Abstract: Methods and a system involve secure communication between an RFID tag and a reader via the over-the-air interface, and to corresponding RFID tags and corresponding readers. A modification of the Rabin method is employed wherein within the framework of the encryption of a plaintext M into which an identification element of the RFID tag or of an object furnished therewith is incorporated, there is computed by the RFID tag, the Montgomery residue (Montgomery reduction) of the square of the plaintext M modulo n with respect to a Montgomery base R, i.e. C*=M2R?1 mod n, and the resultant ciphertext C* is employed for authenticating the RFID tag. The modulus n=p·q is the public key of the reader, the prime numbers p, q are the private key of the reader, and the Montgomery base R is an integer that is larger than the modulus n.

Abstract: Methods and a system involve secure communication between an RFID tag and a reader via the over-the-air interface, and to corresponding RFID tags and corresponding readers. A modification of the Rabin method is employed wherein within the framework of the encryption of a plaintext M into which an identification element of the RFID tag or of an object furnished therewith is incorporated, there is computed by the RFID tag, the Montgomery residue (Montgomery reduction) of the square of the plaintext M modulo n with respect to a Montgomery base R, i.e. C*=M2R?1 mod n, and the resultant ciphertext C* is employed for authenticating the RFID tag. The modulus n=p·q is the public key of the reader, the prime numbers p, q are the private key of the reader, and the Montgomery base R is an integer that is larger than the modulus n.

Abstract: Methods and a system involve secure communication between an RFID tag and a reader via the over-the-air interface, and to corresponding RFID tags and corresponding readers. A modification of the Rabin method is employed wherein within the framework of the encryption of a plaintext M into which an identification element of the RFID tag or of an object furnished therewith is incorporated, there is computed by the RFID tag, the Montgomery residue (Montgomery reduction) of the square of the plaintext M modulo n with respect to a Montgomery base R, i.e. C*=M2R?1 mod n, and the resultant ciphertext C* is employed for authenticating the RFID tag. The modulus n=p·q is the public key of the reader, the prime numbers p, q are the private key of the reader, and the Montgomery base R is an integer that is larger than the modulus n.

Abstract: Methods and a system involve secure communication between an RFID tag and a reader via the over-the-air interface, and to corresponding RFID tags and corresponding readers. A modification of the Rabin method is employed wherein within the framework of the encryption of a plaintext M into which an identification element of the RFID tag or of an object furnished therewith is incorporated, there is computed by the RFID tag, the Montgomery residue (Montgomery reduction) of the square of the plaintext M modulo n with respect to a Montgomery base R, i.e. C*=M2R?1 mod n, and the resultant ciphertext C* is employed for authenticating the RFID tag. The modulus n=p·q is the public key of the reader, the prime numbers p, q are the private key of the reader, and the Montgomery base R is an integer that is larger than the modulus n.

Abstract: The invention relates to sheet material having an electrical circuit and to apparatuses and methods for processing said sheet material. The present invention describes sheet material having an electrical circuit as well as apparatuses and methods for processing same, which reduce the effort required for processing the sheet material and/or facilitate processing and/or improve it and/or make it more reliable. For this purpose, the sheet material has at least one electrical circuit, with energy and/or data being transmitted from the apparatus to the electrical circuit and/or from the electrical circuit to the apparatus and at least part of the transmitted data being used for processing.

Abstract: The invention relates to a cryptographic method with at least one computing step containing a modular exponentiation E according to E=xd(mod p·q), with a first prime factor p, a second prime factor q, an exponent d and a number x, whereby the modular exponentiation E is calculated according to the Chinese Remainder Theorem.

Abstract: The invention relates to sheet material having an electrical circuit and to apparatuses and methods for processing said sheet material. The present invention describes sheet material having an electrical circuit as well as apparatuses and methods for processing same, which reduce the effort required for processing the sheet material and/or facilitate processing and/or improve it and/or make it more reliable. For this purpose, the sheet material has at least one electrical circuit, with energy and/or data being transmitted from the apparatus to the electrical circuit and/or from the electrical circuit to the apparatus and at least part of the transmitted data being used for processing.

Abstract: The invention relates to a cryptographic method with at least one computing step containing a modular exponentiation E according to E=xd (mod p·q), with a first prime factor p, a second prime factor q, an exponent d and a number x, whereby the modular exponentiation E is calculated according to the Chinese Remainder Theorem.

Abstract: A method for secure distribution of data or programs, the transmitted data being provided with an electronic signature. The unit receiving the data or programs checks the electronic signature by executing a modular multiplication, thereby necessitating a multiplication and a division thereof. According to the invention, the unit receiving the data or program checks the signature by performing a modular multiplication according to the Montgomery method wherein an additional multiplication by a factor on the basis of base 2 and even exponents is performed.

Abstract: Cryptographic equipment is used with a number of user identification cards which are distributed to various authorized users, each user identification card being a non-volatile memory which can be overwritten in which a user-associated external crypto-ignition key is stored. Insertion of the user identification card in the cryptographic equipment releases the cryptovariable code by cooperation with an internal crypto-ignition key stored internal in a sub-memory of the cryptographic equipment for every authorized user. The cryptovariable required for setting and controlling the cryptosequence generator is stored in encoded form in another sub-memory of the variable memory, and is capable of being decoded with the cryptovariable code.