Computation of several cyclotomic Swan subgroups

Cyclotomic Swan subgroups and primitive roots

Squaring in cyclotomic subgroups

We propose new squaring formulae for cyclotomic subgroups of certain finite fields. Our formulae use a compressed representation of elements having the property that decompression can be performed at a very low cost. The squaring formulae lead to new exponentiation algorithms in cyclotomic subgroups which outperform the fastest previously-known exponentiation algorithms when the exponent has lo...

On the Linear Complexity of Ding-Helleseth Generalized Cyclotomic Binary Sequences of Order Four and Six

We propose a new computation method for the linear complexity and the minimal polynomial of Ding-Helleseth-generalized cyclotomic sequences. We will find the linear complexity of DingHelleseth-generalized cyclotomic sequences of order four and six and make the results of Tongjiang Yan et. al [19] about the sequences of order four more specific. 2010 Mathematics Subject Classifications: 11B50, 9...

Factor-4 and 6 compression of cyclotomic subgroups of and

Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields F2m and F3m , respectively, have been used to implement pairing-based cryptographic protocols. The pairing values lie in certain prime-order subgroups of the cyclotomic subgroups of orders 22m+1 and 32m−3m+1, respectively, of the multiplicative groups F∗ 24m and F∗ 36m . It was previousl...

Factor - 4 and 6 Compression of Cyclotomic Subgroups

Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields F2m and F3m , respectively, have been used to implement pairing-based cryptographic protocols. The pairing values lie in certain prime-order subgroups of the cyclotomic subgroups of orders 22m+1 and 32m−3m+1, respectively, of the multiplicative groups F∗ 24m and F∗ 36m . It was previousl...