Abstract: Various embodiments relate to a method of encoding data and a related device and non-transitory machine readable storage medium, including: determining a factor set, S, to be used for encoding the value, h, wherein the factor set includes a plurality of subsets that are associated with respective digit positions in the value, h; selecting a plurality of factors from the factor set, S; and computing a product of the plurality of factors to produce an encoded value. Various other embodiments relate to a method of encoding data and a related device and non-transitory machine readable storage medium, including: determining a factor set, S, and weight, w, to be used for encoding the value, h; selecting a set, T, of w factors from the factor set, S, to represent the value, h; and computing a product of the set, T, to produce an encoded value.

Abstract: Various embodiments relate to a method of encoding data and a related device and non-transitory machine readable storage medium, including: determining a plurality of factors of a value, b, to be exponentiated; retrieving, from a lookup table, a plurality of lookup table entries associated with the plurality of factors; calculating a product of the plurality of lookup table entries; and calculating a residue of the product using a cryptographic key modulus, N, to produce an exponentiated value, s.

Abstract: Various embodiments relate to a method of encoding data and related device and non-transitory machine readable storage medium, the method including: determining a set of digits, X, representative of a value to be encoded; determining a set of factor values, S, to be used in generating an encoded value, wherein the set of factor values, S, is a set of input value factors for a modular exponentiated digital signature process; for a given digit, x, of the set of digits, X, determining at least one factor value, s, of the set of factor values, S, corresponding to the given digit, x; and including the at least one factor value, s, in an encoded value.

Abstract: Various embodiments relate to a method, system, and non-transitory machine-readable medium encoded with instructions for execution by a processor for performing modular exponentiation, the non-transitory machine-readable medium including: instructions for iteratively calculating a modular exponentiation, bd mod n, including: instructions for squaring a working value, c; and instructions for conditionally multiplying the working value, c, by a base value, b, dependent on a bit of an exponent, d, including: instructions for unconditionally multiplying the working value, c, by a lookup table entry associated with the base value.

Abstract: Various embodiments relate to a method of generating tokens for use in modular exponentiation and a related device and non-transitory machine readable storage medium, including: generating a public token, ?, based on an identifier associated with another device; generating a private token, L, as a modular exponentiation of the public token, ?, using a private exponent, d, and modulus, N, from a cryptographic key; and communicating the private token, L, to the other device.

Abstract: Various embodiments relate to a method, system, and non-transitory machine-readable medium encoded with instructions for execution by a processor for performing modular exponentiation, the non-transitory machine-readable medium including: instructions for iteratively calculating a modular exponentiation, bd mod n, including: instructions for squaring a working value, c; and instructions for conditionally multiplying the working value, c, by a base value, b, dependent on a bit of an exponent, d, including: instructions for unconditionally multiplying the working value, c, by a lookup table entry associated with the base value.

Abstract: Various embodiments relate to a method of generating tokens for use in modular exponentiation and a related device and non-transitory machine readable storage medium, including: generating a public token, ?, based on an identifier associated with another device; generating a private token, L, as a modular exponentiation of the public token, ?, using a private exponent, d, and modulus, N, from a cryptographic key; and communicating the private token, L, to the other device.

Abstract: Various embodiments relate to a method of encoding data and a related device and non-transitory machine readable storage medium, including: determining a plurality of factors of a value, b, to be exponentiated; retrieving, from a lookup table, a plurality of lookup table entries associated with the plurality of factors; calculating a product of the plurality of lookup table entries; and calculating a residue of the product using a cryptographic key modulus, N, to produce an exponentiated value, s.

Abstract: Various embodiments relate to a method of encoding data and related device and non-transitory machine readable storage medium, the method including: determining a set of digits, X, representative of a value to be encoded; determining a set of factor values, S, to be used in generating an encoded value, wherein the set of factor values, S, is a set of input value factors for a modular exponentiated digital signature process; for a given digit, x, of the set of digits, X, determining at least one factor value, s, of the set of factor values, S, corresponding to the given digit, x; and including the at least one factor value, s, in an encoded value.

Abstract: Various embodiments relate to a method of encoding data and a related device and non-transitory machine readable storage medium, including: determining a factor set, S, to be used for encoding the value, h, wherein the factor set includes a plurality of subsets that are associated with respective digit positions in the value, h; selecting a plurality of factors from the factor set, S; and computing a product of the plurality of factors to produce an encoded value. Various other embodiments relate to a method of encoding data and a related device and non-transitory machine readable storage medium, including: determining a factor set, S, and weight, w, to be used for encoding the value, h; selecting a set, T, of w factors from the factor set, S, to represent the value, h; and computing a product of the set, T, to produce an encoded value.