| CPC H04L 9/3247 (2013.01) [H04L 9/0825 (2013.01); H04L 9/0861 (2013.01); H04L 9/30 (2013.01); H04L 9/3213 (2013.01); H04L 9/3236 (2013.01)] | 17 Claims |

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1. A method programmed in a non-transitory memory of a device of generating a digital signature for data, comprising:
generating, with a processor a hash of the data;
generating the digital signature, with the processor, based at least in part on the hash, random data comprising a first set of non-singular matrices, and a private key comprising a first set of singular matrices and a second set of non-singular matrices, wherein the digital signature corresponds to a set of matrices and to a relation which corresponds to a Diophantine second order equation; and
communicating from the device, over a network, the digital signature and the data to a remote device.
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