Successful implementation of elliptic curve cryptographic systems primarily depends on the efficient and reliable arithmetic circuits for finite fields with very large orders. Thus, the robust encryption/decryption algorithms are elegantly needed. Multiplication would be the most important finite field arithmetic operation. It is much more complex compared to the finite field addition. It is al...

In this paper the first code-disjoint totally self-checking carry-select adder is proposed. The adder blocks are fast ripple adders with a single NAND-gate delay for carry-propagation per cell. In every adder block both the sum-bits and the corresponding inverted sum-bits are simultaneously implemented. The parity of the input operands is checked against the XOR-sum of the propagate signals. Fo...

It has previously been shown that probabilistic quantum logic operations can be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several new quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they can be...

Quantum information offers the promise of being able to perform certain communication and computation tasks that cannot be done with conventional information technology (IT). Optical Quantum Information Processing (QIP) holds particular appeal, since it offers the prospect of communicating and computing with the same type of qubit. Linear optical techniques have been shown to be scalable, but t...

A new method is presented for designing space compactors for either deterministic testing or pseudorandom testing. A tree of elementary gates (AND, OR, NAND, NOR) is used to combine the outputs of the circuit-under-test (CUT) in a way that zero-aliasing is guaranteed with no modification of the CUT. The elementary-tree is synthesized by adding one gate at a time without introducing redundancy. ...

Inspired by the classical Poincaré criterion about instability of orientation preserving minimizing closed geodesics on surfaces, we investigate relation intertwining and variational properties periodic solutions a non-autonomous Lagrangian finite dimensional Riemannian manifold. We establish general for priori detecting linear orbit manifold (maybe not Legendre convex) simply looking at parity...

A bstract We perform a bootstrap analysis of mixed system four-point functions bosonic and fermionic operators in parity-preserving 3d CFTs with O ( N ) global symmetry. Our results provide rigorous bounds on the scaling dimensions )-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live isolated islands space CFT data. focus cases = 1, 2, 4, 8, which have applicat...

The central hypothesis in the theory of resource-bounded measure 6] is the assertion that NP does not have measure 0 in Exponential Time. This is a quantitative strengthening of the assertion that NP does not equal P. We show that the analog in P of this hypothesis fails dramatically. In fact, we show that nondeterministic time n to the power (1=11) has measure zero in P. These follow as conseq...

It has previously been shown that probabilistic quantum logic operations can be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they can be com...