Public Key Arrangement So That Only One Person Can Read
Public Key Encryption
Security in Wireless Systems
Vijay Yard. Garg , in Wireless Communications & Networking, 2007
Public Key (or disproportionate encryption)
Public key encryption uses longer keys than does symmetric encryption. The key direction problem is greatly reduced considering the public key is publicized and the private key is never distributed. In that location is no need to exchange keys.
In a public key organisation, two keys are used, one for encrypting and one for decrypting. The two keys are mathematically related to each other merely knowing one key does not divulge the other key. The ii keys are chosen the "public key" and the "individual key" of the user. The network also has a public primal and a private key.
The sender uses a public primal to encrypt the message. The recipient uses its individual key to decrypt the message. Public key infrastructure (PKI) is a set of hardware, software, organizations, and policies to public primal encryption work on the Internet. There are security firms that provide PKI and deploy encrypted channels to identify users and companies through the use of certificates — VeriSign Inc. Xcert offers products based on PKI.
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Privacy and Security in Healthcare
Timothy Virtue , Justin Rainey , in HCISPP Study Guide, 2015
Public Central Encryption
Public key encryption uses two different keys. Ane fundamental is used to encrypt the information and the other is used to decrypt the information. Sometimes this is referred to equally asymmetric encryption because two keys are required to make the system and/or process work securely. 1 key is known as the public key and should be shared past the owner with anyone who will be deeply communicating with the cardinal owner. Even so, the owner'south secret key is not to be shared and considered a private fundamental. If the private key is shared with unauthorized recipients, the encryption mechanisms protecting the information must exist considered compromised.
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Embedded security
J. Rosenberg , in Rugged Embedded Systems, 2017
Public key encryption
Public cardinal encryption is also referred to as asymmetric encryption because at that place is not only one fundamental used in both directions as with the symmetric encryption. In public cardinal encryption there are 2 keys; whichever one is used to encrypt requires the other exist used to decrypt. In this affiliate we volition stick with the term public fundamental encryption to help institute context and dissimilarity it to shared key encryption.
The keys in public key encryption are nonmatching simply they are mathematically related. One key (it does not matter which) is used for encryption. That key is useless for decryption. But the matching fundamental tin exist used for decryption. This concept provides united states with the disquisitional facility we demand for secure key substitution to establish and transport a shared key.
A diagram showing how basic public central encryption works is shown in Fig. four.
Fig. 4.
A note about Kerberos earlier we proceed with discussions of public fundamental encryption. While information technology is true that Kerberos is an alternative for distributing shared keys, Kerberos but applies to a airtight environment where all principals requiring keys share direct access to trusted key distribution centers (KDCs) and all principals share a key with that KDC. Microsoft Windows natively support Kerberos so within a closed Windows-only environment Kerberos is an choice. No further discussion of Kerberos is independent in this chapter. Nosotros recommend public fundamental systems for this function. Public key systems work with paired keys one of which (the private key) is kept strictly private and the other (the public key) is freely distributed; in particular the public primal is fabricated broadly attainable to the other party in secure communications.
Communicating parties each must generate a pair of keys. One of the keys, the private fundamental, will never get out the possession of its creator. Each party to the communication passes their public central to the other party. The associated public key encryption algorithms are pure mathematical magic because whatever is encrypted with ane half of the key pair tin only be decrypted with its mate. Combining this simple fact with the strict rule that individual keys remain private and only public keys tin be distributed leads to a very interesting and powerful matrix of how public key encryption interrelates to confidentiality and identity. This matrix is shown in Table one.
Table 1. How Public Key Encryption Interrelates to Confidentiality and Identity
| Public Key | Private Key | What This Means |
|---|---|---|
| Encrypt (w/ recipient's) | Decrypt (w/ recipient'due south) | Confidentiality (no one but intended recipient can read) |
| Decrypt (westward/ sender'southward) | Encrypt (westward/ sender'due south) | Signature (identity) (it could only take come from sender) |
For Alice to send a confidential bulletin to Bob, Alice must obtain Bob's public central. That'south easy since anyone can take Bob's public key at no risk to Bob; information technology is simply for encrypting data. Alice takes Bob's public key and provides it to the standard encryption algorithm and encrypts her message to Bob. Because of the nature of the public-private primal pair and the fact that Alice and Bob agree on a public, standard encryption algorithm (like RSA), Bob tin can use his private key to decrypt Alice's message. Most importantly, just Bob—because no i will ever go their hands on Bob's private key—can decrypt Alice's message. Alice just sent Bob a confidential message. Anyone intercepting it will get just scrambled information because they don't take Bob's individual key.
Digital signatures will be described in merely a moment but notice something interesting about doing things simply the contrary of Alice's confidential bulletin. If Alice encrypts a bulletin with her private cardinal, which only Alice could possess, and if Alice makes certain Bob has her public primal, Bob tin see that Alice and only Alice could have encrypted that message. In fact, since Alice'due south public key is in theory accessible to the entire world, anyone tin can tell that Alice and only Alice encrypted that bulletin. The identity of the sender is established. That is the basic principle of digital signature.
Remember: encrypt with your individual key and the whole world using your public key can tell it could be from you and only yous (digital signature) or encrypt with a specific person's public fundamental and they and simply they, using their private cardinal, can read your message (underground or confidential messages).
Public cardinal encryption is based on the mathematics of factoring large numbers into their prime factors. This problem is thought to be computationally intractable if the numbers are large enough. Simply a limitation of public central encryption is that it can only exist applied to pocket-sized messages. To reach our goal of distributing shared keys this is no problem—shared keys are non larger than the message size limitation of public cardinal algorithms. To achieve our goal of digital signatures nosotros will apply a neat play a trick on and remain within this size limitation as we will discuss momentarily.
Public key vs shared central operation
Even when implemented in hardware, shared key algorithms are many orders of magnitude faster than public fundamental encryption. In hardware, RSA is about thousand times slower than DES.
The first performance hit comes from key generation. We must find ii multihundred-bit prime numbers that are near the same length. Then these two primes must be tested for primality, a very expensive operation requiring a serial of steps that each have a certain probability of determining the values are relatively prime and must be run several times to make the probability high enough equally to be of an acceptably infinitesimal risk of being incorrect.
The second reason that public cardinal encryption is so much slower than shared central is that RSA encryption/decryption is based on the mathematics of modular exponentiation. This means we are taking each input value, raising it to a power (a large number of multiplications) and then performing the modulo performance (the remainder subsequently doing integer sectionalisation). On the other hand, shared key ciphers are based on much faster logical operations on bit arrays. Public central algorithms are called disproportionate for a reason. Considering the private key has a much larger exponent than the public key, individual key operations take essentially longer than do public primal operations. In confidentiality applications (i.e., encryption) where the public primal is used for encryption, decryption takes substantially longer than decryption. In integrity applications (i.e., signature) where the private key is used for encryption it is the other way around. This imbalance would be a problem when applied to big letters but is non an issue when applied only to pocket-sized messages such equally the 200-bit key for shared key encryption.
The 3rd reason to be concerned near the computational complexity of public key encryption is the padding bug. The input to RSA encryption operations is interpreted as a number so special padding is required to make the input totally consistent. The full length of the information must be a multiple of the modulus size and the data must exist numerically less than the modulus. A 1024-bit RSA key has a 128-byte modulus. Therefore, data must be encrypted in blocks of 128 bytes. Each input number must be padded with zeros until its numerical value is less than that of the modulus. XML encryption specifies the use of PKCS#1 Block 02 padding. This padding places a disquisitional restriction on the size of information that RSA tin can encrypt. This is why RSA is never used to encrypt the entire plaintext message but only the shared key existence exchanged between communicating parties. Once the shared key is established safely betwixt the parties, AES encryption is used on the plaintext bulletin itself.
On the negative side, shared key cryptography fails to solve the trouble of scalable key distribution. These algorithms are fast and tin can handle infinitely big messages but both ends of the communication need access to the same key and we need to become information technology to them securely. Shared key cryptography also fails to solve the issue of repudiation. We are going to need to exist able to prove that a certain identity created and attests to sending a message (or document) and no i else could accept. They must not be able to deny having sent this verbal document at this moment in time. Shared key cryptography provides no help here. Finally, shared cardinal cryptography fails to solve the issue of data integrity. We know no ane intercepted our message and we have some balls that no blocks of data in the message were substituted thanks to cyclic block chaining, merely we do not have assurance that our message sent and received are identical. For these issues, we need public key cryptography.
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Encryption
Peter Wayner , in Disappearing Cryptography (Third Edition), 2009
two.2.ii Public-Key Encryption
Public-cardinal encryption systems are quite different from the popular private-key encryption systems like DES. They rely on a substantially dissimilar co-operative of mathematics that still generates prissy, random white racket. Fifty-fifty though these foundations are different, the results are all the same the same.
The almost popular public-key encryption organization is the RSA algorithm that was developed by Ron Rivest, Adi Shamir, and Len Adleman when they were at MIT during the late 1970s. Ron Rivest, Adi Shamir, and Len Adleman The organization uses 2 keys. If 1 fundamental encrypts the information, then only the other central can decrypt it. After the encryption, showtime key becomes worthless Information technology can't decrypt the data. This is not a issues, but a feature. Each person can create a pair of keys and publicize one of the pair, perhaps by listing it in some electronic phone volume. The other key is kept secret. If someone wants to transport a message to you, they look up your public key and use it to encrypt the message to you. Simply the other primal tin can decrypt this message now and simply you accept a re-create of it.
In a very abstract sense, the RSA algorithm works by arranging the set of all possible messages in a long, long loop in an abstract mathematical space. The circumference of this loop, call information technology n, is kept a secret. You might think of this equally a long necklace of pearls or beads. Each bead represents a possible message. There are billions of billions of billions of them in the loop. You send a message by giving someone a pointer to a bead.
The public key is just a relatively big number, call it one thousand. A bulletin is encrypted by finding its position in the loop and stepping around the loop thou steps. The encrypted bulletin is the number at this position. The secret key is the circumference of the loop minus k. A message is decrypted past starting at the number marking the encrypted message and marching along the n − k steps. Because the numbers are arranged in a loop, this will bring y'all back to where everything began– the original message.
Two properties about this string of pearls or beads make information technology possible to use it for encryption. The first is that given a bead, it is hard to know its verbal position on the string. If there is some special first bead that serves as the reference location similar on a rosary, then you would need to count through all of the beads to determine the exact location of one of the chaplet. This same issue happens in the mathematics. You would need to multiply numbers over again and again to make up one's mind if a item number is the one y'all want.
The second holding of the cord of beads in this metaphor does not make as much sense, but it can still exist easily explained. If you want to motility along the string k beads, then you lot tin leap there virtually instantaneously. Yous don't need to count each of the thou chaplet along the way. This allows you to encrypt and decrypt messages using the public-key system.
The two special features are similar but they exercise not contradict each other. The second says that it is easy to spring an arbitrary number of beads. The offset says it's hard to count the number of pearls betwixt the commencement bead and any detail dewdrop. If you lot knew the count, so you could use the second feature. Simply you don't so you have to count by hand.
The combination of these 2 features makes it possible to encrypt and decrypt messages by jumping over big numbers of beads. Simply it as well makes information technology impossible for someone to break the system because they tin't make up one's mind the number of steps in the jump without counting.
This metaphor is not exactly right, but it captures the spirit of the organization. Figure two.3 illustrates it. Mathematically, the loop is constructed by computing the powers of a number modulo some other number. That is, the first element in the loop is the number. The second is the foursquare of the number, the tertiary is the cube of the number, and and so on. In reality, the loop is more than ane-dimensional, but the theme is consistent.
Figure 2.three. RSA encryption works by arranging the possible letters in a loop with a clandestine circumference. Encryption is accomplished by moving a random amount, m, down the loop. But the owners know the circumference, n, so they can move north − 1000 steps downwards the loop and recover the original message.
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AI and Cloud Computing
Jinxia Yu , ... Xiaojun Wang , in Advances in Computers, 2021
3.three Public-key encryption
A Public-fundamental Encryption (PKE) with plaintext-space consists of the following three algorithms:
- •
-
: The primal generation algorithm takes the security parameter κ as input, outputs a public primal and a surreptitious primal (pk, sk).
- •
-
c ← Enc (pk, pow;r): the encryption algorithm takes pk and a plaintext every bit inputs, with an internal coin flipping r, outputs a ciphertext c.
- •
-
pw ← Dec(sk,c): the decryption algorithm takes sk and c as inputs, and outputs a plaintext pw or ⊥.
Correctness
For all public central pk and clandestine key sk, any plaintext pw and c, the equation Dec (sk,c) = pw holds with overwhelming probability.
Security
We consider the post-obit game between a challenger and an adversary .
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Data Science: Theory and Applications
Srikanth Cherukupally , in Handbook of Statistics, 2021
two.6.4 Noninteractive proof (example)
In public fundamental encryption system, the authenticity of public key and individual fundamental pair of an entity is ensured past a document authorisation. Harry (verifier) wants to verify that Tom has a private key (i.e., a legitimate user of the system), he tin directly bank check the authenticity of the certificate issued to Tom. The certificate is served as a noninteractive proof.
In a blockchain network, verification of a node's identity uses noninteractive proofs explained equally above. Further, zero-cognition proofs can be used to validate a transaction without revealing identity of sender and recipient. Zcash (Ben-Sasson et al., 2014) is a crypto-currency that provides anonymity of entities involved in its transactions.
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Securing Sockets with SSL
Walter Goralski , in The Illustrated Network (Second Edition), 2017
Pocket Calculator Encryption at the Client
The security that public key encryption provides is a effect of the difficulty of factoring big numbers, not the complication of the method. You lot tin do PKI on whatever pocket computer. The "how" is shown in the "Three Magic Numbers" sidebar and explained in material following.
Three Magic Numbers
- 1.
-
Offset with iii magic numbers: Public "normalizer" Northward=33, public encryption cardinal E=3, and private decryption key D=7.
- 2.
-
Encrypt obviously-text alphabetic character "O" (15th letter of the alphabet) from certificate Northward and E values.
- 3.
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Write down "O" value E times and multiply:
fifteen×fifteen×fifteen×3375
- four.
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Dissever by Northward and compute remainder:
3375/33=102.27272…
0.27272…×33=eight.99976=nine
- 5.
-
Ship 9, the cipher text for plain-text fifteen, over the network.
We have to start with three "magic" numbers, and two of them must exist prime numbers. Usually, you lot cull two large primes first (hundreds of digits) and derive a 3rd huge number called N (for "normalizer") through a very complex process. Due north is never called a cardinal in the documentation, only N is necessary for both encrypting and decrypting. The security comes from the fact that given a large Due north and one of the keys, information technology is next to impossible to derive the second prime number key number. In this example, Due north=33, and the two primes are 3 and 7. There is no obvious relationship between 33 and three and 7, although with these small numbers, a code cracker could figure it out in a minute or two.
Ane of the two primes becomes the public key (it doesn't matter which), and the other becomes the individual key. Never consistently assign the smaller number as the public key. This speeds up client encryption, but is a security take a chance if people know ane cistron must be larger than the other. In this example, N=33, the public encryption key E=iii, and the private decryption key D=7.
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AI and Cloud Calculating
Leqi Jiang , ... Xingming Sun , in Advances in Computers, 2021
four.two Protocols with full general public key encryption
Kaghazgaran's beginning protocol used public key encryption [31]. The DO uploads the ciphertexts of his data to CS. CS selects a random integer l and calculates the different of ciphertexts and the integer, then the results volition be sent to TP. TP recovers the plaintexts. TP adds 1 to N to the result in club, without knowing the integer, and decrypt them. CS gets the magnitude relation from the l-th consequence. The protocol is described in Table 7. The processes is shown in Fig. eight.
Table 7. Kaghazgaran'due south protocols with general public key encryption.
| Algorithm 5: Kaghazgaran'due south kickoff comparison protocol |
|---|
| At Practise: Generates a public/private central pair (pk, sk); Shares the private fundamental sk to TP; Uploads Due east pk (x i )(i = 1, two, ⋯, north), the ciphertexts of his data ten i 's, to CS; At CS: Picks a random integer l(1 < l < L) and computes the values of: c i = E pk (x i ) − l; Sends c i 's to TP; At TP: Decrypts c i 's to become m i,j = D sk (c i + j)(j = ane, 2, ⋯, L); Generates random r and computes Yard i, j = m i,j + r; Sends the north arrays in size of L to CS; At CS: Looks at l-th number of each array sent by CS A, and get the sort of the data it kept. |
Source: author.
Fig. 8. The processes of Kaghazgaran's protocols with full general public cardinal encryption.
Source: writer.This scheme is similar to Yao's scheme. Although TP can get thou i,50 = x i ,l is not known by TP, it cannot derive which ones are the data owner's original data. The functioning M i,j = one thousand i,j + r makes sure that CS can sort those data without knowing the exact values of Exercise's original data. This protocol takes total reward of cloud servers, and makes information technology possible to sorting over encrypted data without data owner involved. However, information technology notwithstanding comes with big ciphering overhead and communication overhead.
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Understanding Cybercrime Prevention
Littlejohn Shinder , Michael Cantankerous , in Scene of the Cybercrime (Second Edition), 2008
Digital Certificates
As mentioned earlier, public fundamental encryption is more secure than surreptitious key encryption because in that location is no need to transmit a central beyond unsecured channels, but public central cryptography is also more complex, and it'southward more hard to implement on a big calibration. In that location must exist a organisation that ensures that public keys that are posted to the Internet are not forgeries posted by someone who purports to be another user. If this happens, the information that is encrypted with that public key (and intended to exist sent to the user whose name was associated with it) could be intercepted by the unauthorized user who posted the key. That unauthorized person would and so exist able to decrypt the data and read the message.
We demand a mechanism that volition provide a way for a trusted tertiary party to confirm that the user who publishes the public central is in fact who he or she claims to be. A digital certificate provides this assurance. To empathise how a digital document works, think of the way a driver'southward license or government-issued ID carte du jour is used for identity verification. If a store or banking concern requires that y'all bear witness your identity past producing a license or ID carte, that entity is relying on the word of a trusted third party (in this instance, the Department of Motor Vehicles [DMV]) that y'all are who you say yous are. The store or bank presumes that the DMV has checked you out and would not accept issued the official identification document unless your identity was confirmed.
Just as the store or depository financial institution accepts your driver'due south license every bit proof of your identity, another computer with which you want to exchange information or make transactions volition accept the digital certificate issued by a trusted third party. In the case of digital certificates, the trusted third party is a document say-so (CA). The CA verifies that a particular identity is bound to the public key that is included in the document.
Some public CAs, such as VeriSign, issue certificates to persons on the Internet. Some private (internal) CAs are prepare by organizations to issue certificates to users within the local network. The CA is a server that runs special software that allows it to outcome, manage, and revoke digital certificates. The CA's role is to guarantee to other users, computers, and applications that a particular public key actually belongs to the entity with whose name information technology is associated.
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Encryption
Sharon Thousand. Black Attorney-at-Law , in Telecommunications Law in the Net Historic period, 2002
nine.v COMPARISON OF Private-Primal AND PUBLIC-Central ENCRYPTION TECHNOLOGIES
Both individual-key and public-key encryption systems were developed in academia in the early 1970s and provide very secure modernistic communications over public networks. Both apply computers and many of the same technical concepts and approaches including (ane) a mathematical process that generates each key, (2) an error checking scheme that also generates a hash, (3) message digests, (iv) cardinal IDs, (5) central certificates, and (six) central rings. Nevertheless, the manner in which the two encryption systems do this differs significantly. The similarities and differences, advantages and disadvantages, of each are compared in Table nine.one on pages 354 and 355.
Tabular array 9.one.
| Private-Fundamental Systems | Public-Key Systems | |
|---|---|---|
| Knowledge of Keys | Both sender and receiver must know the (same) primal before they can substitution encrypted information. |
|
| Knowledge of Recipient | Sender and receiver must know each other, take had previous feel with each other, or have some fashion to commutation key information before they can communicate. |
|
| Use in Internet Age | Difficult to use outside a closed circle because of requirement for communicators to know the key prior to information exchange. |
|
| Key Exchange | Requires secure key substitution. | No need for key substitution. |
| Key Creation and Control | Primal creation, manus-off and command are generally provided by a centralized authority. |
|
| Flexibility to Change Keys |
|
|
| Breakability of Fundamental |
| The possessor of a key controls his or her private key and never needs to reveal it to others. If the owner believes the primal has been compromised, the owner can change the key quickly and easily. Since the user's private cardinal need not be shared with or communicated to anyone else, it has fewer opportunities to be compromised and therefore is generally considered to exist more secure than a private cardinal. In add-on, mistake-checking systems will reveal if the message or code were inverse in whatever way, alerting the key owner to a possible discovery or duplication of the key. |
| Forgibility | Tin be copied and/or forged. | Not forgible. |
| Speed | Fast. |
|
| Revolutionary Characteristics | Bachelor to corporate and individual users because of increased speed and lower cost of computing power. |
|
Given today's technological environment, encryption provides a very effective, efficient, and affordable means of retaining privacy in communications and protecting users against electronic theft, fraud, and forgery. As such, information technology meets the privacy needs of modern communicators, whether over the Net, satellite, optic fiber, wireless, or other paths of modernistic communications.
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