what is RSA keylength the length of?

People talk about "the key length" in discussions of the RSA algorithm.

In learning about it at a textbook level I know that an RSA key is a
pair of integers. (One is used as a power to exponentiate a value and
ususally labeled e or d, the other as a divisor to then divide the
result usually labeled n.)

So what does "the key length," as a singular reference, refer to?? For
example if I hear about a "1024-bit RSA key" what is 1024 bits long?

Daniel Moore <taihaiteki@dslextreme.com> wrote:

> People talk about "the key length" in discussions of the RSA
> algorithm.
>
> In learning about it at a textbook level I know that an RSA key is a
> pair of integers. (One is used as a power to exponentiate a value and
> ususally labeled e or d, the other as a divisor to then divide the
> result usually labeled n.)
>
> So what does "the key length," as a singular reference, refer to?? For
> example if I hear about a "1024-bit RSA key" what is 1024 bits long?

It is the bit length of the modulus, i.e. if you've got an N bits RSA
key, then the modulus is a number smaller than 2^N.


Regards,
Ertugrul.


--
http://ertes.de/

Daniel Moore <taihaiteki@dslextreme.com> writes:


>People talk about "the key length" in discussions of the RSA algorithm.

>In learning about it at a textbook level I know that an RSA key is a
>pair of integers. (One is used as a power to exponentiate a value and
>ususally labeled e or d, the other as a divisor to then divide the
>result usually labeled n.)

NO. The pair of integers are two primes which are multiplied together to
give n. the exponents e and d are easily computed from those. e is usually
only about 6 bits long. d is roughly the same size as n.


>So what does "the key length," as a singular reference, refer to?? For
>example if I hear about a "1024-bit RSA key" what is 1024 bits long?

The product of that pair of primes.
And each of the two primes are half that length.

Unruh <unruh-spam@physics.ubc.ca> wrote:

> > People talk about "the key length" in discussions of the RSA algorithm.
> >
> > In learning about it at a textbook level I know that an RSA key is a
> > pair of integers. (One is used as a power to exponentiate a value
> > and ususally labeled e or d, the other as a divisor to then divide
> > the result usually labeled n.)
>
> NO. The pair of integers are two primes which are multiplied together
> to give n. the exponents e and d are easily computed from those. e is
> usually only about 6 bits long. d is roughly the same size as n.

Actually, Daniel is right. The modulus alone doesn't make a useful RSA
key. The modulus together with an exponent does. That would be a pair
of integers (he didn't talk about primes).


Regards,
Ertugrul.


--
http://ertes.de/

Ertugrul =?UTF-8?B?U8O2eWxlbWV6?= <es@ertes.de> writes:

>Unruh <unruh-spam@physics.ubc.ca> wrote:

>> > People talk about "the key length" in discussions of the RSA algorithm.
>> >
>> > In learning about it at a textbook level I know that an RSA key is a
>> > pair of integers. (One is used as a power to exponentiate a value
>> > and ususally labeled e or d, the other as a divisor to then divide
>> > the result usually labeled n.)
>>
>> NO. The pair of integers are two primes which are multiplied together
>> to give n. the exponents e and d are easily computed from those. e is
>> usually only about 6 bits long. d is roughly the same size as n.

>Actually, Daniel is right. The modulus alone doesn't make a useful RSA
>key. The modulus together with an exponent does. That would be a pair
>of integers (he didn't talk about primes).

Never said that modulus alone makes a useful RSA key.
The modulus is the product of two primes. The length of the modulus is the
length of the RSA "key" commonly quoted . The two exponents are --e is
assumes to be a small number for which exponentiation is easily calculated.
The exponent d is then easily calculated from the two primes. But it is the
length of the modulus that is used as the length of RSA.

(d is roughly of the same length, but its length is not the length of RSA.
The two primes are each of (roughly ) the same size.