Abstract: The present invention relates to a system and to a corresponding method for an automated triggering and management of alarms, in particular in a home environment (1), comprising at least one sensor (21, 22, . . . ) for collecting data and for transmitting the collected data over at least one first data connection (31, 32, . . .

Abstract: A reduction operation is utilized in an arithmetic operation on two binary polynomials X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=tm+am?1tm?1+am?2tm?2+ . . . +a1t+a0, where the coefficients ai are equal to either 1 or 0, and m is a field degree. The reduction operation includes partially reducing a result of the arithmetic operation on the two binary polynomials to produce a congruent polynomial of degree less than a chosen integer n, with m?n. The partial reduction includes using a polynomial M?=(Mm(t)?tm)*tn?m, or a polynomial M?=Mm(t)*tn?m as part of reducing the result to the degree less than n and greater than or equal to m. The integer n can be the data path width of an arithmetic unit performing the arithmetic operation, a multiple of a digit size of a multiplier performing the arithmetic operation, a word size of a storage location, such as a register, or a maximum operand size of a functional unit in which the arithmetic operation is performed.

Abstract: A reduction operation is utilized in an arithmetic operation on two binary polynomials X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=tm+am?1tm?1+am?2tm?2+ . . . +a1t+a0, where the coefficients ai are equal to either 1 or 0, and m is a field degree. The reduction operation includes partially reducing a result of the arithmetic operation on the two binary polynomials to produce a congruent polynomial of degree less than a chosen integer n, with m?n. The partial reduction includes using a polynomial M?=(Mm(t)?tm)*tn?m, or a polynomial M?=Mm(t)*tn?m as part of reducing the result to the degree less than n and greater than or equal to m. The integer n can be the data path width of an arithmetic unit performing the arithmetic operation, a multiple of a digit size of a multiplier performing the arithmetic operation, a word size of a storage location, such as a register, or a maximum operand size of a functional unit in which the arithmetic operation is performed.

Abstract: A reduction operation is utilized in an arithmetic operation on two binary polynomials X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=tm+am?1tm?1+am?2tm?2+ . . . +a1t+a0, where the coefficients ai are equal to either 1 or 0, and m is a field degree. The reduction operation includes partially reducing a result of the arithmetic operation on the two binary polynomials to produce a congruent polynomial of degree less than a chosen integer n, with m?n. The partial reduction includes using a polynomial M?=(Mm(t)?tm)*tn?m, or a polynomial M?=Mm(t)*tn?m as part of reducing the result to the degree less than n and greater than or equal to m. The integer n can be the data path width of an arithmetic unit performing the arithmetic operation, a multiple of a digit size of a multiplier performing the arithmetic operation, a word size of a storage location, such as a register, or a maximum operand size of a functional unit in which the arithmetic operation is performed.

Abstract: A reduction operation is utilized in an arithmetic operation on two binary polynomials X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=tm+am−1tm−1+am−2tm−2+ . . . +a1t+a0, where the coefficients as are equal to either 1 or 0, and m is a field degree. The reduction operation includes partially reducing a result of the arithmetic operation on the two binary polynomials to produce a congruent polynomial of degree less than a chosen integer n, with m≦n. The partial reduction includes using a polynomial M′=(Mm(t)−tm)*tn−m, or a polynomial M″=Mm(t)*tn−m as part of reducing the result to the degree less than n and greater than or equal to m.