Proxy computing system, computing apparatus, capability providing apparatus, proxy computing method, capability providing method, program, and recording medium

摘要

A computing apparatus outputs τ1 and τ2 corresponding to a ciphertext x, a capability providing apparatus uses τ1 to correctly compute f(τ1) with a probability greater than a certain probability and sets the result of the computation as z1, uses τ2 to correctly compute f(τ2) with a probability greater than a certain probability and sets the result of the computation as z2, the computing apparatus generates a computation result u=f(x)bx1 from z1, generates a computation result v=f(x)ax2 from z2, and outputs ub′va′ if the computation results u and v satisfy a particular relation, where G and H are groups, f(x) is a function for obtaining an element of the group G for xεH, X1 and X2 are random variables having values in the group G, x1 is a realization of the random variable X1, and x2 is a realization of the random variable X2.

主权项

1. A proxy computing system comprising a computing apparatus and a capability providing apparatus,
wherein G and H are groups, f(x) is a decryption function for decrypting a certain ciphertext x which is an element of the group H with a particular decryption key to obtain an element of the group G, X1 and X2 are random variables having values in the group G, x1 is a realization of the random variable X1, x2 is a realization of the random variable X2, a and b are natural numbers that are relatively prime to each other; the computing apparatus comprises processing circuitry configured to implement an input information providing unit outputting first input information τ1 and second input information τ2 that correspond to the ciphertext x and are elements of the group H; the capability providing apparatus comprises processing circuitry configured to implement:
a first output information computing unit using the first input information τ1 to correctly compute f(τ1) with a probability greater than a certain probability and sets an obtained result of the computation as first output information z1; anda second output information computing unit using the second input information τ2 to correctly compute f(τ2) with a probability greater than a certain probability and sets an obtained result of the computation as second output information z2; and the processing circuitry of the computing apparatus is further configured to implement:
a first computing unit configured to generate a computation result u=f(x)bx1 from the first output information z1, and generate a computation result u′=ua;a second computing unit configured to generate a computation result v=f(x)ax2 from the second output information z2, and generate a computation result v′=vb;a determining unit configured to determine whether or not there are values of u′ and v′ that satisfy u′=v′ after every calculation of u′ and v′ for no more than a predetermined number of iterations of receiving newly calculated values of u and v from the calculating apparatus; anda final output unit configured to output ub′va′ for integers a′ and b′ that satisfy a′a+b′b=1 when the computation results u and v satisfy u′=v′ and thus ua=vb, wherein the determining unit determines that calculation of ub′va′ is impossible based on a calculation reliability of the capability providing apparatus being lower than a reference value when there are no values of u′ and v′ that satisfy u′=v′ after the predetermined number of iterations are completed.