vector does not reduce a total power of the first vector.
12. A method, comprising: receiving, via a processor, an input vector including a plurality of complex numbers; generating a transformed vector based on the input vector, via the processor, by: applying a permutation to a magnitude vector associated with the input vector, to produce a modified magnitude vector, applying an algorithm and a plurality of nonlinear layers to a sign vector associated with the input vector, to produce a modified sign vector, the modified magnitude vector and the modified sign vector defining an intermediate vector, each nonlinear layer from the plurality of nonlinear layers including at least one of: a permutation, an S-box transformation, a diffusive linear operation, or an XOR operation, and applying a plurality of linear layers to the intermediate vector to produce the transformed vector; and sending a first signal representing the transformed vector to at least one transmitter.
13. The method of claim 12 , further comprising selecting the algorithm based on an encryption mode of operation of the processor.
14. The method of claim 12 , wherein the algorithm includes an Xor operation, and an encryption mode of operation of the processor is one of a cipher block chaining (CBC) mode or an electronic code book (ECB) mode.
15. The method of claim 12 , wherein a number of nonlinear layers in the plurality of nonlinear layers equals a number of linear layers in the plurality of linear layers.
16. The method of claim 12 , wherein a number of nonlinear layers in the plurality of nonlinear layers is different from a number of linear layers in the plurality of linear layers.
17. The method of claim 12 , wherein at least one of a number of linear layers (“L”) in the plurality of linear layers or a number of nonlinear layers (“Q”) in the plurality of nonlinear layers is equal to [log 2 (N)].
18. The method of claim 12 , wherein at least one of a number of nonlinear layers in the plurality of nonlinear layers or a number of linear layers in the plurality of linear layers is based on at least one of a performance constraint or a security constraint.
19. The method of claim 12 , wherein the permutation applied to the magnitude vector does not reduce a total power of the first vector.