Block ciphering system, using permutations to hide the core ciphering function of each encryption round

A method of providing a digital signal processing function ƒ to an executing device having at least one processor in an obfuscated form; the function ƒ including a function cascade including a plurality of signal processing functions ƒi, 1≦i≦N, for processing a digital signal input x to yield a digital signal output, the method including:nperforming the following steps by at least one processor of the executing device:nselecting a set of 2N invertible permutations pi, 1≦i≦2N;calculating a set of N functions gi, where gi is functionally equivalent to p2i−1∘ƒi∘p2i−1, for 1≦i≦N;calculating a set of N−1 functions hi, where hi is functionally equivalent to p2i−1−1∘p2i−2, for 2≦i≦N;equipping the executing device with an execution device function cascade that includes yN∘hN∘yN−1∘hN−1∘ . . . ∘y1, where y1, . . . , yN are function parameters,providing the functions g1, . . . , gN to the executing device; andin the executing device, applying the execution device function cascade to the functions g1, . . . , gN, wherein the execution of the gi and hi functions by the executing device in an interleaved manner enables the functionality of the execution device function cascade to be achieved without function ƒ being directly recognizable.

A computer program product stored on a non-transitory computer readable storage medium that is operative to cause a processor in an execution device to execute a digital signal processing function ƒ including a function cascade including a plurality of signal processing functions fi, where 1≦i≦N, for processing a digital signal input x to yield a digital signal output, by:nperforming the following steps by at least one processor of the execution device:nloading an execution device function cascade that includes yN∘hN∘yN−1∘hN−1∘ . . . ∘y1, where y1, . . . , yN are function parameters,loading a set of functions g1, . . . , gN;applying the execution device function cascade to the set of functions g1, . . . , gN;where:ngi is functionally equivalent to p2i−1∘ƒi∘p2i−1, for 1≦i≦N;hi is functionally equivalent to p2i−1−1∘p2i−2, for 2≦i≦N; andpi is an invertible permutation, for 1≦i≦2N.

A system for providing a digital signal processing function ƒ to an executing device in an obfuscated form; the system including a server (610) and an executing device (620); the function ƒ including a function cascade including a plurality of signal processing functions ƒi, 1≦i≦N, for processing a digital signal input x to yield a digital signal output;nthe server including a processor (612) for performing the following steps, under control of a program:nselecting a set of 2N invertible permutations pi, 1≦i≦2N;calculating a set of N functions gi, where gi is functionally equivalent to p2i−1∘ƒi∘p2i−1, for 1≦i≦N; andcalculating a set of N−1 functions hi, where hi is functionally equivalent to p2i−1−1∘p2i−2, for 2≦i≦N; andmeans (614) for equipping the executing device with an execution device function cascade that includes yN∘hN∘yN−1∘hN−1∘ . . . ∘y1, where y1, . . . , yN are function parameters, andmeans (616) for providing the functions g1, . . . , gN to the executing device; andthe executing device (620) including:nmeans (626) for obtaining the functions g1, . . . , gN from the server; anda processor (622) for, under control of a program, loading the execution device function cascade and applying the loaded execution device function cascade to the functions g1, . . . , gN, wherein the execution of the gi and hi functions by the executing device in an interleaved manner enables the functionality of the execution device function cascade to be achieved without function ƒ being directly recognizable.

A method of providing a digital signal processing function ƒ to a plurality of executing devices, each identified by a unique index j, in an obfuscated, anonymous form; the function ƒ including a function cascade including a plurality of signal processing functions ƒi, where 1≦i≦N, for processing a digital signal input x to yield a digital signal output the method including:nperforming the following steps by at least one processor:nselecting a set of 2N invertible permutations pi, where 1≦i≦2N;calculating a set of N functions gi, where gi is functionally equivalent to p2i−1∘ƒi∘p2i−1, 1≦i≦N;selecting for each device j a corresponding set and/or sequence of 2N invertible permutations pj,i, that is unique for the device and/or a user of the device;calculating for each executing device j a corresponding set of N−1 functions hj,i, where hj,i is functionally equivalent to pj,2i−1−1∘pj,2i−2 for 2≦i≦N;equipping each executing device j with a respective execution device function cascade EDj(y1, . . . , yN) that includes yN∘hj,N∘yN−1∘hj,N−1∘ . . . ∘y1;equipping each executing device j with a respective loader function loaderj(x1, . . . , xN)=(lj,1∘x1∘rj,1, . . . , lj,N∘xN∘rj,N), where lj,i, is functionally equivalent to pj,2i−1∘p2i and rj,i is functionally equivalent to p2i−1−1∘pj,2i−1;providing to the executing device the functions g1, . . . , gN; andin the executing device, executing EDj(loaderj(g1, . . . , gN)).

A computer program product stored on a non-transitory computer readable storage medium that is operative to cause a processor in an execution device j to execute a digital signal processing function ƒ including a function cascade including a plurality of signal processing functions ƒi, where 1≦i≦N, for processing a digital signal input x to yield a digital signal output, the method including:nperforming the following steps by at least one processor of the execution device:nloading an execution device function cascade that is unique for the execution device and that includes yN∘hj,N∘yN−1∘hj,N−1∘ . . . ∘y1, where y1, . . . , yN are function parameters,loading a loader functionloaderj(x1, . . . , xN)≡(lj,1∘x1∘rj,l, . . . , lj,N∘xN∘rj,N), loading a set of functionsg1, . . . , gN;applying the loader function to the set of functions g1, . . . , gN yielding a set of functions gj,1, . . . , gj,N and applying the execution device function cascade to the set of functions gj,1, . . . , gj,N, where:gi is functionally equivalent to p2i−1∘ƒi∘p2i−1, for 1≦i≦N;pi is an invertible permutation, for 1≦i≦N;hj,i is functionally equivalent to pj,2i−1−1∘pj,2i−2 for 2≦i≦N;lj,i is functionally equivalent to pj,2i−1∘p2i;rj,i is functionally equivalent to p2i−1−1∘pj,2i−1; andpj,i are invertible permutations, for 1≦i≦2N, being unique for the device and/or a user of the device.

A system for providing a digital signal processing function ƒ to a plurality of executing devices, in an obfuscated, anonymous form; the system including a server and a plurality of executing devices, each identified by a unique index j; the function ƒ including a function cascade including a plurality of signal processing functions ƒi, where 1≦i≦N, for processing a digital signal input x to yield a digital signal output;nthe server including a processor for performing the following steps, under control of a program:nselecting a set of 2N invertible permutations pi, where 1≦i≦2N;calculating a set of N functions gi, where gi is functionally equivalent to p2i−1∘ƒi∘p2i−1, for 1≦i≦N;selecting for each device j a corresponding set and/or sequence of 2N invertible permutations pj,i, that is unique for the device and/or a user of the device;calculating for each executing device j a corresponding set of N−1 functions hj,i, where hj,i is functionally equivalent to pj,2i−1−1∘pj,2i−2 for 2≦i≦N;equipping each executing device j with a respective execution device function cascade EDj(y1, . . . , yN) that includes yN∘hj,N∘yN−1∘j,hN−1∘ . . . ∘y1;equipping each executing device j with a respective loader function loaderj(x1, . . . , xN)=(lj,1∘x1∘rj,1, . . . , lj,N∘xN∘rj,N), where lj,i is functionally equivalent to pj,2i−1∘p2i and rj,i is functionally equivalent to p2i−1−1∘pj,2i−1; andproviding to the executing device the functions g1, . . . , gN; andeach executing device j,means for obtaining the functions g1, . . . , gN from the server; anda processor for, under control of a program:nloading an execution device function cascade that is unique for the execution device and that includes yN∘j,hN∘yN−1∘hj,N−1∘ . . . ∘y1, where y1, . . . , yN are function parameters,loading a loader functionloaderj(x1, . . . , xN)≡(lj,1∘x1∘rj,1, . . . , lj,N∘xN∘rj,N)napplying the loader function to the set of functions g1, . . . , gN yielding a set of functions gj,1, . . . , gj,N; andapplying the execution device function cascade to the set of functions gj,1, . . . , gj,N.