Provided are a module division assistance device, a module division assistance method, and a module division assistance program for automatically extracting a divisible module by utilizing information relating to a function used by a module. A keyword obtaining unit of an information processing device collects data relating to a function used by a module into keyword use data organized by modules, and a data analysis unit uses the data and a calculation method for an indivisibility calculation item specified by a user and stored in an indivisibility calculation item list, thereby calculating an indivisibility, and stores the indivisibility into indivisibility data. Then, with respect to a module to be subjected to division determination, a module division determination unit compares the indivisibility relating to a function relevant to the indivisibility calculation item specified by the user with a threshold value stored in the indivisibility calculation item list, thereby determining whether the module can be divided or not.

A computer-implemented method for enabling elliptic curve arithmetic to be performed using blockchain transactions, wherein the method is performed by a script generator. A first script of a first blockchain transaction is generated, wherein the first script comprises a modular inversion script configured to obtain a target integer and a modulus value and output a modular inverse of the target integer. The target integer and the modulus value are co-prime. The modular inverse is generated by iteratively computing a first sequence of the extended Euclidean algorithm with the target integer and modulus value as inputs, and using the first sequence to compute a Bezout co-efficient of the target integer, wherein the Bezout co-efficient of the target integer is output as the modular inverse. The first script is outputted for inclusion in the first blockchain transaction.

A computer-implemented method for enabling elliptic curve arithmetic to be performed using blockchain transactions. A first script of a first blockchain transaction is generated, comprising a modular inversion script configured to obtain a target integer and a modulus value, and output a modular inverse of the target integer. The modular inverse is generated by generating a sequence of squaring values; for each set bit of a reduced modulus value expressed in binary, including the corresponding squaring value of the sequence of squaring values in a result; multiplying together the squaring values of the result to generate a resultant value; and computing a modulus of the resultant value with respect to the modulus value, wherein the modulus of the resultant value is output as the modular inverse, and outputting the first script for inclusion in the first blockchain transaction.

A computer-implemented method for enabling elliptic curve arithmetic to be performed using blockchain transactions. A first script comprising a modular inversion script is generated. The modular inversion script is configured to obtain a target integer x, a modulus value p, and a pair of indices for a component of an addition chain identifying a pair of pervious components which, when summed, equal the component of the addition chain. A modular inverse is generated by computing the exponentiation of x to the reduced modulus (p2) using the addition chain. For each component of the addition chain for 3il, each multiplier value is calculated by selecting the multiplier values associated with the pair of indices and multiplying the selected multiplier values to generate the respective multiplier value for the component. For i=l, a remainder of the multiplier value with respect to the modulus value is computed.

A recursive divide operation is performed on a logical address for a predetermined number of iterations. On each iteration of the recursive divide operation, a respective component of a physical address represented by the logical address is derived. The physical address corresponding to the logical address is the constructed from the derived components.