We consider the problem of computing the Hamming weight of an n-bit vector using a circuit with gates for GF2 addition and multiplication only. We show the number of multiplications necessary and sufficient to build such a circuit is n - |n| where |n| is the Hamming weight of the ... more >>>

We present constant-round concurrently secure (sound) resettable
zero-knowledge (rZK-CS) arguments in the bare public-key (BPK)
model. Our constructions deal with general NP ZK-arguments as well
as with highly efficient ZK-arguments for number-theoretic
languages, most relevant to identification scenarios. These are the
first constant-round protocols of ... more >>>

In1985, Shmuley proposed a theorem about intractability of Composite Diffie-Hellman [Sh85]. The Theorem of Shmuley may be paraphrased as saying that if there exist a probabilistic poly-time oracle machine which solves the Diffie-Hellman modulo an
RSA-number with odd-order base then there exist a probabilistic algorithm which factors the modulo. ... more >>>