Public Key Encryption Essay

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A Method for Obtaining Digital Signatures and Public Key Cryptosystems.

About the paper:
Public-Key encryption-system was first outlined by this paper. Public key encryption-system is still in wide use today, and known by the name (initials) of the paper’s three authors i.e. RSA.
The paper presents an encryption method which is presented with the unusual property that publicly revealing an encryption key does not result in revealing the corresponding decryption key. It has two important consequences
• Couriers or other secure means are not needed to transmit the keys.
• By using a privately held decryption key, a message can be signed.
In the paper the theory of “public key cryptosystems” is introduced in the first 4 sections after which
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If these numbers satisfy the conditions that 1 d is co-prime to (p-1)*(q-1), and 2 e*d = 1 holds modulo (p-1)*(q-1), it can be proven and stated that for any non-negative integer M < n the identity (M^e)^d = (M^d)^e = M holds modulo n. Encryption then consists of a number exponentiated by e modulo n, and decryption in exponentiation by d (again, modulo n).

The paper has proposed a method for implementing a public key crypto system whose security rests in part on the difficulty of factoring large numbers. If the security of our method proves to be enough, it allows secure communications to be established without the use of couriers to carry keys, and it also permits one to "sign" digitised documents. Hence security plays an important role.

The Public key (e,n) is public, and using the genearlised Euclidian algorithm d can be derived from (e, p, q), the security of the cryptosystem depends on large numbers being difficult to factor. There is no efficient methods of factorising integers and the problem of factorising integers is a well studied problem in number-theory. Because of this, the authors argue that the system is likely to be broken any time soon. The last sections of the paper briefly describe proposed algorithms on how to generate key-pairs efficeintly, as well as discuss why other methods of deriving d from (e,n) can be
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