# Public-key Cryptography - Security

Security

Some encryption schemes can be proven secure on the basis of the presumed difficulty of a mathematical problem, such as factoring the product of two large primes or computing discrete logarithms. Note that "secure" here has a precise mathematical meaning, and there are multiple different (meaningful) definitions of what it means for an encryption scheme to be "secure". The "right" definition depends on the context in which the scheme will be deployed.

The most obvious application of a public key encryption system is confidentiality - a message that a sender encrypts using the recipient's public key can be decrypted only by the recipient's paired private key. This assumes, of course, that no flaw is discovered in the basic algorithm used.

Another type of application in public-key cryptography is that of digital signature schemes. Digital signature schemes can be used for sender authentication and non-repudiation. In such a scheme, a user who wants to send a message computes a digital signature for this message, and then sends this digital signature (together with the message) to the intended receiver. Digital signature schemes have the property that signatures can be computed only with the knowledge of the correct private key. To verify that a message has been signed by a user and has not been modified, the receiver needs to know only the corresponding public key. In some cases (e.g. RSA), there exist digital signature schemes with many similarities to encryption schemes. In other cases (e.g. DSA), the algorithm does not resemble any encryption scheme.

To achieve both authentication and confidentiality, the sender can first sign the message using his private key and then encrypt both the message and the signature using the recipient's public key.

These characteristics can be used to construct many other (sometimes surprising) cryptographic protocols and applications, such as digital cash, password-authenticated key agreement, multi-party key agreement, time-stamping services, non-repudiation protocols, etc.

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### Famous quotes containing the word security:

It is hard for those who have never known persecution,
And who have never known a Christian,
To believe these tales of Christian persecution.
It is hard for those who live near a Bank
To doubt the security of their money.
—T.S. (Thomas Stearns)

...I lost myself in my work and never felt that marriage would give me the security I wanted. I thought that through the trade union movement we working women could get better conditions and security of mind.
Mary Anderson (1872–1964)

It seems to me that our three basic needs, for food and security and love, are so mixed and mingled and entwined that we cannot straightly think of one without the others. So it happens that when I write of hunger, I am really writing about love and the hunger for it, and warmth and the love of it and the hunger for it ... and then the warmth and richness and fine reality of hunger satisfied ... and it is all one.
M.F.K. Fisher (b. 1908)