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The new proposal belongs to the ``multivariate quadratic\'\'
family but the trap-door is different from existing methods,
and is simpler.
Known quantum algorithms do not appear to help an adversary
attack this trap-door. (Beyond the asymptotic
square-root-speedup which applies to all oracle search
We consider in this paper the problem of finding optimal CAS\'s for incomplete AS\'s. The paper introduces some notions including the connected-super-forbidden-family and the lower-forbidden-family for AS\'s. We show that an optimal CAS can be derived from some smaller sized BIP whose variables (constraints, resp.) are based on the connected-super-forbidden-family (lower-forbidden-family, resp.) of the given AS. The paper further builds the close relationship between the problem of finding optimal CAS\'s and the set covering problem (SCP). We prove that the problem of finding a CAS with minimum cardinality of the primitive share set (or minimum average information rate) is equivalent to the SCP, and thus is NP-hard. Other contributions of the paper include: 1) two types of AS\'s are recognized so that we can construct the corresponding optimal CAS\'s directly; and 2) a greedy algorithm is proposed to find CAS\'s with smaller worst information rate.
In this paper, we propose two secret sharing schemes using non-abelian groups. One scheme is the special case where all the participants must get together to recover the secret. The other one is a $(t,n)$-threshold scheme that is a combination of Shamir\'s scheme and the group-theoretic scheme proposed in this paper.
In this paper, we study pairings on elliptic curves over extension fields from the point of view of accelerating the Miller\'s algorithm to present further advantage of pairing-friendly curves over extension fields, not relying on the much faster field arithmetic. We propose new pairings on elliptic curves over extension fields can make better use of the multi-pairing technique for the efficient implementation. By using some implementation skills, our new pairings could be implemented much more efficiently than the optimal ate pairing and the optimal twisted ate pairing on elliptic curves over extension fields. At last, we use the similar method to give more efficient pairings on Estibals\'s supersingular curves over composite extension fields in parallel implementation.
In this paper, we analyze the security of using Bitcoin for fast payments, where the time between the exchange of currency and goods is short (i.e., in the order of few seconds). We focus on double-
spending attacks on fast payments and demonstrate that these attacks can be mounted at low cost on currently deployed versions of Bitcoin. We further show that the measures recommended by Bitcoin developers for the use of Bitcoin in fast transactions are not always effective in resisting double-spending; we show that if those recommendations are integrated in future Bitcoin implementations, double-spending
attacks on Bitcoin will still be possible. Finally, we leverage on our findings and propose a lightweight countermeasure that enables the detection of double-spending attacks in fast transactions.
length $m\\propto c_0^2$, where $c_0$ is the number of colluders.
In this paper we simplify the security proofs for this code,
making use of the Bernstein inequality and Bennett inequality instead of
the typically used Markov inequality. This simplified proof technique also slightly improves the tightness of the bound on the false negative error probability. We present new results on code length optimization, for both small and asymptotically large coalition sizes.