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Message-ID: <572A871B.5070303@openwall.com>
Date: Thu, 5 May 2016 02:34:51 +0300
From: Alexander Cherepanov <ch3root@...nwall.com>
To: oss-security@...ts.openwall.com
Subject: Re: broken RSA keys
On 2016-05-04 15:42, Solar Designer wrote:
> Now to the point: some of the keys do look to me like they're a result
> of software bugs in key generation. Specifically, as it was noticed and
> noted by many before, Phuctor's list of broken keys includes many with
> non-prime e of the form intended_e*(2^32+1) - that is, with the 32-bit
> value duplicated across 64 bits. (I wrote it that way to show that all
> such e's are non-prime.)
Indeed. From 225 keys listed at http://phuctor.nosuchlabs.com/phuctored,
152 ones have modulus and exponent divisible by 2**32+1:
$ curl -s http://phuctor.nosuchlabs.com/phuctored |
> perl -Mbigint -ln0e 'print join " ", map { $_ % (2**32 + 1) } ($1,
$2) while m{RSA Modulus .N.:.*?<td>(\d+)<.*?<td>(\d+)<}sg' |
> grep -c '^0 0$'
152
Modulus and exponent are divisible by 2**32+1 or not simultaneously.
--
Alexander Cherepanov
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