Abstract: A method for reducing an amount of time needed for a single iteration of arithmetic encoding and arithmetic decoding is provided. Rescaling and range are calculated in parallel, range being a High parameter bound of a symbol-interval—a Low parameter bound of the symbol-interval+1. A new iHigh (iH) parameter and a new iLow (iL) parameter or a given/decoded symbol is found according to a cumulative frequency for an ith symbol. iH parameter and iL parameter rescaling is performed by shifting an amount of most significant bits of iH, iL in accordance with values of iH and iL. iRange is shifted to the left in accordance with a number of digits needed to represent iRange and a total number of bits reserved for iRange. A shifted iRange is divided by CF[N] and saved to Step_tmp while awaiting a result of H,L rescaling.

Abstract: A method for protecting encoded data from algebraic manipulation includes receiving a data word s?Kd to be protected, randomly selecting two integers a ?{0, . . . , q?1} and b ?{0, . . . , ?q?1}, finding a point (?, ?) on a Hermitian curve over a field Fq that corresponds to the randomly selected integers (a, b) from a mapping (a, b)(?, ?)=(ua, ua?q+1z+vb), where u a := { 0 if ? ? a = 0 , ? 1 a - 1 otherwise , ? V b := { 0 if ? ? b = 0 , ? 2 b - 1 otherwise , and z is an element of the field Fq of unit trace, and where ?1 is a fixed primitive element of the field Fq and ?2 is a primitive element of a field F?q?Fq, and calculating a sum fs(?, ?)=?id+1?jd+1+?k=1d?ik?kjk for a set of d+1 integers pairs I ={(ik,jk)}k=1d+1, where the encoded word is a triple (s, (?, ?),fs(?, ?)).

Abstract: A method for reducing an amount of time needed for a single iteration of arithmetic encoding and arithmetic decoding is provided. Resealing and range are calculated in parallel, range being a High parameter bound of a symbol-interval?a Low parameter bound of the symbol-interval+1. A new iHigh (iH) parameter and a new iLow (iL) parameter or a given/decoded symbol is found according to a cumulative frequency for an ith symbol. iH parameter and iL parameter resealing is performed by shifting an amount of most significant bits of iH, iL in accordance with values of iH and iL. iRange is shifted to the left in accordance with a number of digits needed to represent iRange and a total number of bits reserved for iRange. A shifted iRange is divided by CF[N] and saved to Step_tmp while awaiting a result of H,L resealing.

Abstract: A method for protecting encoded data from algebraic manipulation includes receiving a data word s?Kd to be protected, randomly selecting two integers a?{0, . . . , q?1} and b?{0, . . . , ?q?1}, finding a point (?, ?) on a Hermitian curve over a field Fq that corresponds to the randomly selected integers (a, b) from a mapping (a, b)(?, ?)=(ua, ua?q+1z+vb), where u a := { 0 if ? ? a = 0 , ? 1 a - 1 otherwise , ? ? V b := { 0 if ? ? b = 0 , ? 2 b - 1 otherwise , and z is an element of the field Fq of unit trace, and where ?1 is a fixed primitive element of the field Fq and ?2 is a primitive element of a field F?q?Fq, and calculating a sum fs(?, ?)=?id+1?jd+1+?k=1d?ik?kjk or a set of d+1 integers pairs I={(ik,jk)}k=1d+1, where the encoded word is a triple (s, (?, ?),fs(?, ?)).