Abstract: A co-processor (44) executes a mathematical algorithm that computes modular exponentiation equations for encrypting or decrypting data. A pipelined multiplier (56) receives sixteen bit data values stored in an A/B RAM (72) and generates a partial product. The generated partial product is summed in an adder (58) with a previous partial product stored in a product RAM (64). A modulo reducer (60) causes a binary data value N to be aligned and added to the summed value when a particular data bit location of the summed value has a logic one value. An N RAM (70) stores the data value N that is added in a modulo reducer (60) to the summed value. The co-processor (44) computes the Foster-Montgomery Reduction Algorithm and reduces the value of (A*B mod N) without having to first compute the value of &mgr; as is required in the Montgomery Reduction Algorithm.

Abstract: A system for efficiently controlling the exchange of data between a host bus (190) and an input/output (I/O) register (125) of an elliptic curve (EC) processor (120) having a much wider datapath than that of the host device (100) . A spreading/despreading pattern is determined which spans multiple bit positions of the input/output register (125). In one embodiment, a full combinational circuit (300) is provided to connect a bit position of the host bus (190) to a bit position of the input/output register (125). In another embodiment, a combinational circuit (300) and an intermediate register (410) are provided. In still another embodiment, a spreading-by shifting system (500) is provided which comprises a plurality of subfield modules (520) into which data from the host bus (190) is shifted. The spreading/despreading pattern is achieved through multiplexers (540) connected between the subfield modules (520).

Abstract: A programmable versatile digital signal processing system architecture (FIG. 5) allows the implementation of functions for transmitting and receiving a variety of narrow and wide-band communication signaling schemes. The flexibility of the architecture (FIG. 5) makes it possible to receive and transmit many different spectral communication signals in real time by implementing signal processing functions such as filtering, spreading, de-spreading, rake filtering, and equalization under the direction of program instructions (FIGS. 13, 14, 15, and 16).

Abstract: A finite field multiplier with intrinsic modular reduction includes an interface unit (1208) that translates an n bit wide data path to a m bit wide data path where n is less than m. Also included is a finite field data unit (1204) with m bit wide registers that is coupled to a finte field control unit (1202). The finite field control unit (1202) includes a microsequencer (1402) and a finite state machine multiplier (1404). The microsequencer (1402) controls the finite state machine multiplier (1404) which performs a finite field multiply operation with intrinsic modular reduction and presents a finite field multiplication product to the finite field data unit (1204).

Abstract: An elliptic curve (EC) processor circuit (120) comprising a finite field arithmetic logic unit (122), operation registers (124) an EC control unit (123) and a register file (127). A storage element (250) is coupled to the finite field arithmetic logic unit (122). The EC control unit (123) controls the various components of the EC processor circuit (120) to decompress a compressed one-bit representation of a Y coordinate of an elliptic curve point (X, Y). The EC control unit (123) controls the use of the operation register (124), the storage element (250) and the finite field arithmetic logic unit (122) to recursively compute the decompressed version of the compressed Y coordinate based upon the X coordinate and the compressed one-bit representation of the Y coordinate. The circuit and method employ minimal additional hardware and processing in an EC processor circuit (120).

Abstract: A co-processor (44) executes a mathematical algorithm that computes modular exponentiation equations for encrypting or decrypting data. A pipelined multiplier (56) receives sixteen bit data values stored in an A/B RAM (72) and generates a partial product. The generated partial product is summed in a summer (58) with a previous partial product stored in a product RAM (64). A modulo reducer (60) causes a binary data value N to be aligned and added to the summed value when a particular data bit location of the summed value has a logic one value. An N RAM (70) stores the data value N that is added in a modulo reducer (60) to the summed value. The co-processor (44) computes the Foster-Montgomery Reduction Algorithm and reduces the value of (A*B mod N) without having to first compute the value of &mgr; as is required in the Montgomery Reduction Algorithm.

Abstract: A finite field inverse circuit has a finite field data unit (1112) and an inverse control unit (1110). The inverse control unit includes (1110) a k.sub.l and k.sub.u decrementer pair (1108, 1122), a k.sub.l -k.sub.u difference unit (1106), an inverse control finite state machine (1102), and a one-bit memory (1104) coupled to the inverse control finite state machine (1102). The finite field data unit (1112) includes four m bit wide registers that are shift registers designated as B (1120), A (1118), M (1114), and C (1116), where B- is a first register, A- is a second register, M- is a irreducible polynomial register, and C- is a field element register. An the irreducible polynomial is loaded left justified in the M-register, a field element to be inverted is loaded left justified in the C-register, and a single "1" is loaded in an LSB bit of the B-register. The field element is then inverted in 2n+2 system clock cycles where n is a field size associated with the field element.

Abstract: A Galois Field arithmetic logic unit (GF ALU) circuit (200) that generates a GF product of size M includes a first and a second input field element register (205, 210), a result field element register (215), a plurality, I, of subfield sets of logic gates (255, 260, 265), a plurality, S, of extension sets of logic gates (270, 275), and 3M switches (135). M is equal to S multiplied by I. A Galois Field of size M, S, and I each has an optimal normal basis. The first and second input field element registers (205, 210) are alternately coupled to the result field element register (215) by the I subfield sets of logic gates (255, 260, 265) in a first configuration and by the S extension sets of logic gates (270, 275) in a second configuration. The 3M switches (135) alternate the first and second configurations.

Abstract: A finite field inverse circuit (600) for use in an elliptic curve processor (12). The finite field inverse circuit (600) comprises a control circuit (610) and a data circuit (660). The data circuit (610) comprises a data multiplexer (668) for coupling the contents of one of three registers (662, 664, 680) to a finite field arithmetic logic unit (122). A first plurality of bits representing the finite field element to be inverted is initially loaded into a first one of the three registers. The control circuit (660) comprises a shift register (614) suitable for storing a second plurality of bits representing a size of the finite field element to be inverted.

Abstract: A programmable versatile digital signal processing system architecture (FIG. 5) allows the implementation of functions for transmitting and receiving a variety of narrow and wide-band communication signaling schemes. The flexibility of the architecture (FIG. 5) makes it possible to receive and transmit many different spectral communication signals in real time by implementing signal processing functions such as filtering, spreading, de-spreading, rake filtering, and equalization under the direction of program instructions (1300, 1400, 1500, 1600).

Abstract: A circuit and method for computing an exponential signal x.sup.g is provided. The circuit includes a logarithm converter which converts an input signal to binary word that represents the logarithm of an input signal x. A first shift register shifts the binary word in a bit-wise fashion to produce a first intermediate value; while a second shift register shifts the binary word in a bit-wise fashion to produce a second intermediate value. The shift registers may be implemented using multiplexers. The shifting operations are equivalent to multiplying the intermediate values by a factor which is a power of two. The first intermediate value is either added to or subtracted from the second intermediate value to produce a combined value. An inverse-logarithm converter converts the combined value to the exponential signal.

Abstract: A computational array (120) includes at least one computing element (130) that calculates multiple terms in a polynomial. The computing element (130) obtains an input value of each variable in each of the multiple terms and a subscript uniquely identifying the variable, The computing element (130) reads a term identifier and an exponent corresponding to the variable at a memory location based on the subscript, The computing element (130) multiplies the input value by a selected weight value and multiplies the input value by itself a number of times based on the exponent and stores the result at a memory location corresponding to the term identifier. The computing element (130) calculates multiple terms by distinguishing each of the terms with the term identifier.