Abstract: The embodiments relate to a method for the encrypted data exchange between subscribers of a communication system using cryptography based on elliptical curves, wherein upon a query by a first subscriber a scalar multiplication is calculated by the second subscriber, wherein merely part of the result of the scalar multiplication is returned to the first subscriber as a response. The invention relates to a communication system.

Abstract: A method determines an elliptical curve, suitable for a cryptographic method. An elliptical curve to be tested is prepared. The order of a twisted elliptical curve associated with the elliptical curve to be tested is determined. It is automatically checked whether the order of the twisted elliptical curve is a strong prime number. If the order of the twisted elliptical curve is a strong prime number, the elliptical curve to be tested is selected as an elliptical curve suitable for cryptographical methods.

Abstract: Cryptographic products for mass applications, such as RFIDs or special ICs for the protection from plagiarism, always require that the price per unit costs are reduced as low as possible. This is achieved, for example, in that in such methods the required storage space is further reduced for system parameters to be permanently stored. Accordingly, in a method for coding and decoding the cryptographic system parameters of an elliptical curve, when storing the system parameters, storage cells are each completely occupied, and therefore no storage space is wasted.

Abstract: An authentication method authenticates between subscribers of a communications system using an asymmetric elliptic curve encryption algorithm. The method involves providing a first and at least one second subscriber having a first or second secret key known only to the respective subscriber and a public key; authenticating an inquiry transmitted by the first subscriber with respect to the validity of the first certificate contained therein and associated with the first subscriber; calculating the response of the second subscriber associated with the inquiry; randomized encryption of the calculated response and a second certificate associated with the second subscriber using the public key; decryption and authentication of the response transmitted by the second subscriber with respect to the validity of the second certificate contained therein.

Abstract: The aim of the embodiments is to provide a method for the secure processing of data, in which security is increased in relation to side channel attacks. To achieve this, operation codes for commanding co-processors are determined, for example for the bit-dependent transposition of register contents. The solution exploits the fact that as a result of the technical configuration for the co-processor, a shift of register contents, for example from register A to register B cannot be differentiated from the exterior from a shift from register A to register C.

Abstract: A method for securely encrypting or decrypting a message or for generating or verifying a digital signature in a message, in which the message is subjected, with the aid of a processor, to a mathematical operation using a key (k) which can be represented in the form of a binary number with a sequence of bits, and computational operations are sequentially carried out on auxiliary variables for each bit. The dependence of the computational result on the values of individual bits is taken into account by reading the memory addresses from the auxiliary variables and assigning them to address variables. The difference between the addresses is calculated and, depending on the respective current bit, is added to, or subtracted from, the computer addresses. The assignment of the auxiliary variables to the address variables can thus be interchanged. As a result, the order and selection of the computational operations is controlled on the basis of bits without the program sequence having to contain jump instructions.

Abstract: The embodiments provides a method for processing data. According to the invention, an elliptic curve with an order m which corresponds to a product of a first cofactor c and a prime number q is provided, wherein the order (q?1) of the multiplicative group of the prime number q corresponds to a product of a second cofactor I and at least two prime divisors s1, . . . , sk, wherein the at least two prime divisors s1, . . . , sk are each greater than a predetermined bound of 2n; and a chosen method is applied to provided data using the provided elliptic curve for providing cryptographically transformed data. The invention enables cryptographically transformed data to be provided while simultaneously minimizing the probability of a successful attack.

Abstract: Cryptographic products for mass applications, such as RFIDs or special ICs for the protection from plagiarism, always require that the price per unit costs are reduced as low as possible. This is achieved, for example, in that in such methods the required storage space is further reduced for system parameters to be permanently stored. Accordingly, in a method for coding and decoding the cryptographic system parameters of an elliptical curve, when storing the system parameters, storage cells are each completely occupied, and therefore no storage space is wasted.

Abstract: In a system and method for encrypted data exchange between entities (users) of a communication system using cryptography based on elliptic curves, in response to a challenge of a first user a scalar multiplication is calculated by the second user, wherein only part of the result of the scalar multiplication is sent back as response to the first user.

Abstract: Conventional cryptographic methods that are based on elliptic curves are prone to side-channel attacks. Previously known methods for preventing side-channel attacks have the disadvantage of requiring high arithmetic capacity and a large amount of available memory space. The proposed method overcomes said disadvantage by using a process for verifying points on elliptic curves which saves arithmetic capacity and memory space.

Abstract: The aim of the embodiments is to provide a method for the secure processing of data, in which security is increased in relation to side channel attacks. To achieve this, operation codes for commanding co-processors are determined, for example for the bit-dependent transposition of register contents. The solution exploits the fact that as a result of the technical configuration for the co-processor, a shift of register contents, for example from register A to register B cannot be differentiated from the exterior from a shift from register A to register C.

Abstract: The embodiments relate to a method for the encrypted data exchange between subscribers of a communication system using cryptography based on elliptical curves, wherein upon a query by a first subscriber a scalar multiplication is calculated by the second subscriber, wherein merely part of the result of the scalar multiplication is returned to the first subscriber as a response. The invention relates to a communication system.

Abstract: A method determines an elliptical curve, suitable for a cryptographic method. An elliptical curve to be tested is prepared. The order of a twisted elliptical curve associated with the elliptical curve to be tested is determined. It is automatically checked whether the order of the twisted elliptical curve is a strong prime number. If the order of the twisted elliptical curve is a strong prime number, the elliptical curve to be tested is selected as an elliptical curve suitable for cryptographical methods.

Abstract: An authentication method authenticates between subscribers of a communications system using an asymmetric elliptic curve encryption algorithm. The method involves providing a first and at least one second subscriber having a first or second secret key known only to the respective subscriber and a public key; authenticating an inquiry transmitted by the first subscriber with respect to the validity of the first certificate contained therein and associated with the first subscriber; calculating the response of the second subscriber associated with the inquiry; randomized encryption of the calculated response and a second certificate associated with the second subscriber using the public key; decryption and authentication of the response transmitted by the second subscriber with respect to the validity of the second certificate contained therein.

Abstract: A method performs scalar multiplication of points on an elliptic curve by a finite expandable field K of a first field Fp of a p>3 characteristic, wherein said characteristic p has low Hamming weight and the expandable field has a polynomF(X)+Xd?2 of order d in the polynomial representation thereof.

Abstract: Conventional cryptographic methods that are based on elliptic curves are prone to side-channel attacks. Previously known methods for preventing side-channel attacks have the disadvantage of requiring high arithmetic capacity and a large amount of available memory space. The proposed method overcomes said disadvantage by using a process for verifying points on elliptic curves which saves arithmetic capacity and memory space.

Abstract: A method for securely encrypting or decrypting a message or for generating or verifying a digital signature in a message, in which the message is subjected, with the aid of a processor, to a mathematical operation using a key (k) which can be represented in the form of a binary number with a sequence of bits, and computational operations are sequentially carried out on auxiliary variables for each bit. The dependence of the computational result on the values of individual bits is taken into account by reading the memory addresses from the auxiliary variables and assigning them to address variables. The difference between the addresses is calculated and, depending on the respective current bit, is added to, or subtracted from, the computer addresses. The assignment of the auxiliary variables to the address variables can thus be interchanged. As a result, the order and selection of the computational operations is controlled on the basis of bits without the program sequence having to contain jump instructions.