Enhanced randomness for digital systems

1. A method of operating a computing device connected to a network for cryptographic communication over the network with a recipient device, the method comprising:

storing a secret S in a non-transitory storage medium, wherein the secret S is shared with the recipient device;

obtaining a stream of N-bit input data words;

obtaining a value k between 0 and M−1, inclusively, where M>1, wherein the value k is obtained based at least in part on the secret S;

processing each of the N-bit input data words at least based on the k th of M permutation elements to produce a corresponding N-bit output data word by (a) converting each of the N-bit input data words into a corresponding sparse 2 N -element input array, (b) processing the sparse 2 N -element input array with said k th of M permutation elements to produce a sparse 2 N -element output array and (c) converting the sparse 2 N -element output array into the corresponding N-bit output data word; and

sending a stream of the N-bit output data words to the recipient device over the network.

2. The digital processing method defined in claim 1 , wherein the value of k is randomized.

3. The digital processing method defined in claim 1 , wherein obtaining the value of k comprises processing an output of a pseudo-random number generator.

4. The digital processing method defined in claim 1 , further comprising obtaining the value of k from the order in which the N-bit input data words appear in the stream of N-bit input data words.

5. The method defined in claim 1 , wherein the value k is produced by a pseudo-random number generator whose seed is the secret S or is a hash of the secret S.

6. The method defined in claim 1 , wherein the value k is produced by converting an output of a pseudo-random number generator having a value in a range greater than between 0 and M−1 to the value k between 0 and M−1.

7. The method defined in claim 1 , wherein each of the M permutation elements comprises a switch fabric configured to carry out a 2 N -by-2 N blocking switch operation.

8. The method defined in claim 1 , wherein each of the permutation elements carries out an operation that is characterizable as a respective 2 N -by-2 N permutation matrix, and wherein the method further comprises initializing the permutation elements.

9. The method defined in claim 8 , wherein initializing the permutation elements comprises selecting, for each of the permutation elements, a different 2 N -by-2 N permutation matrix.

10. The method defined in claim 9 , wherein the secret S is used to randomize the 2 N -by-2 N permutation matrices for the different permutation elements.

11. The method defined in claim 1 , wherein the method comprises sharing the secret S with the recipient device prior to the processing step.

12. The method defined in claim 1 , wherein a set of permutation elements is usable by the recipient device to decode the N-bit output data words, the set of permutation elements and corresponding ones of the M permutation elements being characterizable as a permutation matrix and its transpose, respectively.

13. The method defined in claim 1 , further comprising receiving the stream of the N-bit input data words from an identified sender that used a set of permutation elements to encode the N-bit input data words, the set of permutation elements of the sender device and corresponding ones of the M permutation elements being characterizable as a permutation matrix and its transpose, respectively.

14. The method defined in claim 1 , further comprising changing the value of k such that successive N-bit input data words are processed with different ones of the permutation elements to produce the subsequent corresponding N-bit output data words.

15. The method defined in claim 1 , further comprising changing the value of k every Q input data words such that each set of Q N-bit input data words is processed with a first one of the M permutation elements to produce the corresponding N-bit output data words and then a subsequent set of Q N-bit input data words arrays is processed with a second one of the M permutation elements different from the first one of the permutation elements to produce the corresponding N-bit output data words, wherein Q>1.

16. The method defined in claim 1 , further comprising changing the value of k for each input data word such that each corresponding 2 N -element input array is processed with a different one of the permutation elements than the one before.

17. The method defined in claim 1 , further comprising changing the value of k for each input data word such that each 2 N -element output array is obtained from a different one of the permutation elements than the one before.

18. The method defined in claim 1 , further comprising periodically changing the secret S.

19. The method defined in claim 1 , wherein M is at least as large as 64.

20. The method defined in claim 1 , wherein the value k is produced by a first pseudo-random number generator, the method further comprising using a second pseudo-random number generator to produce the N-bit input data words.

21. A digital communications system, comprising:

a sender device connected to a network and configured for:

storing a secret S in a memory of the sender device;

obtaining N-bit first data words;

obtaining a value k between 0 and M−1, inclusively, where M>1, wherein the value k is obtained based at least in part on the secret S;

processing each of the N-bit first data words at least based on the kth of M first permutation elements to produce corresponding N-bit second data words by (a) converting each of the N-bit first data words into a corresponding sparse 2 N -element input array, (b) processing the sparse 2 N -element input array with said kth of M permutation elements to produce a sparse 2 N -element output array and (c) converting the sparse 2 N -element output array into the corresponding N-bit second data word; and

releasing the N-bit second data words on the network towards a recipient device connected to the network; and

the recipient device configured for:

receiving the N-bit second data words;

obtaining a value j between 0 and M−1, inclusively wherein the secret S was shared by the sender device and wherein the value j is obtained based at least in part on the secret S;

processing each of the N-bit second data words at least based on the j th of M second permutation elements to produce corresponding N-bit third data words by (a) converting each of the N-bit second data words into a corresponding sparse 2 N -element second input array, (b) processing the sparse 2 N -element second input array with said kth of M permutation elements to produce a sparse 2 N -element second output array and (c) converting the sparse 2 N -element second output array into the corresponding N-bit third data word,

the values of j and k being synchronized so that k and j are the same when a particular N-bit second data word is processed by the k th permutation element of the sender device and the j th permutation element of the recipient device, the k th and j th permutation elements being characterizable as permutation matrices that are transposes of one another; and

outputting the N-bit third data words on the network or storing the N-bit third data words in a memory of the recipient device.

22. A system for cryptographic communication over a network with a recipient device, comprising:

a memory storing instructions;

a network I/O for connection to the network; and

a processor accessing the instructions and, based on the instructions, being configured to:

store a secret S in the memory, wherein the secret S is shared with the recipient device;

obtain a stream of N-bit input data words,

obtain a value k between 0 and M−1, inclusively, where M>1, wherein the value k is obtained based at least in part on the secret S;

process each of the N-bit input data words at least based on the kth of M permutation elements to produce a corresponding N-bit output data word by (a) converting each of the N-bit input data words into a corresponding sparse 2 N -element input array, (b) processing the sparse 2 N -element input array with said kth of M permutation elements to produce a sparse 2 N -element output array and (c) converting the sparse 2 N -element output array into the corresponding N-bit output data word; and

send a stream of the N-bit output data words to the recipient device via the network I/O.

23. A computer-readable medium comprising computer-readable instructions which, when executed by a processor, cause the processor to carry out the digital processing method defined in claim 1 .

24. The method defined in claim 1 , wherein each of the permutation elements carries out an operation that is characterizable as a respective permutation matrix with 2 N rows and 2 N columns, and wherein processing each N-bit input data word at least based on the k th of M permutation elements to produce a corresponding N-bit output data word comprises:

obtaining a row index of the k th permutation matrix from each of the N-bit input data words;

obtaining the column index of the non-zero element in the row; and

obtaining the corresponding N-bit output data word from the column index.

25. The system defined in claim 22 , wherein to obtain the value of k, the processor is configured to process an output of a pseudo-random number generator.

26. The system defined in claim 22 , wherein the value of k is obtained from the order in which the N-bit input data words appear in the stream of N-bit input data words.

27. The system defined in claim 22 , wherein each of the M permutation elements comprises a switch fabric configured to carry out a 2 N -by-2 N blocking switch operation.

28. The system defined in claim 22 , wherein each of the permutation elements carries out an operation that is characterizable as a respective 2 N -by-2 N permutation matrix, and wherein the processor is further configured to initialize the permutation elements.

29. The system defined in claim 28 , wherein to initialize the permutation elements, the processor is configured to select, for each of the permutation elements, a different 2 N -by-2 N permutation matrix, wherein the secret S is used to randomize the 2 N -by-2 N permutation matrices for the different permutation elements.

30. The system defined in claim 22 , wherein the processor is further configured to change the value of k every Q input data words such that each set of Q N-bit input data words is processed with a first one of the M permutation elements to produce the corresponding N-bit output data words and then a subsequent set of Q N-bit input data words arrays is processed with a second one of the M permutation elements different from the first one of the permutation elements to produce the corresponding N-bit output data words, wherein Q>1.

31. The system defined in claim 22 , wherein the processor is further configured to change the value of k for each input data word such that each corresponding 2 N -element input array is processed with a different one of the permutation elements than the one before.