[sf-lug] Ex 11.7 Exponentiation (understandable) & RSA algorithm (not so!)
Alex Kleider
a_kleider at yahoo.com
Mon Jan 12 11:52:24 PST 2009
when I went to school, the three horizontal lines meant "same as" or "equivalent to." Has that changed?
Also, how do you generate that symbol with your keyboard??????
a_kleider at yahoo.com
--- On Mon, 1/12/09, Thomas DiZoglio <tomdiz at yahoo.com> wrote:
> From: Thomas DiZoglio <tomdiz at yahoo.com>
> Subject: Re: [sf-lug] Ex 11.7 Exponentiation (understandable) & RSA algorithm (not so!)
> To: "Asheesh Laroia" <asheesh at asheesh.org>, "jim" <jim at well.com>
> Cc: sf-lug at linuxmafia.com
> Date: Monday, January 12, 2009, 10:28 AM
> I don't think that is an equal sign. It has 3 horizontal
> lines, not two. Not sure what that means, but think it is
> "inverse".
> -------------------
> t0md
>
>
> --- On Mon, 1/12/09, jim <jim at well.com> wrote:
>
> > From: jim <jim at well.com>
> > Subject: Re: [sf-lug] Ex 11.7 Exponentiation
> (understandable) & RSA algorithm (not so!)
> > To: "Asheesh Laroia"
> <asheesh at asheesh.org>
> > Cc: sf-lug at linuxmafia.com
> > Date: Monday, January 12, 2009, 10:13 AM
> > i'm sorry too: i still don't get it. for their
>
> > example:
> > 3 * x = 1 (mod 11)
> > their solution is 4.
> >
> > i read this as x = 4, and therefore
> > 3 * 4 = 1 (mod 11)
> >
> > assuming i'm reading correctly, the mystery is
> > how to understand 1(mod 11) == 12
> > i read 1(mod 11) as 1%11 == the remainder after
> > 11 is divided into 1: integer arithmetic 1/11 == 0
> > and 1%11 yields 1.
> >
> > if my assumption is incorrect, then the mystery is
> > 3 * x = 1(mod 11)
> >
> >
> >
> > On Mon, 2009-01-12 at 09:09 -0800, Asheesh Laroia
> wrote:
> > > On Mon, 12 Jan 2009, jim wrote:
> > >
> > > > i'd like verification of my
> understanding of
> > this:
> > > > "Let d be the reciprocal of e mod
> r."
> > >
> > > > my arithmetic:
> > > > if e is 35 and r is 9111,
> > > > then d = 1/(35%9111) ## == 1/35 ==
> 0.028571429
> > >
> > > No, sorry! Reciprocal isn't defined that way
> in
> > modulo arithmetic. I'm
> > > glad you asked.
> > >
> > > Quoth Wikipedia: "In modular arithmetic, the
> > modular multiplicative
> > > inverse of x is also defined: it is the number a
> such
> > that a*x ≡ 1 (mod
> > > n). This multiplicative inverse exists if and
> only if
> > a and n are coprime.
> > > For example, the inverse of 3 modulo 11 is 4
> because
> > it is the solution to
> > > 3*x ≡ 1 (mod 11). The extended Euclidean
> algorithm
> > may be used to compute
> > > it."
> > >
> > > In modular arithmetic, 1/a mod b is an *integer*
> (iff
> > a and b are
> > > relatively prime).
> > >
> > > There are some Java (not JavaScript) calculators
> for
> > this on the web, e.g.
> > >
> >
> http://www.mtholyoke.edu/~mpeterso/Applets/CalculatorApplet.html
> > . I
> > > haven't found any working ones in JavaScript
> yet;
> > perhaps you or another
> > > list member can.
> > >
> > > -- Asheesh.
> > >
> > > --
> > > You're definitely on their list. The
> question to
> > ask next is what list it is.
> > > _______________________________________________
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