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# 数学代写|密码学代写Cryptography Theory代考|CSE208

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## 数学代写|密码学Cryptography Theory代考|RSA digital signature scheme with message recovery

We now describe an RSA digital signature scheme based on the second approach identified in Section 7.3.3. Before we describe this scheme, it is worth identifying what advantages this second approach might offer.
ADVANTAGES OF DIGITAL SIGNATURE SCHEMES WITH MESSAGE RECOVERY
There are a couple of disadvantages with the digital signature schemes with appendix approach:

1. It requires the use of a hash function, so it might be advantageous to design schemes where no hash function is required.
2. Both the data and the digital signature need to be sent to the verifier. This involves a degree of message expansion, since the message sent is necessarily longer than the underlying data that is digitally signed.

The reasons we discussed for hashing, rather than signing the data directly, primarily applied to ‘long’ data which needs to be split into more than one block for direct processing using RSA. However, if the data to be signed is less than one RSA block in length (in other words, less than the length of the RSA modulus), then the case for hashing before signing is not so strong. Digital signature schemes with message recovery are typically proposed for precisely this situation. This is why they are sometimes also referred to as digital signature schemes for short messages.

Recall from Section 7.3.3 that if the data does not accompany the digital signature, then the verifier faces the problem of recognising the correct data associated with the digital signature. Digital signature schemes with message recovery address this problem by adding redundancy to the data before it is signed, in order to later make it recognisable to a verifier. The data to be digitally signed must therefore be sufficiently short that it remains less than one RSA block in length after this redundancy has been added.

## 数学代写|密码学Cryptography Theory代考|Enforced trust

REDUNDANCY TECHNIQUES
Exactly what should the predefined redundancy that we add during the digital signature creation process look like? Simple examples of redundancy, which serve only as illustrations, include:

• repeating the data twice, with the second copy concatenated to the first;
• adding a fixed data string;
• adding a counter specifying the length of the data; and
• adding a hash of the data.
Any of these techniques could be used in theory, so long as the technique is agreed upon by all potential users of the digital signature scheme. However, just like in other areas of cryptography, it is vital appropriate standards are consulted before adopting a technique for adding redundancy. There have been sophisticated attacks against cryptosystems which exploit poor redundancy processes, and so advice should be sought on what the current recommendations are for suitable methods of adding redundancy.

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