Cryptography Reference
In-Depth Information
one may employ symmetric cryptosystems (such as Triple-DES, IDEA, or Rijndael;
see Chapter 11 and [Schn], Chapters 12, 13, 14), with which the process goes
much more quickly and with equivalent security. For an encrypted transmittal of
the necessary key, which must be kept secret with symmetric procedures, the RSA
algorithm is perfectly suited.
17.3 Digital RSA Signatures
“Please, your Majesty,” said the Knave, “I didn't write it, and they can't prove
that I did: there's no name signed at the end.”
—Lewis Carroll, Alice's Adventures in Wonderland
To clarify how the RSA algorithm is used for generating digital signatures we
consider the following process, by which a participant A sends a message M with
her digital signature to a participant B , upon which B checks the validity of the
signature.
1. A generates her RSA key with components n A , d A , and e A . She then
transmits her public key
e A ,n A
to B .
2. A would now like to send a message M with her signature to B .Tothisend
A generates the redundancy R = µ ( M ) with R<n A using a redundancy
function µ (see below). Then A calculates the signature
S = R d A mod n A
and sends ( M, S ) to B .
3. B possesses the public key
of A . After B has received the message
M and the signature S from A ,then B calculates
e A ,n A
R = µ ( M ) ,
R = S e A mod n A ,
e A ,n A
of A .
with the public key
4. B now checks whether R = R .Ifthisisthecase,then B accepts the digital
signature of A . Otherwise, B rejects it.
Digital signatures that must be checked by a separate transmittal of the
signed message M are called digital signatures with appendix .
The signature procedures with appendix are used primarily for signing
messages of variable lengths whose numerical representation exceeds the
modulus, so that M
n . In principle, one could, as we did above, divide the
message into blocks M 1 , M 2 , M 3 , ... of suitable lengths M i <n and encrypt
and sign each block separately. However, leaving aside the fact that in such a case
 
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