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So in a single 32-bit multiplier, two 16-bit multiplications (N/2 multiplication) or one 32-bit multiplication (N bit multiplication) can be performed.
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Here we can split the partial product bits of the N b multiplier in such a way that N/2 b multiplication can be performed in the least significant part (LSP) of the multiplier in parallel with another N/2 b multiplication in the most significant part (MSP).
If this number is multiplied by a constant c n with B c bits, the resulting B c × B x multiplication can be divided into several smaller multiplications by rearranging the partial sum terms: c n · x ⏟ B c × B x Mult.
Furthermore, the laws of operations of addition and multiplication can be extended to apply to differences.
Multiplication can be thought of as repeated addition.
One complex multiplication can be represented by four times of real multiplications.
This paper proposes systolic vector m-bit GF(p) and GF 2m) multipliers (m= log2p), where four numbers of m2-bit GF multiplications can be done in parallel.
Similarly, twelve and sixteen numbers of GF 2m4) and m4-bit GF(p) multiplications can be done in parallel respectively.
It can be noticed, however, that if we select N=2 m,m=1,2,…, then the multiplications can be replaced by bit shifts which simplifies the implementation.
One bit can be embedded in encrypted domain by modifying magnitude relationships between the encrypted LSB values of two adjacent pixels with homomorphic multiplication.
Multiplication by a positive number can be thought of as stretching; multiplying by a negative number makes something shrink.
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