The Weil and Tate pairings are a popular new gadget in cryptography and have found many applications, including identity-based cryptography. In particular, the pairings have been used for key exchange protocols. This paper studies the bit security of keys obtained using protocols based on pairings (that is, we show that obtaining certain bits of the common key is as hard as computing the entire...

Mammalian hibernators are unique in their ability to cope with freezing temperatures. Some mammals can lower their body temperatures to as low as –2.9°C for several weeks. In the golden-mantle ground squirrel, Spermophilus lateralis, this period of low body temperature, called torpor, is interrupted by arousals during which body temperature rises as much as 30°C in a matter of hours. Squirrels ...

We initiate the complexity theoretic study of the problem of computing the bits of (real) algebraic numbers. This extends the work of Yap on computing the bits of transcendental numbers like π, in Logspace. Our main result is that computing a bit of a fixed real algebraic number is in C=NC 1⊆ L when the bit position has a verbose (unary) representation and in the counting hierarchy when it has ...