Abstract: An RFID tag possesses a group key issued by an authorized entity. When a reader requests some information from the tag, such as an identifier, the tag transmits a random number to the reader. The tag then determines one or more reader characteristics based on a response received from the reader. In one embodiment, the tag generates a verification value based on the random number and the group key and compares the verification value to the received response. If the comparison succeeds, the tag may treat the reader as possessing particular functionality, authorized to implement a particular feature, and/or authorized to receive information from the tag. If the comparison fails, the tag may treat the reader as lacking particular functionality, not authorized to implement a particular feature, and/or not authorized to receive information from the tag. The tag may request additional response(s) from the reader before determining the reader characteristic(s).

Abstract: An RFID tag possesses a group key issued by an authorized entity. When a reader requests some information from the tag, such as an identifier, the tag transmits a random number to the reader. The tag then determines one or more reader characteristics based on a response received from the reader. In one embodiment, the tag generates a verification value based on the random number and the group key and compares the verification value to the received response. If the comparison succeeds, the tag may treat the reader as possessing particular functionality, authorized to implement a particular feature, and/or authorized to receive information from the tag. If the comparison fails, the tag may treat the reader as lacking particular functionality, not authorized to implement a particular feature, and/or not authorized to receive information from the tag. The tag may request additional response(s) from the reader before determining the reader characteristic(s).

Abstract: A device and a method of cryptographically hashing a message M, including the following steps: forming a sequence (M1, . . . , Mi, . . . , Mc) of data m-tuples M1=(a1,1, . . . , a1,m), . . . Mi=(ai,1, . . . , ai,m), . . . , Mc=ac,1, . . . , ac,m), where m is a strictly positive integer, from said message M; iteratively calculating successive output p-tuples V1, . . . , Vi, . . . , Vc, where p is a strictly positive integer, corresponding to said sequence (M1, . . . , Mi, . . . , Mc) of data m-tuples as a function of at least one set of multivariate polynomials defined over a finite field; and determining a hashing value of said message M as a function of the last output p-tuple Vc.

Abstract: A device and a method of cryptographically hashing a message M, including the following steps: forming a sequence (M1, . . . , Mi, . . . , Mc) of data m-tuples M1=(a1,1, . . . , a1,m), . . . Mi=(ai,1, . . . , ai,m), . . . , Mc=ac,1, . . . , ac,m), where m is a strictly positive integer, from said message M; iteratively calculating successive output p-tuples V1, . . . , vi, . . . , Vc, where p is a strictly positive integer, corresponding to said sequence (M1, . . . , Mi, . . . , Mc) of data m-tuples as a function of at least one set of multivariate polynomials defined over a finite field; and determining a hashing value of said message M as a function of the last output p-tuple Vc.

Abstract: A cryptographic device and a cryptographic method of generating pseudo-random numbers. Initial data is divided into a plurality of words on b bits defined in a finite body GF(2b). The words are assigned to cells of a state table to form an initial state block. The cells of the state table are grouped to assign a group of cells to each set of d/b words, where d is a multiple of b strictly greater than b. And, a succession of state blocks is iteratively generated from the initial state block to form a final state block, so that on each iteration each set of d/b words of a current state block is replaced by another set of d/b words to form a next state block using a reference table including substitution elements on d bits.