Abstract: A method of obscuring the input and output of a modular exponentiation function, including: receiving modular exponentiation parameters including an exponent e having N bits and a modulus m; generating randomly a pre-multiplier; calculating a post-multiplier based upon the pre-multiplier, exponent e, and modulus m; multiplying an input to the modular exponentiation function by the pre-multiplier; performing the modular exponentiation function; and multiplying the output of the modular exponentiation function by the post-multiplier, wherein multiplying an input to the modular exponentiation function by the pre-multiplier, performing the modular exponentiation function, and multiplying the output of the modular exponentiation function by the post-multiplier are split variable operations.

Abstract: A method of implementing a keyed cryptographic operation using a plurality of basic blocks, includes: generating a balanced encoding function; applying the balanced encoding function to the output of a first basic block; and applying an inverse of the encoding function to the input of a second basic block, wherein the second basic block receives the encoded output of first basic block as an input.

Abstract: A method of obscuring software code including a plurality of basic blocks wherein the basic blocks have an associated identifier (ID), including: determining, by a processor, for a first basic block first predecessor basic blocks, wherein first predecessor basic blocks jump to the first basic block and the first basic block jumps to a next basic block based upon a next basic block ID; producing, by the processor, a mask value based upon the IDs of first predecessor basic blocks, wherein the mask value identifies common bits of the IDs of the first predecessor basic blocks; and inserting, by the processor, an instruction in the first basic block to determine a next basic block ID based upon the mask value and an ID of one of the first predecessor basic blocks.

Abstract: A method of performing a cryptographic operation using a cryptographic implementation in a cryptographic system, including: receiving, by the cryptographic system, an identifying string value; receiving, by the cryptographic system, an input message; performing, by the cryptographic system, a keyed cryptographic operation mapping the input message into an output message wherein the output message is the correct result when the identifying string value is one of a set of binding string values, wherein the set includes a plurality of binding string values.

Abstract: A method of obscuring the input and output of a modular exponentiation function, including: receiving modular exponentiation parameters including an exponent e having N bits and a modulus m; generating randomly a pre-multiplier; calculating a post-multiplier based upon the pre-multiplier, exponent e, and modulus m; multiplying an input to the modular exponentiation function by the pre-multiplier; performing the modular exponentiation function; and multiplying the output of the modular exponentiation function by the post-multiplier, wherein multiplying an input to the modular exponentiation function by the pre-multiplier, performing the modular exponentiation function, and multiplying the output of the modular exponentiation function by the post-multiplier are split variable operations.

Abstract: A method of obscuring the input and output of a modular exponentiation function, including: receiving modular exponentiation parameters including an exponent e having N bits and a modulus m; generating randomly a pre-multiplier; calculating a post-multiplier based upon the pre-multiplier, exponent e, and modulus m; multiplying an input to the modular exponentiation function by the pre-multiplier; performing the modular exponentiation function; and multiplying the output of the modular exponentiation function by the post-multiplier, wherein multiplying an input to the modular exponentiation function by the pre-multiplier, performing the modular exponentiation function, and multiplying the output of the modular exponentiation function by the post-multiplier are split variable operations.

Abstract: A method of obscuring software code implementing a modular exponentiation function, including: receiving modular exponentiation parameters including an exponent e having N bits; generating a bitwise exponent array and inverse bitwise exponent array; and generating modular exponentiation function operations using the bitwise exponent array, inverse bitwise exponent array, and N, wherein the generated modular exponentiation function operations are split variable operations.

Abstract: A method of obscuring software code including a data array and a plurality of operations, including: identifying, by a processor, a data array with an index to be obscured and an operation using the data array; permutating the identified data array using a permutating function; and replacing the identified operation using the permutated data array and equivalent encoded permutation function.

Abstract: A method for a keyed cryptographic operation by a cryptographic system mapping an input message to an output message, including: receiving input data for the keyed cryptographic operation; calculating a first mask value based upon the input data; and applying the first mask value to a first intermediate value of the keyed cryptographic operation.

Abstract: A method of obscuring software code implementing an elliptic curve cryptography (ECC) point multiplication function, including: receiving ECC parameters including a multiplier d having N bits; transforming multiplier d into an array d(i) with ?1, 0, and +1 values while maintaining the same value for d; and generating ECC point multiplication function operations using the transformed multiplier array d(i) and N, wherein the generated ECC point multiplication function operations are split variable operations.

Abstract: A method of performing a keyed cryptographic operation mapping an input message to an output message, wherein the cryptographic operation includes at least one round including a non-linear mapping function configured to map input data to output data, including: splitting the input data into n split input data, wherein the splitting of the input data varies based upon the value of the input message; inputting each split input data into the non-linear mapping function to obtain n split output data, wherein a combination the n split output data indicates an output data, wherein the output data results when the input data is input to the non-linear mapping function.

Abstract: A method of performing a keyed cryptographic operation mapping an input message to an output message, wherein the input message comprises m input data and the output message comprises m output data and wherein the cryptographic operation includes at least one round and the cryptographic operation specifies a substitution box for mapping input data into output data, including: transforming each of the m input data into n output data using n split substitution boxes, wherein the n split substitution boxes sum to the specified substitution box; and mixing and combining the m×n output data.

Abstract: A method of implementing a cryptographic operation using a substitution box, comprising: specifying a set of self-equivalent functions for the substitution box; determining the minimum diversification number of the substitution box over the set of self-equivalent functions; comparing the minimum diversification number to a threshold value; including and implementing a cryptographic operation with selected substitution box when the minimum diversification number is greater or equal to a threshold value.

Abstract: A non-transitory machine-readable storage medium encoded with instructions for execution by a keyed encryption operation by a cryptographic system mapping an input message having an encoded portion and a padding portion to an output message, including: instructions for receiving a padding value k; instructions for receiving the input message, wherein the padding portion has a size indicated by the padding value k; instructions for computing a first portion of the encryption operation to produce a first portion output; instructions for computing a compensation factor corresponding to the padding portion of the input message; and instructions for compensating the first portion output based upon the compensation factor.

Abstract: A method of performing a secure function on data inputs by a security module, including: receiving an encrypted data value by the security module; decrypting the encrypted data value using a white-box decryption block cipher and encoding the decrypted data value, wherein the data value is invisible to an attacker; performing a function on the encoded data value and producing an encoded result of the function, wherein the data value and the result are invisible to the attacker; decoding the encoded result of the programmed function and then encrypting the result using a white-box encryption block cipher, wherein the result is invisible to the attacker.

Abstract: A method of performing a keyed cryptographic operation mapping an input message to an output message, wherein the cryptographic operation includes at least one round including a non-linear mapping function configured to map input data to output data, including: splitting the input data into n split input data, wherein the splitting of the input data varies based upon the value of the input message; inputting each split input data into the non-linear mapping function to obtain n split output data, wherein a combination the n split output data indicates an output data, wherein the output data results when the input data is input to the non-linear mapping function.

Abstract: A method of gluing a cryptographic implementation of a cryptographic function to a surrounding program in a cryptographic system, including: receiving, by the cryptographic system, an input message; receiving a computed value from the surrounding program; performing, by the cryptographic system, a keyed cryptographic operation mapping the input message into an output message using the computed value from the surrounding program, wherein the output message is a correct output message when the computed value has a correct value; and outputting the output message.

Abstract: A method of performing a keyed cryptographic operation by a cryptographic system mapping an encoded input message to an output message, including: receiving an encoding selection parameter p; receiving the encoded input message, wherein the encoding on the input message corresponds to the encoding selection parameter p; decoding the input message using an inverse of a default input encoding; computing a first portion of the cryptographic operation on the decoded input message to produce a first portion output; and compensating the first portion output based upon the encoding selection parameter p.

Abstract: A device and method for performing a keyed cryptographic operation mapping an input message to an output message including a first and a second round, wherein the cryptographic operation includes a key scheduling method that produces round keys based upon the encryption key, including: instructions for receiving a first input by the first round; instructions for receiving a second input by the first round; instructions for outputting the second input as a third input to the second round; instructions for performing a first cryptographic operation on the second input using a first static round key to produce a first cryptographic output; and instructions for combining first input, the first cryptographic output, and a second encoded dynamic round key to produce a fourth input to the second round, wherein the second encoded dynamic round key is produced by inputting an encoded dynamic encryption key into the key scheduling method.

Abstract: A method of performing a keyed cryptographic operation mapping an input message to an output message, wherein the cryptographic operation includes at least one round including a non-linear mapping function configured to map input data to output data, including: splitting the input data into n split input data, wherein the splitting of the input data varies based upon the value of the input message; inputting each split input data into the non-linear mapping function to obtain n split output data, wherein a combination the n split output data indicates an output data, wherein the output data results when the input data is input to the non-linear mapping function.