Public-key Cryptography

Public-key Cryptography (Asymmetric Encryption)

Public-key Cryptography (Asymmetric Encryption) uses a separate key for encryption and decryption. Anyone can use the encryption key (public key) to encrypt a message. However, decryption keys (private keys) are secret. This way only the intended receiver can decrypt the message. The most common asymmetric encryption algorithm is RSA.
Public-key Cryptography
Asymmetric keys are typically 1024 or 2048 bits. However, keys smaller than 2048 bits are no longer considered safe to use. 2048-bit keys have enough unique encryption codes that we won’t write out the number here (it’s 617 digits). Though larger keys can be created, the increased computational burden is so significant that keys larger than 2048 bits are rarely used. To put it into perspective, it would take an average computer more than 14 billion years to crack a 2048-bit certificate.
Since asymmetric keys are bigger than symmetric keys, data that is encrypted asymmetrically is tougher to crack than data that is symmetrically encrypted. However, this does not mean that asymmetric keys are better. Rather than being compared by their size, these keys should compared by the following properties: computational burden and ease of distribution.

How SSL Uses both Asymmetric and Symmetric Encryption?

Public Key Infrastructure (PKI) is the set of hardware, software, people, policies, and procedures that are needed to create, manage, distribute, use, store, and revoke digital certificates. PKI is also what binds keys with user identities by means of a Certificate Authority (CA). PKI uses a hybrid cryptosystem and benefits from using both types of encryption. For example, in SSL communications, the server’s SSL Certificate contains an asymmetric public and private key pair. The session key that the server and the browser create during the SSL Handshake is symmetric. This is explained further in the diagram below.
Public-key Cryptography
  • Server sends a copy of its asymmetric public key.
  • Browser creates a symmetric session key and encrypts it with the server's asymmetric public key. Then sends it to the server.
  • Server decrypts the encrypted session key using its asymmetric private key to get the symmetric session key.
  • Server and Browser now encrypt and decrypt all transmitted data with the symmetric session key. This allows for a secure channel because only the browser and the server know the symmetric session key, and the session key is only used for that session. If the browser was to connect to the same server the next day, a new session key would be created.

Public-Key Encryption Algorithms

Public-key cryptography (asymmetric) uses encryption algorithms like RSA and Elliptic Curve Cryptography (ECC) to create the public and private keys. These algorithms are based on the intractability* of certain mathematical problems.
With asymmetric encryption it is computationally easy to generate public and private keys, encrypt messages with the public key, and decrypt messages with the private key. However, it is extremely difficult (or impossible) for anyone to derive the private key based only on the public key.
  • RSA
    RSA is based on the presumed difficulty of factoring large integers (integer factorization). Full decryption of an RSA ciphertext is thought to be infeasible on the assumption that no efficient algorithm exists for integer factorization. A user of RSA creates and then publishes the product of two large prime numbers, along with an auxiliary value, as their public key. The prime factors must be kept secret. Anyone can use the public key to encrypt a message, but only someone with knowledge of the prime factors can feasibly decode the message.RSA stands for Ron Rivest, Adi Shamir, and Leonard Adleman— the men who first publicly described the algorithm in 1977.
  • ECC
    Elliptic curve cryptography (ECC) relies on the algebraic structure of elliptic curves over finite fields. It is assumed that discovering the discrete logarithm of a random elliptic curve element in connection to a publicly known base point is impractical. The use of elliptic curves in cryptography was suggested by both Neal Koblitz and Victor S. Miller independently in 1985; ECC algorithms entered common use in 2004. The advantage of the ECC algorithm over RSA is that the key can be smaller, resulting in improved speed and security. The disadvantage lies in the fact that not all services and applications are interoperable with ECC-based SSL Certificates.
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