Asymmetric (or public-key)cryptography consists of a broad set of algorithms. These are based on mathematical problems that are relatively easy to perform in one direction, but which cannot be easily reversed.

One famous example of this type of problem is the factoring problem: for carefully chosen prime numbers p and q, we can compute the product N=p*q quickly. However, given only N, it is very hard to recover p and q.

A common public-key cryptographic algorithm based on the factoring problem is the Rivest-Shamir-Adleman (RSA) function. When combined with an appropriate padding scheme, RSA can be used for multiple purposes, including asymmetric encryption.

An encryption scheme is calledasymmetricif it uses one keythe public keyto encrypt data, and a different but mathematically related keythe private keyto decrypt data.

It must be computationally infeasible to determine the private key if the only thing one knows is the public key. Therefore, the public key can be distributed broadly while the private key is kept secret and secure. Together the keys are referred to as akey pair.

One popular asymmetric encryption scheme is RSA-OAEP, which is a combination of the RSA function with the Optimal Asymmetric Encryption Padding (OAEP) padding scheme. RSA-OAEP is typically only used to encrypt small amounts of data because it is slow and has ciphertexts which are much larger than the plaintext.

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Types of Cryptographic Algorithms

There are many types of cryptographic algorithms available. They vary in complexity and security, depending on the type of communication and the sensitivity of the information being shared.

Secret Key Cryptography

Secret key cryptography, also known as symmetric encryption, uses a single key to encrypt and decrypt a message. The sender encrypts the plaintext message using the key and sends it to the recipient who then uses the same key to decrypt it and unlock the original plaintext message.

Stream Ciphers

Stream ciphers work on a single bit or byte at any time and constantly change the key using feedback mechanisms. A self-synchronizing stream cipherensures the decryption process stays in sync with the encryption process by recognizing where it sits in the bit keystream. A synchronous stream cipher generates the keystream independently of the message stream and generates the same keystream function at both the sender and the receiver.

Block Ciphers

Block ciphers encrypt one block of fixed-size data at a time. It will always encrypt a plaintext data block to the same ciphertext when the same key is used. A good example of this is the Feistel cipher, which uses elements of key expansion, permutation, and substitution to create vast confusion and diffusion in the cipher.

The stages of encryption and decryption are similar if not identical, which means reversing the key reduces the code size and circuitry required for implementing the cipher in a piece of software or hardware.

Public Key Cryptography

Public key cryptography (PKC), or asymmetric cryptography, uses mathematical functions to create codes that are exceptionally difficult to crack. It enables people to communicate securely over a nonsecure communications channel without the need for a secret key. For example, proxy reencryption enables a proxy entity to reencrypt data from one public key to another without requiring access to the plaintext or private keys.

A common PKC type is multiplication vs. factorization, which takes two large prime numbers and multiplies them to create a huge resulting number that makes deciphering difficult. Another form of PKC is exponentiation vs. logarithms such as 256-bit encryption, which increases protection to the point that even a computer capable of searching trillions of combinations per second cannot crack it.

Generic forms of PKC use two keys that are related mathematically but do not enable either to be determined. Put simply, a sender can encrypt their plaintext message using their private key, then the recipient decrypts the ciphertext using the senders public key.

Common PKC algorithms used for digital signatures and key exchanges include:

RSA

RSA was the first and remains the most common PKC implementation. The algorithm is named after its MIT mathematician developers, Ronald Rivest, Adi Shamir, and Leonard Adleman, and is used in data encryption, digital signatures, and key exchanges. It uses a large number that is the result of factoring two selected prime numbers. It is impossible for an attacker to work out the prime factors, which makes RSA especially secure.

Elliptic Curve Cryptography (ECC)

ECC is a PKC algorithm based on the use of elliptic curves in cryptography. It is designed for devices with limited computing power or memory to encrypt internet traffic. A common use of ECC is in embedded computers, smartphones, and cryptocurrency networks like bitcoin, which consumes around 10% of the storage space and bandwidth that RSA requires.

Digital Signature Algorithm (DSA)

DSA is a standard that enables digital signatures to be used in message authentication. It was introduced by the National Institute of Standards and Technology (NIST) in 1991 to ensure a better method for creating digital signatures.

Identity-based Encryption (IBE)

IBE is a PKC system that enables the public key to be calculated from unique information based on the users identity, such as their email address. A trusted third party or private key generator then uses a cryptographic algorithm to calculate a corresponding private key. This enables users to create their own private keys without worrying about distributing public keys.

Public Key Cryptography Standards (PKCS)

All PKC algorithms and usage are governed by a set of standards and guidelines designed by RSA Data Security. These are as follows:

Diffie-Hellman and Key Exchange Algorithm (KEA)

The Diffie-Hellman algorithm was devised in 1976 byStanford University professor Martin Hellman and his graduate student Whitfield Diffie, who are considered to be responsible for introducing PKC as a concept. It is used for secret key exchanges and requires two people to agree on a large prime number.

KEA is a variation of the Diffie-Hellman algorithm and was proposed as a method for key exchange in the NIST/National Security Agencys (NSA) Capstone project, which developed cryptography standards for public and government use.

Hash Function

Hash functions ensure that data integrity is maintained in the encryption and decryption phases of cryptography. It is also used in databases so that items can be retrieved more quickly.

Hashing is the process of taking a key and mapping it to a specific value, which is the hash or hash value. A hash function transforms a key or digital signature, then the hash value and signature are sent to the receiver, who uses the hash function to generate the hash value and compare it with the one they received in the message.

A common hash function is folding, which takes a value and divides it into several parts, adds parts, and uses the last four remaining digits as the key or hashed value. Another is digit rearrangement, which takes specific digits in the original value, reverses them, and uses the remaining number as the hash value. Examples of hash function types include Secure Hash Algorithm 1 (SHA-1), SHA-2, and SHA-3.

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What is Cryptography? Definition, Importance, Types | Fortinet

Cryptography definition

Cryptography is the art of keeping information secure by transforming it into form that unintended recipients cannot understand. In cryptography, an original human readable message, referred to as plaintext, is changed by means of an algorithm, or series of mathematical operations, into something that to an uninformed observer would look like gibberish; this gibberish is called ciphertext.

Cryptographic systems require some method for the intended recipient to be able to make use of the encrypted messageusually, though not always, by transforming the ciphertext back into plaintext.

Before we move into the meat of this article, let's define a couple terms related to cryptography. The syllable crypt may make you think of tombs, but it comes from a Greek word that means "hidden" or "secret." Cryptography literally means "secret writing." Cryptology, meanwhile, means something like "knowledge of secrecy"; if cryptography is the practice of writing secret messages, then cryptology is the theory, although the two words are often used interchangeably. Encryption"making secret"is what we call the process of turning plaintext into ciphertext Encryption is an important part of cryptography, but doesn't encompass the entire science. Its opposite is decryption.

One important aspect of the encryption process is that it almost always involves both an algorithm and a key. A key is just another piece of information, almost always a number, that specifies how the algorithm is applied to the plaintext in order to encrypt it. In a secure cryptographic system, even if you know the method by which some message is encrypted, it should be difficult or impossible to decrypt without that key. Keep algorithms and keys in your mind, because they'll be important as we move on.

This is all very abstract, and a good way to understand the specifics of what we're talking about is to look at one of the earliest known forms of cryptography. It's known as the Caesar cipher, because Julius Caesar used it for his confidential correspondence; as his biographer Suetonius described it, "if he had anything confidential to say, he wrote it in cipher, that is, by so changing the order of the letters of the alphabet ... If anyone wishes to decipher these, and get at their meaning, he must substitute the fourth letter of the alphabet, namely D, for A, and so with the others."

Suetonius's description can be broken down into the two cryptographic elements we've discussed, the algorithm and the key. The algorithm here is simple: each letter is replaced by another letter from later in the alphabet. The key is how many letters later in the alphabet you need to go to create your ciphertext. It's three in the version of the cipher Suetonius describes, but obviously other variations are possiblewith a key of four, A would become E, for instance.

A few things should be clear from this example. Encryption like this offers a fairly simple way to secretly send any message you like. Contrast that with a system of code phrases where, say, "Let's order pizza" means "I'm going to invade Gaul." To translate that sort of code, people at both ends of the communication chain would need a book of code phrases, and you'd have no way to encode new phrases you hadn't thought of in advance. With the Caesar cipher, you can encrypt any message you can think of. The tricky part is that everyone communicating needs to know the algorithm and the key in advance, though it's much easier to safely pass on and keep that information than it would be with a complex code book.

The Caesar cipher is what's known as a substitution cipher, because each letter is substituted with another one; other variations on this, then, would substitute letter blocks or whole words. For most of history, cryptography consisted of various substitution ciphers deployed to keep government and military communications secure. Medieval Arab mathematicians pushed the science forward, particularly the art of decryptiononce researchers realized that certain letters in a given language are more common than others, it becomes easier to recognize patterns, for instance. But most pre-modern encryption is incredibly simple by modern standards, for the obvious reason that, before the advent of computers, it was difficult to perform mathematical transformations quickly enough to make encryption or decryption worthwhile.

In fact, the development of computers and advances in cryptography went hand in hand. Charles Babbage, whose idea for the Difference Engine presaged modern computers, was also interested in cryptography. During World War II, the Germans used the electromechanical Enigma machine to encrypt messagesand, famously, Alan Turing led a team in Britain that developed a similar machine to break the code, in the process laying some of the groundwork for the first modern computers. Cryptography got radically more complex as computers became available, but it remained the province of spies and generals for several more decades.

Before we move on here to modern cryptography, let's pause to discuss two important principles that underlie it. The first is what's come to be known as Kerckhoffss principle, named after the 19th century Dutch cryptographer Auguste Kerckhoffs. Remember, as we said, any cryptographic system involves both an algorithm and a key. Kerckhoffs believed that "a cryptographic system should be secure even if everything about the system, except the key, is public knowledge."

Now, these were the days when cryptography had almost entirely military applications. The idea here is that, while it would be nice to keep your cryptographic system a secret, your opponent will almost certainly eventually figure it out. Claude Shannon, a World War II cryptographer who would go on to be a pioneer in information theory, put it more succinctly: "The enemy knows the system." What Kerckhoffs and Shannon are getting at is that you want to design an algorithm that doesn't need to be a secret in order to successfully conceal information.

That said, in today's world, the public nature of cryptographic algorithms is seen as something good in and of itself, rather than an unavoidable evil. Standard cryptographic algorithms have been widely studied and stress-tested, and trying to come up with your own private algorithms is doomed to failure as security through obscurity usually is.

What you do need to keep secret is your cryptographic key. We'll get to the mathematics of how that works in a moment, but for now, we'll touch on another cryptographic principle that makes that math possible: a reliance on one-way functions, mathematical operations that are very difficult to reverse. The classic example of a one-way function is the multiplication of two very large prime numbers together. While that calculation is simple to do, if you only had the end result, it would be very difficult, verging on impossible, to figure out the original two prime numbers. The question of whether any function can truly be one-way is debated by mathematicians, but many are irreversible in practice at the limits of our current computing power, so we'll leave that question aside as we move on.

It was the formation of the first computer networks that started civilians thinking about the importance of cryptography. Computers were talking to each other over the open network, not just via direct connections to one another; that sort of networking was transformative in many great ways, but also made it trivially easy to snoop on data traveling across the network. And with financial services being an early use case for computer communication, it was necessary to find a way to keep information secret.

IBM led the way in the late 1960s with an encryption method known as "Lucifer", which was eventually codified by the US National Bureau of Standards as the first Data Encryption Standard (DES). As the internet began to grow in importance, more and better encryption was needed, and today a significant portion of data flying around the world is encrypted using varying techniques that we'll discuss in more detail in a moment.

We've already discussed some of the specific applications of cryptography, from keeping military secrets to transmitting financial data safely across the internet. In the bigger picture, though, there are some broad cybersecurity goals that we use cryptography to help us achieve, as cybersecurity consultant Gary Kessler explains. Using cryptographic techniques, security pros can:

You may recognize some of these principles from variations of the CIA triad. The first of these uses is the obvious oneyou can keep data secret by encrypting it. The others take a bit of explanation, which we'll get into as we describe the different types of cryptography.

There are numerous cryptographic algorithms in use, but in general they can be broken into three categories: symmetric cryptography, asymmetric cryptography, and hash functions. Each has its own role to play within the cryptographic landscape.

Symmetric cryptography. The Caesar cipher we discussed above is a great example of symmetric cryptography. In the example we used, if encrypted messages were being exchanged between Caesar and one of his centurions, both parties would have to know the keyin this case, how many letters forward or backwards in the alphabet you need to move to transform plaintext to ciphertext or vice versa. That's what makes it symmetrical. But the key needs to stay a secret between the two of them, which is why this is sometimes also called secret key cryptography. You couldn't send the key along with the message, for instance, because if both fell into enemy hands the message would be easy for them to decipher, defeating the whole purpose of encrypting it in the first place. Caesar and his centurion would presumably have to discuss the key when they saw each other in person, though obviously this is less than ideal when wars are being fought over long distances.

Symmetric cryptography is widely used to keep data confidential. It can be very useful for keeping a local hard drive private, for instance; since the same user is generally encrypting and decrypting the protected data, sharing the secret key is not an issue. Symmetric cryptography can also be used to keep messages transmitted across the internet confidential; however, to successfully make this happen, you need to deploy our next form of cryptography in tandem with it.

Asymmetric cryptography. Caesar may have been able to confer with his centurions in person, but you don't want to go into your bank and talk to the teller just to learn what the private key is for encrypting your electronic communication with the bankthat would defeat the purpose of online banking. In general, in order to function securely, the internet needs a way for communicating parties to establish a secure communications channel while only talking to each other across an inherently insecure network. The way this works is via asymmetric cryptography, which is sometimes called public key cryptography.

In asymmetric cryptography, each participant has two keys. One is public and is sent to anyone the party wishes to communicate with. That's the key used to encrypt messages. But the other key is private, shared with nobody, and it's necessary to decrypt those messages. To use a metaphor: think of the public key as opening a slot on a mailbox just wide enough to drop a letter in. You give that key to anyone who you think might send you a letter so they can open the slot and deliver the envelope. The private key is what you use to open the mailbox so you can get the letters out.

The mathematics of how you can use one key to encrypt a message and another to decrypt it are where the idea of one-way functions that we discussed above come into play: the two keys should be related to each other mathematically such that it's easy to derive the public key from the private key but not vice versa. For instance, the private key might be those two very large prime numbers, which you'd multiply together to get the public key. The Infosec Institute has a deep dive if you're interested.

The computations needed for asymmetric cryptography are much more complex and resource intensive that those behind symmetric infrastructure. Fortunately, you don't need to use it to protect every message you send online. Instead, what usually happens is that one party will use symmetric cryptography to encrypt a message containing yet another cryptographic key. This key, having been safely transmitted across the insecure internet, will then become the private key that encodes a much longer communications session encrypted via symmetric encryption.

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