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SQUARING IN CYCLOTOMIC SUBGROUPS
"... Abstract. 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 ..."
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Abstract. 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 previouslyknown exponentiation algorithms when the exponent has low Hamming weight. Our algorithms can be adapted to accelerate the final exponentiation step of pairing computations. 1.
DOUBLEEXPONENTIATION IN FACTOR4 GROUPS AND ITS APPLICATIONS
"... Abstract. In previous work we showed how to compress certain primeorder subgroups of the cyclotomic subgroups of orders 22m + 1 of the multiplicative groups of F ∗ 24m by a factor of 4. We also showed that singleexponentiation can be efficiently performed using compressed representations. In this ..."
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Abstract. In previous work we showed how to compress certain primeorder subgroups of the cyclotomic subgroups of orders 22m + 1 of the multiplicative groups of F ∗ 24m by a factor of 4. We also showed that singleexponentiation can be efficiently performed using compressed representations. In this paper we show that doubleexponentiation can be efficiently performed using factor4 compressed representation of elements. In addition to giving a considerable speed up to the previously known fastest singleexponentiation algorithm for general bases, doubleexponentiation can be used to adapt our compression technique to ElGamal type signature schemes. 1.
TORUSBASED Compression by . . .
, 2010
"... We extend the torusbased compression technique for cyclotomic subgroups and show how the elements of certain subgroups in characteristic two and three fields can be compressed by a factor of 4 and 6, respectively. Our compression and decompression functions can be computed at a negligible cost. In ..."
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We extend the torusbased compression technique for cyclotomic subgroups and show how the elements of certain subgroups in characteristic two and three fields can be compressed by a factor of 4 and 6, respectively. Our compression and decompression functions can be computed at a negligible cost. In particular, our techniques lead to very efficient exponentiation algorithms that work with the compressed representations of elements and can be easily incorporated into pairingbased protocols that require exponentiations or products of pairings.