Public Key Cryptography

On a broader scale cryptography can be classified in to two forms Symmetric key Cryptography and Public key cryptography also called as asymmetric cryptography. Public key cryptography is the form of cryptography where different keys are used for encryption and decryption. Every uses will have a pair of keys and private key and a public key. The private key is kept secret and public key is widely distributed. These public key-private key pairs are trap door one way functions i.e. its very easy to encrypt the message but very hard to decrypt the same unless some more secret is known. The messages are encrypted with recipients public key and these messages can be decrypted with only his private key which is known to the person only. Public key cryptography solves the problem of key distribution and shared secret.

The two main branches of public key cryptography are

• Public key Encryption - The message is encrypted with recipients public key and can be decrypted with his private key only.
• Digital Signatures - The message signed with senders private key and can be verified by anyone who has access to his public key. This way any one can easily prove that the message is actually transmitted by the sender and its non-tampered.

This video talks about the need to public key cryptography and the basics about one way functions and trap door functions. In the later part it explains the process of encryption with public key cryptography with the typical encryption algorithm involving alice and bob.

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An analogy for public-key encryption is that of a locked mailbox with a mail slot. The mail slot is exposed and accessible to the public; its location (the street address) is in essence the public key. Anyone knowing the street address can go to the door and drop a written message through the slot; however, only the person who possesses the key can open the mailbox and read the message.

Compared with symmetric-key encryption, public-key encryption requires more computation and is therefore not always appropriate for large amounts of data. However, it's possible to use public-key encryption to send a symmetric key, which can then be used to encrypt additional data. This is the approach used by the SSL protocol.

n general, the strength of encryption is related to the difficulty of discovering the key, which in turn depends on both the cipher used and the length of the key. For example, the difficulty of discovering the key for the RSA cipher most commonly used for public-key encryption depends on the difficulty of factoring large numbers, a well-known mathematical problem.

Different ciphers may require different key lengths to achieve the same level of encryption strength. The RSA cipher used for public-key encryption, for example, can use only a subset of all possible values for a key of a given length, due to the nature of the mathematical problem on which it is based. Other ciphers, such as those used for symmetric key encryption, can use all possible values for a key of a given length, rather than a subset of those values. Thus a 128-bit key for use with a symmetric-key encryption cipher would provide stronger encryption than a 128-bit key for use with the RSA public-key encryption cipher.

Related links:

• Public Key Cryptography- Wiki
• Books on Cryptography
• Public Key - FAQs

Amit Vartak, 27 is working in wired and wireless security fields since last 3-4 years. His current area of interest includes IEEE 802.11 (Wi-Fi) suite of protocols, vulnerabilities in these protocols and countermeasure for those vulnerabilities. Working on cutting edge tools and technology always keeps him busy. He has contributed from concept level to final prototyping for the presentations in Defcon 2007 (The Emperor Has No Cloak - WEP Cloaking Exposed) and Toorcon 2007 (Caffe latte attack). He holds 2 patents with USPTO (current status: Patent Pending) and a few papers in IEEE journals on wireless protocol vulnerabilities. Prior to this, he was working on MEMS (Micro Electro Mechanical Systems) and has published a few papers in SPIE and ICMAT. (Yeah… kindda orthogonal fields… but technology really doesn’t limit the talent :) He did his masters in Electrical Engineering from one of the premier institutes in India, Indian Institute of Technology, Bombay (IIT-Bombay) and his under graduation, from University of Mumbai in Electronics and Telecommunication Engineering. He is currently working with AirTight Networks Inc. as a team lead in technology group since last 3 years.You can get in touch with him at amitcv[at]gmail[dot]com