Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 10 of 10 for “"Galois Field"”.
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Exploring platform (semi)groups for non-commutative key-exchange protocols
… explore polycyclic groups generated from number fields as platform for the AAG key-exchange protocol. This is done by implementing four different variations of the length-based attack, one of the major attacks for AAG, and submitting polycyclic groups to all four variations with a variety of …
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On Dihedral Codes and the Double Circulant Conjecture for Binary Extended Quadratic Residue Codes
… Let S = F2[x]/⟨1 + xk⟩ where F2 is the Galois field of two elements. We identify the binary extended quadratic residue codes of length 2k as principal left ideals in the group algebra F2Dk where Dk is the dihedral group of order 2 k. We prove that these codes have a double circulant …
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FPGA Implementations of Elliptic Curve Cryptography and Tate Pairing over Binary Field
… The bases of both ECC and Tate pairing are Galois field arithmetic units. In this thesis, I propose the FPGA implementations of the elliptic curve point multiplication in GF (2283) as well as Tate pairing computation on supersingular elliptic curve in GF (2283). I have designed and …
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Exploring fields with shift registers
… used in the AES algorithm are generated by field extensions of the Galois field over two elements, called GF(2). Therefore, understanding the field extensions provides a method of analysis, potentially efficient implementation, and efficient attacks. Different polynomials can be used to …
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High-level synthesis and its application in the design of Reed-Solomon decoders
… of arithmetic circuits dealing with finite field elements, such as Galois Field ${\rm GF}(2\sp{m}).$ A case study for such a design is versatile time-domain Reed-Solomon RS(n,k) decoders. The structure of the time-domain RS decoder is simple and modular which makes it fit for VLSI …
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Error-Correcting Codes Associated With Generalized Hadamard Matrices Over Groups
… codewords consist of real numbers in finite Galois field <em>Gf</em>(<em> p</em>) can be associated in a simple way with each Butson Hadamard matrix <em>BH</em>(<em>p, q</em>), where <em>p</em> > 0 is a prime number. Distance properties of such codes are studied, as well as conditions for the …
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Torsion Subgroups Of Rational Elliptic Curves Over Odd Degree Galois Fields
… Theorem states that if K is a number field and E/K is an elliptic curve that the group of K-rational points E(K) is a finitely generated abelian group, i.e. E(K) = Z^{r_K} ⊕ E(K)_tors, where r_K is the rank of E and E(K)_tors is the subgroup of torsion points on E. Unfortunately, very …
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Torsion Subgroups of Rational Elliptic Curves Over Odd Degree Galois Fields
… Theorem states that if K is a number field and E/K is an elliptic curve that the group of K-rational points E(K) is a finitely generated abelian group, i.e. E(K) = Z^{r_K} ⊕ E(K)_tors, where r_K is the rank of E and E(K)_tors is the subgroup of torsion points on E. Unfortunately, very …
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Efficient Binary Field Multiplication on a VLIW DSP
… We present several strategies for different field sizes and field polynomials, and show that a 360MHz DSP easily outperforms the 500MHz ARM.