phc-discussions - Re: [PHC] Information theoretic security for delegated hardening was: winner selection

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Message-ID: <CAOLP8p7Q7sMWxsy7_eTG4pxfMfPFV7dye+3T0B82YXAe52TMzw@mail.gmail.com>
Date: Fri, 17 Apr 2015 06:39:12 -0700
From: Bill Cox <waywardgeek@...il.com>
To: "discussions@...sword-hashing.net" <discussions@...sword-hashing.net>
Subject: Re: [PHC] Information theoretic security for delegated hardening was:
 winner selection

On Mon, Apr 13, 2015 at 5:17 PM, Andy Lutomirski <luto@...capital.net>
wrote:

> Can you elaborate on this straightforward way?
>
> Thanks,
> Andy
>

I found this:

     https://bitcointalk.org/index.php?topic=311000.0

The scheme seems similar to Makwa, but simpler.  Here's the math from that
link:

public params:

n=pq (primes p & q deleted at setup)
g=shared generator
e=2^(2^w)-1 ie a big, big number w is work factor
    (Bill: why subtract 1?)
y=g^e mod n (generated cheaply at setup, or computable one-off cost
afterwards)

blind:

m=message
b=random blinding factor
r=g^b*m (broacast r to miners)
    (Bill: this is mod n, right?  Also, that's (g^b)*m, not g^(b*m))

work:

s=r^e mod n (expensive because e is big and carm(n)=(p-1)(q-1)/2 is unknown)

unblind:

u=y^b (unblinding factor)
    (Bill: again mod n, right?)
m^e = s/u (as s/y^b=r^e/g^{be}=g^{be}*m^e/g^{be})
    (Bill: by /u, I assume we find g-inverse, and compute y differently)


This is simpler than Makwa, but I haven't put any thought into attacking
it.  Thomas Porin, what do you think of this again?

Bill

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