Orange

Olivier Sanders

Sébastien Canard

Jacques Traore

Julien Devigne

Florian Bourse

A cryptographic method including: generating by a first device having a datum x an RSA module N; computing by the first device a number C=gh1, g being an element of sub-group G of order b, h1 being an element of sub-group H of order f, and a, b, d, f being integers, b and f being mutually prime, and x and y being less than d/a; sending C to a second device having datum y; computing by the second device D=C(gh3)h2, u and v being random numbers and h2 and h3 being elements of H, and a first fingerprint (gh3); sending to the first device, D and the first fingerprint; computing by the first device (D)', f′=1/f; obtaining based on (D)′ a second fingerprint; and determining whether x is greater than or equal to y or x is less than y by comparing the first and the second fingerprints.

Cryptographic method of secure comparison of two secret data x and y

A method for searchable encryption of a system defining a secret key and a public is provided. A data stream cipher can include n elementary data (b, b, . . . , b). The method can include generation of a variate for all elementary data b, for values of j from 1 to n, generation of an element function of the public key (g) and the variate, the element being associated with a random element of a group of a bilinear environment, the element associated with the random element of the group forming first encryption data (C). The method can also include generation of a shift factor (g) function of the variate and the public key, and associated with the random element of the group, the shift factor representing a position of the monomial in the encrypted stream, the shift factor associated with the random element of the group forming second encryption data. The data stream cipher can include the first and second encryption data for all values of j from 1 to n.

Searchable encryption method

A cryptographic method for signing a message m by a user device on behalf of a group managed by a group manager, which has a secret key generated from two variates x and y, the group having a public key formed from a plurality of elements comprising an element g and an element gz pertaining to a cyclic group of order p, p being a whole prime number and z a variate, and an element h, an element hx, an element h/z and an element hy/z pertaining to a cyclic group of order p. The method includes: receiving a certificate from the group manager, including elements Sgr, Sgr(x+y.u) and Sgz.r where r is a variate selected by the group manager for the user device; and generating a group signature for the message m, based on the certificate, a variate t generated by the user device, and the secret u.

Cryptographic method for group signature

One embodiment relates to a method for enabling an entity to delegate calculation of a bilinear pairing value e(A,B) between two values A and B to a calculation server. The entity may select public elements Pand Pand secret elements Sand S, two of the elements from among P, P, S, and Sbeing selected to be equal to A and B, generate elements R=vS, R=uS, T=uP+S, T=vP=S, whereandare random numbers, and transmit R, R, T, and Tto the calculation server. The server may calculate (a)=e(T,T)[e(R,P)e(P,R)], and (a)=e(D,D),anddesignating two integers equal to 1 or to an integer, Dand Ddesignating two public elements from among A and B or from among Rand Rand transmit aand ato the entity. The entity may obtain the value e(A,B) from aor a

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Châtillon, France

Olivier Sanders