Secure computation system, secure computation device, secure computation method, and program

A secure computation system comprising three or more secure computation devices,

• the secure computation device comprises circuitry configured to:
• receive a secure text array <a>=(<a[0]>, . . . , <a[n−1]>) where an array a=(a[0], . . . , a[n−1]) having a size of n is secured, secure text <x> of an integer x that is equal to or higher than 0 and less than n, and a natural number m;
• secure-shift the secure text array <a> by <x> to obtain a secure text array <a′>=(<a′[0]>, . . . , <a′[n−1]>) where an array a′=(a′[0], . . . , a′[n−1]) obtained by shifting leftward the array a by x is secured;
• and
• generate a secure text array <b>=(<a′[0]>, . . . , <a′[m−1]>) from the secure text array <a′>.

A secure computation device comprises circuitry configured to:

• receive a secure text array <a>=(<a[0]>, . . . , <a[n−1]>) where an array a=(a[0], . . . , a[n−1]) having a size of n is secured, secure text <x> of an integer x that is equal to or higher than 0 and less than n, and m integers i0, . . . , im-1 that are equal to or higher than 0 and less than n;
• secure-shift the secure text array <a> by <x> to obtain a secure text array <a′>=(<a′[0]>, . . . , <a′[n−1]>) where an array a′=(a′[0], . . . , a′[n−1]) obtained by shifting leftward the array a by x is secured;
• and
• generate a secure text array <b>=(<a′[i0]>, . . . , <a′[im-1]>) from the secure text array <a′>.

A secure computation device comprises circuitry configured to:

• receive a secure text array <a>=(<a[0]>, . . . , <a[n−1]>) where an array a=(a[0], . . . , a[n−1]) having a size of n is secured, secure text <x> of an integer x that is equal to or higher than 0 and less than n, and a natural number m;
• secure-shift the secure text array <a> by <x> to obtain a secure text array <a′>=(<a′[0]>, . . . , <a′[n−1]>) where an array a′=(a′[0], . . . , a′[n−1]) obtained by shifting leftward the array a by x is secured;
• and
• generate a secure text array <b>=(<a′[0]>, . . . , <a′[m−1]>) from the secure text array <a′>.

A secure computation method, comprising:

• receiving a secure text array <a>=(<a[0]>, . . . , <a[n−1]>) where an array a=(a[0], . . . , a[n−1]) having a size of n is secured, secure text <x> of an integer x that is equal to or higher than 0 and less than n, and m integers i0, . . . , im-1 that are equal to or higher than 0 and less than n by circuitry of a secure computation device;
• secure-shifting the secure text array <a> by <x> to obtain a secure text array <a′>=(<a′[0]>, . . . , <a′[n−1]>) where an array a′=(a′[0], . . . , a′[n−1]) obtained by shifting leftward the array a by x is secured by the circuitry of the secure computation device;
• and
• generating a secure text array <b>=(<a′[i0]>, . . . , <a′[im-1]>) from the secure text array <a′> by the circuitry of the secure computation device.

A secure computation method, comprising:

• receiving a secure text array <a>=(<a[0]>, . . . , <a[n−1]>) where an array a=(a[0], . . . , a[n−1]) having a size of n is secured, secure text <x> of an integer x that is equal to or higher than 0 and less than n, and a natural number m by circuitry of a secure computation device;
• secure-shifting the secure text array <a> by <x> to obtain a secure text array <a′>=(<a′[0]>, . . . , <a′[n−1]>) where an array a′=(a′[0], . . . , a′[n−1]) obtained by shifting leftward the array a by x is secured by the circuitry of the secure computation device;
• and
• generating a secure text array <b>=(<a′[0]>, . . . , <a′[m−1]>) from the secure text array <a′> by the circuitry of the secure computation device.

A non-transitory computer readable medium including computer executable instructions that make a secure computation device perform a method comprising:

• receiving a secure text array <a>=(<a[0]>, . . . , <a[n−1]>) where an array a=(a[0], . . . , a[n−1]) having a size of n is secured, secure text <x> of an integer x that is equal to or higher than 0 and less than n, and m integers i0, . . . , im-1 that are equal to or higher than 0 and less than n;
• secure-shifting the secure text array <a> by <x> to obtain a secure text array <a>=(<a′[0]>, . . . , <a′[n−1]>) where an array a′=(a′[0], . . . , a′[n−1]) obtained by shifting leftward the array a by x is secured;
• and
• generating a secure text array <b>=(<a′[i0]>, . . . , <a′[im-1]>) from the secure text array <a′>.

A non-transitory computer readable medium including computer executable instructions that make a secure computation device perform a method comprising,

• receiving a secure text array <a>=(<a[0]>, . . . , <a[n−1]>) where an array a=(a[0], . . . , a[n−1]) having a size of n is secured, secure text <x> of an integer x that is equal to or higher than 0 and less than n, and a natural number m;
• secure-shifting the secure text array <a> by <x> to obtain a secure text array <a>=(<a′[0]>, . . . , <a′[n−1]>) where an array a′=(a′[0], . . . , a′[n−1]) obtained by shifting leftward the array a by x is secured;
• and
• generating a secure text array <b>=(<a′[0]>, . . . , <a′[m−1]>) from the secure text array <a′>.