Abstract: A calculating device (100) arranged to perform calculations on elements of a ring (R), a ring addition and a ring multiplication being defined on the ring The calculating device comprises an operator module (120) comprising multiple operator units, and a calculation manager (130) arranged to perform a ring multiplication by applying a sequence of the multiple operator units, and perform a ring addition be applying a sequence of the multiple operator units, wherein the sequence for the ring multiplication is the same as the sequence for the ring addition.

Abstract: An electronic calculating device (100) is provided arranged for encoded addition in an Abelian group N. The calculating device comprises a storage (140) configured to store encoded elements of the Abelian group N, an addition unit (150) arranged to add multiple encoded addends, wherein the addition unit is configured to form an encoded element comprising at least the encoded parts of the multiple encoded addends, and reduction unit (160) arranged to reduce an encoded element, by replacing in a sequence of the encoded elements, two encoded elements with a further encoded element.

Abstract: An electronic generation device arranged to generate parameters for digital obfuscated arithmetic including a prime number unit arranged to generate a prime modulus (p) and a base element unit arranged to generate a prime modulus and a base element such that each ring-element modulo the prime modulus may be expressed as a difference between two powers of the potential base element.

Abstract: An electronic calculating device (100) arranged to perform obfuscated arithmetic in a commutative ring (ZM; Zn[x]/M(x)) defined by a combined modulus (M; M(x)) in a residue number system, the residue number system being defined for a series of moduli (m1, m2, . . . , mN), each modulus defining a commutative ring (ZM1; Zn[x]/m1(x)), for each modulus (mi) of the series there exists an associated base element (ui) satisfying the condition that each ring element (xj) modulo the modulus (mj) may be expressed as an integer-list ((aj, bj)) such that the ring elements equal a linear combination of powers of the base element (xj=uiaj?uibj), wherein the powers have exponents determined by the integer-list.

Abstract: An electronic calculating device for performing arithmetic in a commutative ring includes a storage configured to store an increment table defined for an increment ring element, the increment table mapping an input ring element to an output integer-list encoding an output ring element, such that the output ring element equals the increment ring element ring-added to the input ring element. Using the increment table, a ring addition unit adds a first addition-input integer-list encoding a first addition-input ring element and a second addition-input integer list encoding a second addition-input ring element. The device may include a ring multiplication unit also using the increment table.

Abstract: A calculating device (100) arranged to perform calculations on elements of a field (F), a field addition and a field multiplication being defined on the field. Encoded field elements are encoded according to one of at least two different encodings. A calculation manager (130) is arranged to selectively add or multiply a first encoded field element ((a, b)) and a second encoded field element (c, d), by for adding: apply the second translation operator unit to any encoded field element encoded according to the second encoding, and apply the set of addition operator units, and for multiplication: apply the first translation operator unit to any encoded field element encoded according to the first encoding, and apply the set of multiplication operator units.

Abstract: An electronic calculating device (100) for performing obfuscated arithmetic in a commutative ring (Zn; Zn[x]/f(x)) is presented. The calculating device comprising a storage (110) arranged to store an increment table (T) defined for an increment ring element (1; ut), the increment table mapping an input ring element (k=uk1?uk2) to an output integer-list (T((k1,k2))=(l1, l2)) encoding an output ring element (I=ul1?ul2), such that the output ring element equals the increment ring element ring-added to the input ring element (I=k+1). Using the increment table, a ring addition unit (130) adds a first addition-input integer-list ((a1, a2)) encoding a first addition-input ring element and a second addition-input integer list ((b1, b2)) encoding a second addition-input ring element. The device may comprise a ring multiplication unit (140) also using the increment table.

Abstract: An electronic calculating device arranged to add two elements of a main group ((M, +)), the main group being a finite Abelian group Formula (I), the calculating device comprising—an addition table storage (110) storing for each element (mi) of the second subset (M0) a look-up table (Pi), —an addition unit arranged to receive a first addition input (?0X0) and a second addition input (?0mi0h0+?1mi1h1+?2mi2h2+ . . . ), the first and second addition inputs being elements of the main group (M), wherein the first addition input is received in normalized representation and the second addition input in generalized representation, and to compute a sum in the main group (M) of the first addition input and the second addition input.

Abstract: An electronic calculating device (100) arranged to perform obfuscated arithmetic in a commutative ring (ZM; Zn[x]/M(x)) defined by a combined modulus (M; M(x)) in a residue number system, the residue number system being defined for a series of moduli (m1, m2, . . . , mN), each modulus defining a commutative ring (ZM1; Zn[x]/m1(x)), for each modulus (mi) of the series there exists an associated base element (ui) satisfying the condition that each ring element (xj) modulo the modulus (mj) may be expressed as an integer-list ((aj, bj)) such that the ring elements equal a linear combination of powers of the base element (xj=uiaj?uibj), wherein the powers have exponents determined by the integer-list.

Abstract: An electronic generation device (100) arranged to generate parameters for digital obfuscated arithmetic is provided. The generation device includes a prime number unit (110) arranged to generate a prime modulus (p) a base element unit (120) arranged to generate a prime modulus and a base element such that each ring-element modulo the prime modulus may be expressed as a difference between two powers of the potential base element.

Abstract: An electronic calculating device (100) for performing obfuscated arithmetic in a commutative ring (Zn; Zn[x]/f(x)) is presented. The calculating device comprising a storage (110) arranged to store an increment table (T) defined for an increment ring element (1; ut), the increment table mapping an input ring element (k=uk1?uk2) to an output integer-list (T((k1,k2))=(l1, l2)) encoding an output ring element (I=ul1?ul2), such that the output ring element equals the increment ring element ring-added to the input ring element (I=k+1). Using the increment table, a ring addition unit (130) adds a first addition-input integer-list ((a1, a2)) encoding a first addition-input ring element and a second addition-input integer list ((b1, b2)) encoding a second addition-input ring element. The device may comprise a ring multiplication unit (140) also using the increment table.

Abstract: An electronic calculating device (100) for performing arithmetic in a commutative ring (Zn; Zn [x]/f(x)) is presented. The calculating device comprising a storage (110) arranged to store an increment table (T) defined for an increment ring element (1; ut), the increment table mapping an input ring element (k=uk1?uk2) to an output integer-list (T((k1 k2))=(I1, I2)) encoding an output ring element (I=uI1?uI2), such that the output ring element equals the increment ring element ring-added to the input ring element (I=k?1). Using the increment table, a ring addition unit (130) adds a first addition-input integer-list ((a1, a2)) encoding a first addition-input ring element and a second addition-input integer list ((b1, b2)) encoding a second addition-input ring element. The device may comprise a ring multiplication unit (140) also using the increment table.