METHOD FOR DETERMINING A STATISTIC VALUE ON DATA BASED ON ENCRYPTED DATA

• US 20150154422A1
• Filed: 11/29/2014
• Published: 06/04/2015
• Est. Priority Date: 11/29/2013
• Status: Abandoned Application

• Current Assignee: Thomson Licensing (Vantiva SA)
• Original Assignee: Thomson Licensing (Vantiva SA)
• Inventors: Joye, Marc, Libert, Benoit, Ben Hamouda, Fabrice
• Application Number:
  US14/556,146
• Publication Number:
  US 20150154422A1
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: G06F 21/71 to assure secure computing or processing of information
• CPC Class Codes: H04L 2209/46 Secure multiparty computation, e.g. millionaire problem
• CPC Class Codes: H04L 2209/50 Oblivious transfer
• CPC Class Codes: H04L 9/008 involving homomorphic encryption
• CPC Class Codes: H04L 9/14 using a plurality of keys or algorithms
• CPC Class Codes: H04L 9/3013 involving the discrete logarithm problem, e.g. ElGamal or Diffie-Hellman systems
• CPC Class Codes: H04L 9/3073 involving pairings, e.g. identity based encryption [IBE], bilinear mappings or bilinear pairings, e.g. Weil or Tate pairing
• CPC Class Codes: Y04S 40/20 Information technology specific aspects, e.g. CAD, simulation, modelling, system security

Abstract

In one embodiment, it is proposed a method for determining a statistic value, for a given time period t, on a set of n≧2 of plaintext data {x_i,t}_1≦i≦n with x_i,tε_p, p being a primer number, only based on a set of corresponding ciphertext data {c_i,t=E_ski(x_i,t,t)}_1≦i≦n, where E is an encryption method and sk_i an encryption key, without having access to all elements of the set of corresponding encryption key {sk_i}_1≦i≦n. The method is implemented by an electronic device and is remarkable in that it comprises:

• • obtaining said given time period t, and said set of corresponding ciphertext data {c_i,t=E_ski(x_i,t,t)}_1≦i≦n for which E_ski(x_i,t,t)=ƒ(x_i,t) Π_j=1^k+1H_j(t)^sj,i where functions H₁, . . . , H_k+1:→ are hash functions, is a group of prime order q, k≧1 and said encryption key sk_i={s_j,i}_1≦j≦k+1 which comprises (k+1) random elements in /q, and ƒ is a function defined according to said statistic value, and having for codomain said group ;
  • obtaining an aggregator private key sk₀={s_j,0}_1≦j≦k+1={−Σ_i=1ⁿs_j,i mod q}_1≦j≦k+1;
  • determining said statistic value based on sk₀ and said set of corresponding ciphertext data {c_i,t=E_ski(x_i,t,t)}_1≦i≦n.

Claims

1. A method for determining a statistic value, for a given time period t, on a set of n≧

2 of plaintext data {x_i,t}<sub>1≦

i≦

n</sub> with x_i,tε

_p, p being a primer number, only based on a set of corresponding ciphertext data {c_i,t=E_ski(x_i,t,t)}<sub>1≦

i≦

n</sub>, where E is an encryption method and sk_i an encryption key, without having access to all elements of the set of corresponding encryption key {sk_i}<sub>1≦

i≦

n</sub>, said method being implemented by an electronic device and wherein it comprises;

obtaining said given time period t, and said set of corresponding ciphertext data {c_i,t=E_ski(x_i,t,t)}<sub>1≦

i≦

n</sub> for which E_ski(x_i,t,t)=ƒ

(x_i,t) Π

_j=1^k+1H_j(t)^sj,i where functions H₁, . . . , H_k+1;

→

are hash functions, is a group of prime order q, k>

1 and said encryption key sk_i={s_j,i}<sub>1≦

j≦

k+1</sub> which comprises (k+1) random elements in /q, and ƒ

is a function defined according to said statistic value, and having for codomain said group ;

obtaining an aggregator private key sk₀={s_j,0}<sub>1≦

j≦

k+1</sub>γ

{−

Σ

_i=1ⁿs_j,i mod q}<sub>1≦

j≦

k+1</sub>;

determining said statistic value based on sk₀ and said set of corresponding ciphertext data {c_i,t=E_ski(x_i,t,t)}<sub>1≦

t≦

n</sub>.

2. The method according to claim 1, wherein k=1.

3. The method according to claim 1, wherein said function ƒ

is a function defined by an equation ƒ

(x)=xⁿ, where n is a real number, and said group corresponds to _p.

4. The method according to claim 1, wherein said function ƒ

is a function defined by an equation

5. The method according to claim 4, wherein n′

is equal to one, and said statistic value corresponds to a sum of plaintexts associated to encrypted data, and in that said step of determining said statistic value comprises;

obtaining V_t;

=Π

_j=1^k+1H_j(t)^sj,0·

Π

_i=1ⁿc_i,t=g^Xt;

determining the discrete logarithm of V_t with regards to basis g.

6. The method according to claim 5, wherein said determining the discrete logarithm of V_t comprises executing a Pollard'"'"'s kangaroo algorithm.

7. The method according to claim 5, wherein said determining the discrete logarithm of V_t comprises executing an index calculus algorithm.

8. The method according to claim 5, wherein said determining the discrete logarithm of V_t comprises executing a Pohlig-Hellman algorithm.

9. The method according to claim 1, wherein said plaintext data {x_i,t}_1≦

i≦

n correspond to data provided by a device belonging to a smart grid.

10. An electronic device comprising a first module configured to determine a statistic value, for a given time period t, on a set of n≧

2 of plaintext data {x_i,t}<sub>1≦

i≦

n</sub> with x_i,tε

_p, p being a primer number, only based on a set of corresponding ciphertext data {c_i,t=E_ski(x_i,t,t)}<sub>1≦

i≦

n</sub>, where E is an encryption method and sk_i an encryption key, without having access to all elements of the set of corresponding encryption key {sk_i}<sub>1≦

i≦

n</sub>, wherein said electronic device comprises;

a second module configured to obtain said given time period t, and said set of corresponding ciphertext data {c_i,t=E_ski(x_i,t,t)}<sub>1≦

i≦

n</sub> for which E_ski(x_i,t,t)=ƒ

(x_i,t) Π

_j=1^k+1H_j(t)^sj,i where functions H₁, . . . , H_k+1;

→

are hash functions, is a group of prime order q, k≧

1 and said encryption key sk_i={s_j,i}<sub>1≦

j≦

k+1</sub> which comprises (k+1) random elements in /q, and ƒ

is a function defined according to said statistic value, and having for codomain said group ;

a third module configured to obtain an aggregator private key sk₀={s_j,0}<sub>1≦

i≦

k+1</sub>={−

Σ

_i=1ⁿs_j,i mod q}<sub>1≦

j≦

k+1</sub>;

a fourth module configured to determine said statistic value based on sk₀ and said set of corresponding ciphertext data {c_i,t=E_ski(x_i,t,t)}<sub>1≦

i≦

n</sub>.

11. The electronic device according to claim 10, wherein k=1.

12. The electronic device according to claim 10, wherein said function ƒ

is a function defined by an equation ƒ

(x)=xⁿ, where n is a real number, and said group corresponds to _p.

13. The electronic device according to claim 10, wherein said function ƒ

is a function defined by an equation

14. The electronic device according to claim 13, wherein n′

is equal to one, and said statistic value corresponds to a sum of plaintexts associated to encrypted data, and in that said fourth module configured to determine said statistic value comprises;

a fifth module configured to obtain V_t;

=Π

_j=1^k+1H_j(t)^sj,0·

Π

_j=1ⁿc_i,t=g^Xt;

a sixth module configured to determine the discrete logarithm of V_t with regards to basis g.