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

```Yet another paper on the topic:

Deterministic Polynomial Time Equivalence of Computing the RSA Secret
Key and Factoring
by Jean-Sebastien Coron and Alexander May
http://eprint.iacr.org/2004/208

Max

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

```Dan Boneh had an interesting paper on this topic a few years back
giving some evidence that that breaking RSA might in fact be easier
than factoring.However, it defines breaking RSA as being able
to DO the private-key operation, not as knowing the private key
(because the latter lets you factor).

Boneh and Venkatesan. Breaking RSA may not be equivalent to
factoring. Eurocrypt '98. Springer-Verlag LNCS 1233. 1998.

--Sean

Sean W. Smith, Ph.D.  [EMAIL PROTECTED]  www.cs.dartmouth.edu/~sws/
Department of Computer Science, Dartmouth College, Hanover NH USA

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

```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?

```
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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