is breaking RSA at least as hard as factoring or vice-versa?

2006-04-02 Thread Travis H.
So I'm reading up on unconditionally secure authentication in Simmon's
Contemporary Cryptology, and he points out that with RSA, given d,
you could calculate e (remember, this is authentication not
encryption) if you could factor n, which relates the two.  However,
the implication is in the less useful direction; namely, that
factoring n is at least as hard as breaking RSA.  As of the books
publication in 1992, it was not known whether the decryption of almost
all ciphers for arbitrary exponents e is as hard as factoring.

This is news to me!  What's the current state of knowledge?
--
Security Guru for Hire http://www.lightconsulting.com/~travis/ --
GPG fingerprint: 9D3F 395A DAC5 5CCC 9066  151D 0A6B 4098 0C55 1484

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Re: Unforgeable Blinded Credentials

2006-04-02 Thread Apu Kapadia


I came across the same problem a couple of years ago (and indeed  
iterated through private/public key solutions with a colleague). The  
problem is that you can still give your private key to somebody else.  
There's no real deterrent unless that private key is used for many  
other purposes, thereby discouraging sharing. But if that's the case,  
there's no real anonymity anymore, since the private key is tied to  
the person's identity.


I found that Chameleon Certificates had nice properties. You have a  
master certificate that lists all your attributes. For  
authentication, you generate an unlinkable slave certificate with any  
subset of attributes. You have to possess the master certificate at  
time of use to generate the slave certificate, so you can't pass a  
slave certificate to a friend for later use. Then you just need to  
ensure that the master certificate includes personal details like  
credit card number, SSN, etc. to deter sharing of master  
certificates. Note that the slave certificates won't have this  
information, so this personal information is safe as long as the  
master certificate is not leaked. Since sharing an attribute amounts  
to sharing all your attributes, including personal information, this  
property serves as a good deterrent. Maybe somebody else can comment  
on the technical viability + crypto details of the paper.


P. Persiano and I. Visconti. An Anonymous Credential System and a  
Privacy-Aware PKI. In Information Security
and Privacy, 8th Australasian Conference, ACISP 2003, volume 2727 of  
Lecture Notes in Computer Science. Springer Verlag, 2003.
http://springerlink.metapress.com/openurl.asp? 
genre=articleissn=0302-9743volume=2727spage=27


Here's the abstract:
 In this paper we present a non-transferable anonymous credential  
system that is based on the concept of a chameleon certificate. A  
chameleon certificate is a special certificate that enjoys two  
interesting properties. Firstly, the owner can choose which  
attributes of the certificate to disclose. Moreover, a chameleon  
certificate is multi-show in the sense that several uses of the same  
chameleon certificate by the same user cannot be linked together.


We adopt the framework of Brands [2] and our construction improves  
the results of Camenisch et al. [5] and Verheul [16] since it allows  
the owner of a certificate to prove general statements on the  
attributes encoded in the certificate and our certificates enjoy the  
multi-show property.


Apu

--
Apu Kapadia, Ph.D.
Research Fellow, Institute for Security Technology Studies (ISTS)
Dartmouth College, Hanover NH 03755, USA
http://www.cs.dartmouth.edu/~akapadia/


On Apr 1, 2006, at 6:35 AM, Ben Laurie wrote:


It is possible to use blind signatures to produce anonymity-preserving
credentials. The general idea is that, say, British Airways want to
testify that I am a silver BA Executive Club cardholder. First I  
create
a random number (a nonce), I blind it, then send it to BA. They  
sign it

with their “this guy is a silver member” signing key, I unblind the
signature and then I can show the signed nonce to anyone who wants to
verify that I am silver. All they need to do is check the signature
against BA’s published silver member key. BA cannot link this nonce  
back

to me because they have never seen it, so they cannot distinguish me
from any other member.

However, anyone I show this proof to can then masquerade as a silver
member, using my signed nonce. So, it occurred to me that an easy  
way to

prevent this is to create a private/public key pair and instead of the
nonce use the hash of the public key. Then to prove my silver status I
have to show that both the hash is signed by BA and that I possess the
corresponding private key (by signing a nonce, say).

It seems to me quite obvious that someone must have thought of this
before - the question is who? Is it IP free?

Obviously this kind of credential could be quite useful in identity
management. Note, though, that this scheme doesn’t give me  
unlinkability
unless I only show each public/private key pair once. What I really  
need

is a family of unlinkable public/private key pairs that I can somehow
get signed with a single “family” signature (obviously this would need
to be unlinkably transformed for each member of the key family).

Permalink: http://www.links.org/?p=88

Cheers,

Ben.



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Re: Unforgeable Blinded Credentials

2006-04-02 Thread Adam Back
On Sat, Apr 01, 2006 at 12:35:12PM +0100, Ben Laurie wrote:
 However, anyone I show this proof to can then masquerade as a silver
 member, using my signed nonce. So, it occurred to me that an easy
 way to prevent this is to create a private/public key pair and
 instead of the nonce use the hash of the public key. Then to prove
 my silver status I have to show that both the hash is signed by BA
 and that I possess the corresponding private key (by signing a
 nonce, say).  It seems to me quite obvious that someone must have
 thought of this before - the question is who? Is it IP free?

Well I thought of this a few years ago also.  However I suspect you'd
find the same idea earlier as a footnote in Stefan Brands book.  (Its
amazing how much stuff is in there, I thought I found something else
interesting -- offline transferable cash, turns out that also was a
footnote referring to someone's MSc thesis.)

 Obviously this kind of credential could be quite useful in identity
 management. Note, though, that this scheme doesn’t give me
 unlinkability unless I only show each public/private key pair
 once. What I really need is a family of unlinkable public/private
 key pairs that I can somehow get signed with a single “family”
 signature (obviously this would need to be unlinkably transformed
 for each member of the key family).

This is harder, I thought about this a bit also.

I was thinking a way to do this would be to have a self-reblindable
signature.  Ie you can re-blind the certificate signature such that
the signature remains, but it is unlinkable.  I didn't so far find a
way to do this with any of the schemes.

So it would for example be related to the more recent publicly
re-encryptable Elgamal based signatures.  (Third party can re-encrypt
the already encrypted message with out themselves being able to
decrypt the message).


Brands also has a mechanism to simplify the use each cert once method.
He can have the CA reissue you a new cert without having to go through
the attribute verification phase.  Ie you present an old cert and get
it reblinded, and the CA does not even if I recall see what attributes
you have.  So you just periodically get yourself another batch.
Mostly does what you want just with some assistance from the CA.

Adam

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Re: is breaking RSA at least as hard as factoring or vice-versa?

2006-04-02 Thread Taral
On 4/2/06, Travis H. [EMAIL PROTECTED] wrote:
 So I'm reading up on unconditionally secure authentication in Simmon's
 Contemporary Cryptology, and he points out that with RSA, given d,
 you could calculate e (remember, this is authentication not
 encryption) if you could factor n, which relates the two.

This implication runs both ways. Given d and e (and pq), one can
compute p and q. Proving this is an exercise left to the reader.

--
Taral [EMAIL PROTECTED]
You can't prove anything.
-- Gödel's Incompetence Theorem

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Re: is breaking RSA at least as hard as factoring or vice-versa?

2006-04-02 Thread Greg Rose

At 1:41  -0600 2006/04/02, Travis H. wrote:

So I'm reading up on unconditionally secure authentication in Simmon's
Contemporary Cryptology, and he points out that with RSA, given d,
you could calculate e (remember, this is authentication not
encryption) if you could factor n, which relates the two.  However,
the implication is in the less useful direction; namely, that
factoring n is at least as hard as breaking RSA.  As of the books
publication in 1992, it was not known whether the decryption of almost
all ciphers for arbitrary exponents e is as hard as factoring.

This is news to me!  What's the current state of knowledge?


It's conceivable that there might be a way to decrypt RSA messages 
without knowing d. If you don't know d, you still can't factor n. 
Whereas if you can factor n, you can find d, and decrypt messages. So 
the problems are not equivalent, and the RSA problem might be easier 
than the integer factorization problem. (At least, the above is my 
understanding.)


Greg.

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