what is RSA keylength the length of?

Discussion in 'Computer Security' started by Daniel Moore, Apr 28, 2008.

  1. Daniel Moore

    Daniel Moore Guest

    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, Apr 28, 2008
    #1
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  2. Daniel Moore <> 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/
     
    Ertugrul Söylemez, Apr 28, 2008
    #2
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  3. Daniel Moore

    Unruh Guest

    Daniel Moore <> 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, Apr 28, 2008
    #3
  4. Unruh <> 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 Söylemez, Apr 29, 2008
    #4
  5. Daniel Moore

    Unruh Guest

    Ertugrul =?UTF-8?B?U8O2eWxlbWV6?= <> writes:

    >Unruh <> 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.
     
    Unruh, Apr 29, 2008
    #5
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