منابع مشابه
Computing Mod Without Mod
Encryption algorithms are designed to be difficult to break without knowledge of the secrets or keys. To achieve this, the algorithms require the keys to be large, with some algorithms having a recommend size of 2048-bits or more. However most modern processors only support computation on 64-bits at a time. Therefore standard operations with large numbers are more complicated to implement. One ...
متن کاملReduction mod p of Subgroups of the Mordell-Weil Group of an Elliptic Curve
Let E be an elliptic curve defined over Q. Let Γ be a free subgroup of rank r of E(Q). For any prime p of good reduction, let Γp be the reduction of Γ modulo p and Ep be the reduction of E modulo p. We prove that if E has CM then for all but o(x/ log x) of primes p ≤ x, |Γp| ≥ p r r+2 + , where (p) is any function of p such that (p)→ 0 as p→∞. This is a consequence of two other results. Denote ...
متن کاملLower Bounds for (MOD p - MOD m) Circuits
Modular gates are known to be immune for the random restriction techniques of Ajtai Ajt83], Furst, Saxe, Sipser FSS84], Yao Yao85] and H astad H as86]. We demonstrate here a random clustering technique which overcomes this diiculty and is capable to prove generalizations of several known modular circuit lower bounds of Barrington, Straubing, Th erien BST90], Krause and Pudll ak KP94], and other...
متن کاملA Degree-Decreasing Lemma for (MOD q - MOD p) Circuits
Consider a (MODq;MODp) circuit, where the inputs of the bottom MODp gates are degree-d polynomials with integer coefficients of the input variables (p, q are different primes). Using our main tool — the Degree Decreasing Lemma — we show that this circuit can be converted to a (MODq;MODp) circuit with linear polynomials on the input-level with the price of increasing the size of the circuit. Thi...
متن کاملMod 2 and Mod 5 Icosahedral Representations
We shall call a simple abelian variety A/Q modular if it is isogenous (over Q) to a factor of the Jacobian of a modular curve. In this paper we shall call a representation ρ̄ : GQ→GL2(F̄l) modular if there is a modular abelian variety A/Q, a number field F/Q of degree equal to dimA, an embedding OF ↪→ End(A/Q) and a homomorphism θ : OF→F̄l such that ρ̄ is equivalent to the action of GQ on the ker θ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1991
ISSN: 0021-8693
DOI: 10.1016/0021-8693(91)90287-i