The number of zero bits added to the message is the same as the width of the checksum (what I call c); in this case four bits were added. The divisor is a c+1-bit number known as the generator polynomial. Figure 1. An example of modulo-2 binary division The modulo-2 division ...
We describe an FEC code using an ordered pair (n, k) in which k denotes the data payload and n denotes the length and symbols of the complete FEC codeword. FEC starts at the transmitter, where the FEC encoder uses a complex polynomial function to oversample the data block to ge...
The use of FPGA Spartan XC3S400-4PQG208C in this area is new, but their utilization is intriguing for their security capabilities as well as for their performance and power characteristics. In addition, the nonvolatility of FPGA is useful for polynomial and key storage within devices, and ...
The hardware implementation uses Barrett reduction, which can be implemented using only shifting and addition operations. Therefore, when analysing the implementation of polynomial multiplication, the rejection loop and the polynomial arithmetic units bear a high degree of parallelism, resulting in a large...
The Toffoli gate (controlled-controlled-NOT gate) is one typical three-qubit gate, it plus a Hadamard gate form a universal set of gates in quantum computation. We present an efficient method to implement the Toffoli gate using an array of coupled caviti
As a progressive security strategy, the zero trust model has attracted notable attention and importance within the realm of network security, especially in the context of the Internet of Things (IoT). This paper aims to evaluate the current research rega
All we need to do is choose a few random values, solve for the root of the polynomial, and sieve the values close to zero. At this point we could just call it good enough: if you throw enough stones in random directions, you're bound to break a window sooner or later....
// Performs carryless multiplication of the upper pairs of source and constants and the lower pairs of source and constants, // then folds them into target using carryless addition. [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Vector128<ulong> FoldPolynomialPair(Vector128<ulong> ...
In addition, the field of the coefficients of the parameterizations is either of minimal degree or involves one possibly unneeded square root. We prove upper bounds on the size of the coefficients of the output parameterizations and compare these bounds to observed ...
Here the matrix Y is formed in the same way as X was in the other case, as shown in Figure 9. For this example, a memory term has been included and the number of polynomial orders included has been reduced. To solve for w, we need to get the inverse of Y. Y is not square (...