AW: RSA key sizes

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AW: RSA key sizes

thomas.beckmann
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

> -----Urspr√ľngliche 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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Re: AW: RSA key sizes

Tan Eng Ten
Cool.. but the key below has 128 bytes in total, but reported as being
1023-bit

-----
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:

-----
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
>
>
>>-----Urspr√ľngliche 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?
>>______________________________________________________________________
>>OpenSSL Project                                 http://www.openssl.org
>>User Support Mailing List                    [hidden email]
>>Automated List Manager                           [hidden email]
>>
>
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>
>
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RE: AW: RSA key sizes

JoelKatz

> Cool.. but the key below has 128 bytes in total, but reported as being
> 1023-bit
>
> -----
> 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)
> -----

        Half of the 128-byte numbers can be expressed in 1,023 bits. This one can,
since it's high nibble is '5' or '0100'. The leading zero can be omitted,
resulting in 1,023 bits.

> 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:
>
> -----
> 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)
> -----

        Why is what? This number requires 1,024 bits to express it. The lead nibble
is 'd' in hex, which is '1101', so there's no leading zero in the nibble
that can be dropped.

        DS


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