From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (majordomo@vger.kernel.org) by vger.kernel.org via listexpand id S271924AbTHOWQ2 (ORCPT ); Fri, 15 Aug 2003 18:16:28 -0400 Received: (majordomo@vger.kernel.org) by vger.kernel.org id S271969AbTHOWQ2 (ORCPT ); Fri, 15 Aug 2003 18:16:28 -0400 Received: from mail.jlokier.co.uk ([81.29.64.88]:59777 "EHLO mail.jlokier.co.uk") by vger.kernel.org with ESMTP id S271924AbTHOWQ0 (ORCPT ); Fri, 15 Aug 2003 18:16:26 -0400 Date: Fri, 15 Aug 2003 23:16:08 +0100 From: Jamie Lokier To: Matt Mackall Cc: M?ns Rullg?rd , linux-kernel@vger.kernel.org Subject: Re: [RFC][PATCH] Make cryptoapi non-optional? Message-ID: <20030815221608.GC19707@mail.jlokier.co.uk> References: <20030813032038.GA1244@think> <20030813040614.GP31810@waste.org> <20030814165320.GA2839@speare5-1-14> <20030815001713.GD5333@speare5-1-14> <20030815093003.A2784@pclin040.win.tue.nl> <20030815004004.52f94f9a.davem@redhat.com> <20030815095503.C2784@pclin040.win.tue.nl> <20030815151116.GY325@waste.org> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <20030815151116.GY325@waste.org> User-Agent: Mutt/1.4.1i Sender: linux-kernel-owner@vger.kernel.org X-Mailing-List: linux-kernel@vger.kernel.org Matt Mackall wrote: > No, it's a premise stated at the beginning of the thread. We're > assuming perfect distribution for x and y. The problem here is that x > and y can be dependent or independent. If they're independent, then > there's no issue. If they're dependent (for instance correlated or > anticorrelated) then x^y biases toward zero or one. Which clearly has > less entropy. Sure, but that only holds when you assume a specific mix of independence and dependence among the bits. (Bits within x are independent of each other, and also within y, while at the same time x and y are dependent.) In general, bits from x^y do not have more bias towards zero or one than bits from x or y alone. Consider an extreme: x = [ random_bit_0, random_bit_0 ] y = [ random_bit_1, ~random_bit_1 ] Then: entropy(x) = entropy(y) = 1 entropy(x^y) = 2 This is no more arbitrary a mix of dependence and independence than your assumption. -- Jamie