AW: AW: RSA key sizes

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AW: AW: RSA key sizes

thomas.beckmann
see below

> -----Ursprüngliche Nachricht-----
> Von: [hidden email]
> [mailto:[hidden email]]Im Auftrag von Tan Eng Ten
> Gesendet: Mittwoch, 17. August 2005 11:28
> An: [hidden email]
> Betreff: Re: AW: RSA key sizes
>
>
> Cool.. but the key below has 128 bytes in total, but reported
> as being
> 1023-bit

Because it only consits of 1023 bit and a leading zero... which is not
counted.

>
> -----
> Modulus (1023 bit):
>       5d:10:63:d3:d8:00:2a:50:ab:65:8a:f0:92:83:b0:
>       6a:39:e3:0c:38:aa:f5:32:23:71:25:8e:4a:8d:50:
>       fd:80:a3:95:59:33:27:92:88:d0:1d:28:dd:05:7c:
>       b6:a0:5e:68:9e:b4:70:c9:bd:28:8a:fb:6d:95:0a:
>       38:83:f9:8d:15:b1:3a:33:bf:d7:ab:1c:5e:1b:d3:
>       d6:c1:1a:f8:05:7f:ef:22:23:48:ef:48:a2:8d:99:
>       90:10:81:8a:54:dd:16:9e:7f:d0:88:a8:b7:34:68:
>       be:4d:8f:dc:4b:5d:d9:72:c5:a4:88:a6:40:fa:f2:
>       f7:16:79:a8:35:3d:f2:ad
> Exponent: 3 (0x3)
> -----
>
> I notice that for 1024-bit RSA key generated by openssl, the
> modulus has
> 129 bytes but having the first byte = 0. Why is this?, for example:

This is correct because in BER a leading "1" tells you, that this is a
negativ integer. But while we are working with positve integer we have to
add at least one leading "0"... so we have to add one byte.

>
> -----
> Modulus (1024 bit):
>      00:d8:6e:77:67:5e:29:bb:4e:83:52:fe:fa:fc:58:
>      04:d8:07:3e:43:11:92:10:45:dc:f2:f7:7a:77:49:
>      91:cf:cc:0d:5e:ec:d9:44:15:2d:61:19:cd:9d:79:
>      9e:27:80:61:6c:a3:db:34:21:cf:87:60:7a:e4:d9:
>      a5:02:59:57:fb:4e:8c:e4:32:fb:5e:cb:1a:99:7b:
>      76:b2:79:ae:2f:1f:62:1d:f6:fc:9e:32:e5:bd:46:
>      8f:c7:05:63:aa:10:2c:be:60:46:4a:44:c5:63:94:
>      b1:ab:d5:c5:33:cd:d7:69:f0:2b:36:54:dd:82:92:
>      66:6c:0d:50:81:a1:23:79:67
> Exponent: 65537 (0x10001)
> -----
>
>
> [hidden email] wrote:
> > The main reason why we take 512, 768, 1024, 2048, 4096,...
> bit is, that
> > these numbers are multiples of 8 ans though can be
> fractioned into bytes
> > (1024 bit = 128 byte).
> > Withe the increase of calculation power the key size was
> increased, in the
> > end by doubling the number of bits.
> >
> > To answer our second question: A real 1024-bit-key must
> have at least 1017
> > bit, so it consits of 128 byte (= 1024 bit) with 7 leading zeros.
> >
> > Regards
> >
> > Thomas Beckmann
> >
> >
> >>-----Ursprüngliche Nachricht-----
> >>Von: [hidden email]
> >>[mailto:[hidden email]]Im Auftrag von Tan Eng Ten
> >>Gesendet: Mittwoch, 17. August 2005 08:22
> >>An: [hidden email]
> >>Betreff: RSA key sizes
> >>
> >>
> >>Hi all,
> >>
> >> This is a general crypto question and I hope someone
> >>could help me out.
> >>
> >> Often we use RSA of 512, 1024, 2048, 4096, etc. bit
> >>lengths. Are other
> >>sizes such as 520/1045 bit "valid"? Mathematically, it should
> >>work, but
> >>are there reasons why odd sizes are not to be used?
> >>____________________________________________________________
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