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A guide to asymmetric Encryption designed with CIE A-level exams in mind.

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A guide to asymmetric Encryption designed with CIE A-level exams in mind.

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Asymmetric Encryption

The problem with secret keys is exchanging them over the Internet or a large network while preventing them from falling into the wrong hands. Anyone who knows the secret key can decrypt the message. One answer is asymmetric encryption, in which there are two related keys--a key pair. A public key is made freely available to anyone who might want to send you a message. A second, private key is kept secret, so that only you know it.

Any message (text, binary files, or documents) that are encrypted by using the public key can only be decrypted by applying the same algorithm, but by using the matching private key. Any message that is encrypted by using the private key can only be decrypted by using the matching public key.

This means that you do not have to worry about passing public keys over the Internet (the keys are supposed to be public). A problem with asymmetric encryption, however, is that it is slower than symmetric encryption. It requires far more processing power to both encrypt and decrypt the content of the message.

Asymmetric encryption,
also known as public-key encryption, utilizes a pair of keys – a public key and a private key. If you encrypt data with the public key, only the holder of the corresponding private key can decrypt the data, hence ensuring confidentiality.

The first practical algorithm for asymmetric encryption was proposed by Diffie and Hellman in 1976. Subsequently, RSA became the most widely deployed asymmetric encryption algorithm.

Many “secure” online transaction systems rely on asymmetric encryption to establish a secure channel. SSL, for example, is a protocol that utilizes asymmetric encryption to provide communication security on the Internet.

An asymmetric encryption algorithms typically involve exponential operations, they are not lightweight in terms of performance. For that reason, asymmetric algorithms are often used to secure key exchanges rather than used for bulk data encryption.

The case for asymmetric-key cryptography

In a large network, asymmetric key cryptography yields a more efficient system for key management, as you don’t have to manage pair-wise keys for every communicating pair.

Asymmetric key cryptosystems are good for digital signatures and key exchange use cases

In many cases, the public and private key pairs in an asymmetric-key cryptosystem can remain intact for many years without compromising the security of the system. SSL certificates are one such example.

One of the most interesting facts about asymmetric key cryptosystems is that the security of these systems is based on a small set of number-theory problems that are presumed difficult but were never mathematically proven to be difficult. Factoring, for instance, is one such problem. Advances in number theory could one day render factoring a much easier problem hence diminishing security of many asymmetric key cryptosystems.

For CipherCloud, as we routinely protect customer data migrating to the cloud. We chose AES, a symmetric cipher, with a strong 256-bit implementation. With this choice, not only our implementation remains efficient, it also lends itself to a model where our customers retain exclusive control of the key.

How Encryption Works

Public Key Encryption

One of the weaknesses some point out about symmetric key encryption is that two users attempting to communicate with each other need a secure way to do so; otherwise, an attacker can easily pluck the necessary data from the stream. In November 1976, a paper published in the journal IEEE Transactions on Information Theory, titled "New Directions in Cryptography," addressed this problem and offered up a solution:public-key encryption.

Also known as asymmetric-key encryption, public-key encryption uses two different keys at once -- a combination of a private key and a public key. The private key is known only to your computer, while the public key is given by your computer to any computer that wants to communicate securely with it. To decode an encrypted message, a computer must use the public key, provided by the originating computer, and its own private key. Although a message sent from one computer to another won't be secure since the public key used for encryption is published and available to anyone, anyone who picks it up can't read it without the private key. The key pair is based on prime numbers (numbers that only have divisors of itself and one, such as 2, 3, 5, 7, 11 and so on) of long length. This makes the system extremely secure, because there is essentially an infinite number of prime numbers available, meaning there are nearly infinite possibilities for keys. One very popular public-key encryption program is Pretty Good Privacy (PGP), which allows you to encrypt almost anything.

Asymmetrical Encryption (Public and Private Key Encryption)
https://www.youtube.com/watch?v=k5ngaAmI2yA

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The process of Asymmetric encryption

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Asymmetric encryption is also known as public-key cryptography. Asymmetric encryption differs from symmetric encryption primarily in that two keys are used: one for encryption and one for decryption. The most common asymmetric encryption algorithm is RSA.

Compared to symmetric encryption, asymmetric encryption imposes a high computational burden, and tends to be much slower. Thus, it isn't typically employed to protect payload data. Instead, its major strength is its ability to establish a secure channel over a nonsecure medium (for example, the Internet). This is accomplished by the exchange of public keys, which can only be used to encrypt data. The complementary private key, which is never shared, is used to decrypt.

Robust encryption solutions such as IPsec implement the strengths of both symmetric and asymmetric encryption. First, two endpoints exchange public keys, which allows for the setup of a slow but secure channel. Then the two hosts decide on and exchange shared symmetric encryption keys to construct much faster symmetric encryption channels for data.

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INTRODUCTION
Asymmetric encryption, also known as Public-Key encryption, uses two different keys - a public key to encrypt the message, and a private key to decrypt it. The public key can only be used to encrypt the message and the private key can only be used to decrypt it. This allows a user to freely distribute his or her public key to people who are likely to want to communicate with him or her without worry of compromise because only someone with the private key can decrypt a message. To secure information between two users, the sender encrypts the message using the public key of the receiver. The receiver then uses the private key to decrypt the message. Unlike with single or shared keys, in the asymmetric key system only the recipient can decrypt a message; once the sender has encrypted the message he or she cannot decrypt it. The private key is never distributed, therefore an attacker cannot intercept a key that decrypts the message.

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Public key cryptography, or asymmetric cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner. This accomplishes two functions: authentication, which is when the public key is used to verify that a holder of the paired private key sent the message, and encryption, whereby only the holder of the paired private key can decrypt the message encrypted with the public key.

In a public key encryption system, any person can encrypt a message using the public key of the receiver, but such a message can be decrypted only with the receiver's private key. For this to work it must be computationally easy for a user to generate a public and private key-pair to be used for encryption and decryption. The strength of a public key cryptography system relies on the degree of difficulty (computational impracticality) for a properly generated private key to be determined from its corresponding public key. Security then depends only on keeping the private key private, and the public key may be published without compromising security.[1]

Public key cryptography systems often rely on cryptographic algorithms based on mathematical problems that currently admit no efficient solution—particularly those inherent in certain integer factorization, discrete logarithm, and elliptic curve relationships. Public key algorithms, unlike symmetric key algorithms, do not require a secure channel for the initial exchange of one (or more) secret keys between the parties.

Because of the computational complexity of asymmetric encryption, it is usually used only for small blocks of data, typically the transfer of a symmetric encryption key (e.g. a session key). This symmetric key is then used to encrypt the rest of the potentially long message sequence. The symmetric encryption/decryption is based on simpler algorithms and is much faster.[2]

In a public key signature system, a person can combine a message with a private key to create a short digital signature on the message. Anyone with the corresponding public key can combine a message, a putative digital signature on it, and a known public key to verify whether the signature was valid—made by the owner of the corresponding private key. Changing the message, even replacing a single letter, will cause verification to fail: in a secure signature system, it is computationally infeasible for anyone who does not know the private key to deduce it from the public key or from any number of signatures, or to find a valid signature on any message for which a signature has not hitherto been seen. Thus the authenticity of a message can be demonstrated by the signature, provided the owner of the private key keeps the private key secret.[3][4]

Public key algorithms are fundamental security ingredients in cryptosystems, applications and protocols. They underpin various Internet standards, such as Transport Layer Security (TLS), S/MIME, PGP, and GPG. Some public key algorithms provide key distribution and secrecy (e.g., Diffie–Hellman key exchange), some provide digital signatures (e.g., Digital Signature Algorithm), and some provide both (e.g., RSA).

Public key cryptography finds application in, among others, the information technology security discipline, information security. Information security (IS) is concerned with all aspects of protecting electronic information assets against security threats.[5] Public key cryptography is used as a method of assuring the confidentiality, authenticity and non-repudiability of electronic communications and data storage.

Contents

https://www.youtube.com/watch?v=v2zneLle2wY

Aymmetric Algorithms - XTR

In cryptography, XTR is an algorithm for public-key encryption. XTR stands for ‘ECSTR’, which is an abbreviation for Efficient and Compact Subgroup Trace Representation. It is a method to represent elements of a subgroup of a multiplicative group of a finite field. To do so, it uses the trace over G F ( p 2){\displaystyle GF(p^{2})}to represent elements of a subgroup of G F ( p 6) ∗{\displaystyle GF(p^{6})^{*}}.

From a security point of view, XTR relies on the difficulty of solving Discrete Logarithm related problems in the full multiplicative group of a finite field. Unlike many cryptographic protocols that are based on the generator of the full multiplicative group of a finite field, XTR uses the generator g{\displaystyle g}of a relatively small subgroup of some prime order q{\displaystyle q}of a subgroup of G F ( p 6) ∗{\displaystyle GF(p^{6})^{*}}. With the right choice of q{\displaystyle q}, computing Discrete Logarithms in the group, generated by g{\displaystyle g}, is, in general, as hard as it is in G F ( p 6) ∗{\displaystyle GF(p^{6})^{*}}and thus cryptographic applications of XTR use G F ( p 2){\displaystyle GF(p^{2})}arithmetics while achieving full G F ( p 6){\displaystyle GF(p^{6})}security leading to substantial savings both in communication and computational overhead without compromising security. Some other advantages of XTR are its fast key generation, small key sizes and speed.

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SAMBUNGAN :-

HOW IT WORKS

1. Bob creates a pair of keys, one of which he keeps secret and one of which he sends to Alice.

2. Alice composes a confidential message and encrypts it using the key that Bob has sent to her.

3. Alice sends the encrypted data to Bob.

4. Bob uses his secret key to decrypt the data and reads the confidential message.

IMPLEMENT THIS ASYMETRIC ENCRYPTION FOR ORGANIZATION THAT :-

Asymmetric Encryption Algorithms, Diffie-Hellman, RSA, ECC, ElGamal, DSA.
The following are the major asymmetric encryption algorithms used for encrypting or digitally signing data.
Diffie-Hellman key agreement: -Diffie-Hellman key agreement algorithm was developed by Dr. Martin Hellman and Dr. Whitfield Diffie  in 1976.

DEFINITION OF ASYMETRIC ENCRYPTION:-
Asymmetric Encryption is a form of Encryption where keys come in pairs. What one key encrypts, only the other can decrypt.

Frequently (but not necessarily), the keys are interchangeable, in the sense that if key A encrypts a message, then B can decrypt it, and if key B encrypts a message, then key A can decrypt it. While common, this property is not essential to asymmetric encryption.

Asymmetric Encryption is also known as Public Key Cryptography, since users typically create a matching key pair, and make one public while keeping the other secret.

Users can "sign" messages by encrypting them with their private keys. This is effective since any message recipient can verify that the user's public key can decrypt the message, and thus prove that the user's secret key was used to encrypt it. If the user's secret key is, in fact, secret, then it follows that the user, and not some impostor, really sent the message.

Users can send secret messages by encrypting a message with the recipient's public key. In this case, only the intended recipient can decrypt the message, since only that user should have access to the required secret key.

The key to successful use of Asymmetric Encryption is a Key Management system, which implements a Public Key Infrastructure. Without this, it is difficult to establish the reliability of public keys, or even to conveniently find suitable ones.

LINK:https://www.youtube.com/watch?v=E5FEqGYLL0o

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A much more secure cryptosystem is the asymmetric key cryptosystem and was invented in the 1970s. Asymmetric key cryptosystem requires a pair of keys: a public key and a private key for encryption and decryption.

In this cryptosystem, a message sender needs to get a public key from a message receiver and then encrypt the message by using the given key. Message receiver decrypts the message by using a corresponding private key which only the message receiver has. In an asymmetric key cryptosystem, the key for encryption (public key) and the key for decryption (private key) are completely non-identical to assure high security for the message.

In the open networks (e.g. Internet) the messages go through systems controlled by different service providers, thus not only the addressee might get access to them. The aim of increasing security is that the sender and the receiver could unequivocally be identified; the original message could not be changed as well as others could not access it. The most up-to-date technical solution for this problem is asymmetric (also named public key) encryption procedure and its most widespread version RSA. (The letters RSA are the initials of the surnames of the describers = Ronald Rivest, Adi Shamir, Leonard Adlemann.)

Advantage of the public key encryption is that the coding party (sender) and the decoding party (receiver) do not have to exchange a secret password or key. Instead every user has a key pair ensuring secure communication. One of the keys is private while the other is public. The two keys are derived from the same key generation procedure; they belong completely to each other, but none of them can be concluded from the other. Every user must keep his/her private key confidential, while the public key has to be presented to everyone with whom you wish to communicate (e.g. by means of the so-called key data base available for everyone). In case of asymmetric encryption the communicating parties need no reliable channel or personal meeting, only the authenticity of the key and the connection with the owner have to be proved.

During the encryption process the data are encrypted (encoded) by the public key belonging to the encrypting certificate of the receiving party while on the receiving side decoding is possible only by the private counterpart of the public key used for encrypting.

For the above reason the encrypted data can only and exclusively be interpreted/read by the person who has the private counterpart of the public key. Accordingly private encrypted data can only be sent to the person who has a valid encryption certificate issued by a reliable Certification Authority.

YOUTUBE LINK : https://www.youtube.com/watch?v=E5FEqGYLL0o

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Bersambung....

How it works
1.The key that Bob sends to Alice is the public key, and the key he keeps to himself is the "private" key; jointly, they form Bob's "key pair."

2.The most striking aspect of asymmetric encryption is that Alice is not involved in selecting the key: Bob creates a pair of keys without any input or agreement from Alice and simply sends her the public key. Bob retains the private key and keeps it secret. Alice uses an asymmetric algorithm to encrypt a message with Bob's public key and sends him the encrypted data, which he decrypts using the private key.

3.Asymmetric algorithms include a "key generation" protocol that Bob uses to create his key pair, as shown by Figure 15-2. Following the protocol results in the creation of a pair of keys that have a mathematical relationshipthe exact detail of the protocol and the relationship between the keys is different for each algorithm.
4.When we talk about an asymmetric encryption algorithm, we are actually referring to two related functions that perform specific tasks: an encryption function that encrypts a message using a public key, and a decryption function that uses a secret key to decrypt a message encrypted with the corresponding public key.

5.The encryption function can only encrypt data. Alice cannot decrypt ciphertext that she has created using the encryption function. This means that Bob can send his public key to several people, and each of them can create ciphertext that only Bob's secret key can decrypt .

ORGANIZATION THAT IMPLEMENT THIS ENCRYPTION

In the most common, Alice and Bob each own two keys, one for encryption and one for decryption. In a secure asymmetric key encryption scheme, the private key should not be deducible from the public key. ... In the alternative, when a message is encrypted with the public key, only the private key can decrypt it.

Link
https://www.youtube.com/watch?v=E5FEqGYLL0o

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INTRODUCTION
Asymmetric Encryption is a form of Encryption where keys come in pairs. What one key encrypts, only the other can decrypt.

Frequently (but not necessarily), the keys are interchangeable, in the sense that if key A encrypts a message, then B can decrypt it, and if key B encrypts a message, then key A can decrypt it. While common, this property is not essential to asymmetric encryption.

Asymmetric Encryption is also known as Public Key Cryptography, since users typically create a matching key pair, and make one public while keeping the other secret.

Users can "sign" messages by encrypting them with their private keys. This is effective since any message recipient can verify that the user's public key can decrypt the message, and thus prove that the user's secret key was used to encrypt it. If the user's secret key is, in fact, secret, then it follows that the user, and not some impostor, really sent the message.

Users can send secret messages by encrypting a message with the recipient's public key. In this case, only the intended recipient can decrypt the message, since only that user should have access to the required secret key.

The key to successful use of Asymmetric Encryption is a Key Management system, which implements a Public Key Infrastructure. Without this, it is difficult to establish the reliability of public keys, or even to conveniently find suitable ones.

HOW IT WORKS

In the open networks (e.g. Internet) the messages go through systems controlled by different service providers, thus not only the addressee might get access to them. The aim of increasing security is that the sender and the receiver could unequivocally be identified; the original message could not be changed as well as others could not access it. The most up-to-date technical solution for this problem is asymmetric (also named public key) encryption procedure and its most widespread version RSA. (The letters RSA are the initials of the surnames of the describers = Ronald Rivest, Adi Shamir, Leonard Adlemann.)

Advantage of the public key encryption is that the coding party (sender) and the decoding party (receiver) do not have to exchange a secret password or key. Instead every user has a key pair ensuring secure communication. One of the keys is private while the other is public. The two keys are derived from the same key generation procedure; they belong completely to each other, but none of them can be concluded from the other. Every user must keep his/her private key confidential, while the public key has to be presented to everyone with whom you wish to communicate (e.g. by means of the so-called key data base available for everyone). In case of asymmetric encryption the communicating parties need no reliable channel or personal meeting, only the authenticity of the key and the connection with the owner have to be proved.

During the encryption process the data are encrypted (encoded) by the public key belonging to the encrypting certificate of the receiving party while on the receiving side decoding is possible only by the private counterpart of the public key used for encrypting.

For the above reason the encrypted data can only and exclusively be interpreted/read by the person who has the private counterpart of the public key. Accordingly private encrypted data can only be sent to the person who has a valid encryption certificate issued by a reliable Certification Authority.

The process of encryption:

ASYMMETRIC ENCRYPTION ALGORITHM
Rivest Shamir Adleman (RSA): Ron Rivest, Adi Shamir, and Len Adleman released the Rivest-Shamir-Adleman (RSA) public key algorithm in 1978. This algorithm can be used for encrypting and signing data. The encryption and signing processes are performed through a series of modular multiplications.

The basic RSA algorithm for confidentiality can be explained as below.

Ciphertext = (plaintext)^e mod n
Plaintext = (ciphertext)^d mod n
Private Key = {d, n}
Public Key = {e, n}

The basic RSA algorithm for authentication can be explained as below.

ciphertext = (plaintext)^d mod n
plaintext = (ciphertext)^e mod n
private key = {d, n}
public key = {e, n}

Encryption key management tips

Key management is not simple: If encrypting data, somebody must manage the keys and you must have key recovery procedures in place.

Within large businesses, key management processes must be capable of being distributed across multiple business functions with the same standards, rules and quality levels.

Have one point of contact for cryptography; don't spread it among operational users.

Ensure the central key repository is well protected.

Decide whether your outsourcer will have any role in key management, such as key pair generation, recovery of keys and escrow access.

Decide whether you will have a 'two person' rule for aspects of key management.

Decide whether information security should manage keys as well as encryption policy. (In practice, during development, key management is the responsibility of the project, but handed over to security at implementation.)

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INTRODUCTION

Asymmetric Encryption is a form of Encryption where keys come in pairs. What one key encrypts, only the other can decrypt.

Frequently (but not necessarily), the keys are interchangeable, in the sense that if key A encrypts a message, then B can decrypt it, and if key B encrypts a message, then key A can decrypt it. While common, this property is not essential to asymmetric encryption.

Asymmetric Encryption is also known as Public Key Cryptography, since users typically create a matching key pair, and make one public while keeping the other secret.

Users can "sign" messages by encrypting them with their private keys. This is effective since any message recipient can verify that the user's public key can decrypt the message, and thus prove that the user's secret key was used to encrypt it. If the user's secret key is, in fact, secret, then it follows that the user, and not some impostor, really sent the message.

Users can send secret messages by encrypting a message with the recipient's public key. In this case, only the intended recipient can decrypt the message, since only that user should have access to the required secret key.

The key to successful use of Asymmetric Encryption is a Key Management system, which implements a Public Key Infrastructure. Without this, it is difficult to establish the reliability of public keys, or even to conveniently find suitable ones.

Source :
http://hitachi-id.com/concepts/asymmetric_encryption.html

HOW IT WORKS

To decode an encrypted message, a computer must use the public key, provided by the originating computer, and its own private key. Although a message sent from one computer to another won't be secure since the public key used for encryption is published and available to anyone, anyone who picks it up can't read it without the private key. The key pair is based on prime numbers (numbers that only have divisors of itself and one, such as 2, 3, 5, 7, 11 and so on) of long length. This makes the system extremely secure, because there is essentially an infinite number of prime numbers available, meaning there are nearly infinite possibilities for keys. One very popular public-key encryption program is Pretty Good Privacy (PGP), which allows you to encrypt almost anything.
The sending computer encrypts the document with a symmetric key, then encrypts the symmetric key with the public key of the receiving computer. The receiving computer uses its private key to decode the symmetric key. It then uses the symmetric key to decode the document.

Source : http://computer.howstuffworks.com/encryption3.htm

ORGANISATION THAT IMPLEMENT THIS STANDARD
Digital signatures are based on asymmetric cryptography and can provide assurances of evidence to origin, identity and status of an electronic document, transaction or message, as well as acknowledging informed consent by the signer. To create a digital signature, signing software (such as an email program) creates a one-way hash of the electronic data to be signed. The user's private key is then used to encrypt the hash, returning a value that is unique to the hashed data. The encrypted hash, along with other information such as the hashing algorithm, forms the digital signature. Any change in the data, even to a single bit, results in a different hash value. This attribute enables others to validate the integrity of the data by using the signer's public key to decrypt the hash. If the decrypted hash matches a second computed hash of the same data, it proves that the data hasn't changed since it was signed. If the two hashes don't match, the data has either been tampered with in some way (indicating a failure of integrity) or the signature was created with a private key that doesn't correspond to the public key presented by the signer (indicating a failure of authentication).

A digital signature also makes it difficult for the signing party to deny having signed something (the property of non-repudiation). If a signing party denies a valid digital signature, their private key has either been compromised, or they are being untruthful. In many countries, including the United States, digital signatures have the same legal weight as more traditional forms of signatures.

Source :
http://searchsecurity.techtarget.com/definition/asymmetric-cryptography

ASYMMETRIC ALGORITHMS
Digital Signature Algorithm

Digital Signature Algorithm (DSA) is a United States Federal Government standard or FIPS for digital signatures. It was proposed by the National Institute of Standards and Technology (NIST) in August 1991 for use in their Digital Signature Algorithm (DSA), specified in FIPS 186 [1], adopted in 1993. A minor revision was issued in 1996 as FIPS 186-1 [2], and the standard was expanded further in 2000 as FIPS 186-2 [3]. Digital Signature Algorithm (DSA) is similar to the one used by ElGamal signature algorithm. It is fairly efficient though not as efficient as RSA for signature verification. The standard defines DSS to use the SHA-1 hash function exclusively to compute message digests.
The main problem with DSA is the fixed subgroup size (the order of the generator element), which limits the security to around only 80 bits. Hardware attacks can be menacing to some implementations of DSS. However, it is widely used and accepted as a good algorithm.

Source :
http://www.encryptionanddecryption.com/algorithms/asymmetric_algorithms.html

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INTRODUCTION
Asymmetric cryptography, also known as public key cryptography, uses public and private keys to encrypt and decrypt data. The keys are simply large numbers that have been paired together but are not identical (asymmetric). One key in the pair can be shared with everyone; it is called the public key. The other key in the pair is kept secret; it is called the private key. Either of the keys can be used to encrypt a message; the opposite key from the one used to encrypt the message is used for decryption.

HOW IT'S WORK AND ORGANIZATION THAT IMPLEMENT THIS ENCRIPTION
Many protocols like SSH, OpenPGP, S/MIME, and SSL/TLS rely on asymmetric cryptography for encryption and digital signature functions. It is also used in software programs, such as browsers, which need to establish a secure connection over an insecure network like the internet or need to validate a digital signature. Encryption strength is directly tied to key size and doubling key length delivers an exponential increase in strength, although it does impair performance. As computing power increases and more efficient factoring algorithms are discovered, the ability to factor larger and larger numbers also increases.

For asymmetric encryption to deliver confidentiality, integrity, authenticity and non-repudiability, users and systems need to be certain that a public key is authentic, that it belongs to the person or entity claimed and that it has not been tampered with or replaced by a malicious third party. There is no perfect solution to this public key authentication problem. A public key infrastructure (PKI), where trusted certificate authorities certify ownership of key pairs and certificates, is the most common approach, but encryption products based on the Pretty Good Privacy (PGP) model (including OpenPGP), rely on a decentralized authentication model called a web of trust, which relies on individual endorsements of the link between user and public key

Whitfield Diffie and Martin Hellman, researchers at Stanford University, first publicly proposed asymmetric encryption in their 1977 paper, "New Directions in Cryptography." The concept had been independently and covertly proposed by James Ellis several years before, while working for the Government Communications Headquarters (GCHQ), the British intelligence and security organization. The asymmetric algorithm as outlined in the Diffie-Hellman paper uses numbers raised to specific powers to produce decryption keys.

RSA (Rivest-Shamir-Adleman), the most widely used asymmetric algorithm, is embedded in the SSL/TLS protocol which is used to provide communications security over a computer network. RSA derives its security from the computational difficulty of factoring large integers that are the product of two large prime numbers. Multiplying two large primes is easy, but the difficulty of determining the original numbers from the total -- factoring -- forms the basis of public key cryptography security. The time it takes to factor the product of two sufficiently large primes is considered to be beyond the capabilities of most attackers, excluding nation state actors who may have access to sufficient computing power. RSA keys are typically 1024- or 2048-bits long, but experts believe that 1024-bit keys could be broken in the near future, which is why government and industry are moving to a minimum key length of 2048-bits.

Elliptic Curve Cryptography (ECC) is gaining favor with many security experts as an alternative to RSA for implementing public-key cryptography. ECC is a public key encryption technique based on elliptic curve theory that can create faster, smaller, and more efficient cryptographic keys. ECC generates keys through the properties of the elliptic curve equation. To break ECC, one must compute an elliptic curve discrete logarithm, and it turns out that this is a significantly more difficult problem than factoring. As a result, ECC key sizes can be significantly smaller than those required by RSA yet deliver equivalent security with lower computing power and battery resource usage making it more suitable for mobile applications than RSA.

Digital signatures and asymmetric cryptography

Digital signatures are based on asymmetric cryptography and can provide assurances of evidence to origin, identity and status of an electronic document, transaction or message, as well as acknowledging informed consent by the signer. To create a digital signature, signing software (such as an email program) creates a one-way hash of the electronic data to be signed. The user's private key is then used to encrypt the hash, returning a value that is unique to the hashed data. The encrypted hash, along with other information such as the hashing algorithm, forms the digital signature. Any change in the data, even to a single bit, results in a different hash value. This attribute enables others to validate the integrity of the data by using the signer's public key to decrypt the hash. If the decrypted hash matches a second computed hash of the same data, it proves that the data hasn't changed since it was signed. If the two hashes don't match, the data has either been tampered with in some way (indicating a failure of integrity) or the signature was created with a private key that doesn't correspond to the public key presented by the signer (indicating a failure of authentication).

A digital signature also makes it difficult for the signing party to deny having signed something (the property of non-repudiation). If a signing party denies a valid digital signature, their private key has either been compromised, or they are being untruthful. In many countries, including the United States, digital signatures have the same legal weight as more traditional forms of signatures.

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How asymmetric (public key) encryption works

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How asymmetric (public key) encryption works

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Asymetric Encryption

INTRODUCTION
Public key cryptography, or asymmetric cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner. In a public key encryption system, any person can encrypt a message using the public key of the receiver, but such a message can be decrypted only with the receiver's private key. For this to work it must be computationally easy for a user to generate a public and private key-pair to be used for encryption and decryption. The strength of a public key cryptography system relies on the degree of difficulty (computational impracticality) for a properly generated private key to be determined from its corresponding public key. Security then depends only on keeping the private key private, and the public key may be published without compromising security.[1]

Public key cryptography systems often rely on cryptographic algorithms based on mathematical problems that currently admit no efficient solution—particularly those inherent in certain integer factorization, discrete logarithm, and elliptic curve relationships. Public key algorithms, unlike symmetric key algorithms, do not require a secure channel for the initial exchange of one (or more) secret keys between the parties.

Because of the computational complexity of asymmetric encryption, it is usually used only for small blocks of data, typically the transfer of a symmetric encryption key (e.g. a session key). This symmetric key is then used to encrypt the rest of the potentially long message sequence. The symmetric encryption/decryption is based on simpler algorithms and is much faster.[2]

In a public key signature system, a person can combine a message with a private key to create a short digital signature on the message. Anyone with the corresponding public key can combine a message, a putative digital signature on it, and a known public key to verify whether the signature was valid—made by the owner of the corresponding private key. Changing the message, even replacing a single letter, will cause verification to fail: in a secure signature system, it is computationally infeasible for anyone who does not know the private key to deduce it from the public key or from any number of signatures, or to find a valid signature on any message for which a signature has not hitherto been seen. Thus the authenticity of a message can be demonstrated by the signature, provided the owner of the private key keeps the private key secret.[3][4]

Public key algorithms are fundamental security ingredients in cryptosystems, applications and protocols. They underpin various Internet standards, such as Transport Layer Security (TLS), S/MIME, PGP, and GPG. Some public key algorithms provide key distribution and secrecy (e.g., Diffie–Hellman key exchange), some provide digital signatures (e.g., Digital Signature Algorithm), and some provide both (e.g., RSA).

Public key cryptography finds application in, among others, the information technology security discipline, information security. Information security (IS) is concerned with all aspects of protecting electronic information assets against security threats.[5] Public key cryptography is used as a method of assuring the confidentiality, authenticity and non-repudiability of electronic communications and data storage.

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INTRODUCTION
The object of secure communications has been to provide privacy or secrecy, i.e., to hide the contents of a publicly exposed message from unauthorized recipients. In contemporary commercial and diplomatic applications, however, it is frequently of equal or even greater concern that the receiver be able to verify that the message has not been modified during transmission or that it is not a counterfeit from an unauthorized transmitter. In at least one important class of problems message authentication is needed at the same time that the message itself is revealed. In this paper secure communications are discussed with emphasis on applications that cannot be satisfactorily handled by present cryptographic techniques. Fortunately, an entirely new concept--the asymThis article was sponsored by the U.S Department of Energy under Contract DE-AC04-76DP00789. metric encryption/decryption channel-- solves the new requirements in secure communications. For perspective, the reader should keep in mind that all current cryptosystems are symmetric in the sense that either the same piece of information (key) is held in secret by both communicants, or else that each communicant holds one from a pair of related keys where either key is easily derivable from the other. These secret keys are used in the encryption process to introduce uncertainty (to the unauthorized receiver), which can be removed in the process of decryption by an authorized receiver using his copy of the key or the "inverse key." This means, of course, that if a key is compromised, further secure communications are impossible with that key. The new cryptosystems are asymmetric in the sense that the transmitter and receiver hold different keys at least one of which it is computationally infeasible to derive from the other.

HOW IT WORKS

ORGANIZATION IMPLEMENT THIS

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1 Introduction

We have now defined two functions that are hard to perform: computing the inverse of a one-way function and distinguishing the output of a pseudo-random function from a random function. We then gave high-level definitions of more useful operations: cryptographic hash functions and encryption, which can be based on one-way functions and pseudo-random functions, respectively. But shared keys are inherently limiting; these keys must be shared between each pair of principals and complicate the process of adding new principals to the system. Similarly, shared key operations are not easily applicable to cases where one principal performs an operation that affects many principals. An asymmetric key setup would solve both of these problems: each principal has its own key information that it does not need to share in secret with other principals.

For an example of how problems arise in symmetric-key settings, consider how we might perform some of our shared-key operations in a context with, say, three principals, A, B, and C. Principal A wants to send a message to B and C in such a way that both know that it came from A. If A and B share key kAB and A and C share key kAC, then it's not obvious how to send a bit string that guarantees this property (though such schemes exist); the naive solution of computing a pair (MAC(m, kAB), MAC(m, kAC)) and sending it as an authenticator doesn't work if B and C don't trust each other or don't trust A, since one element of the pair might pass the check for one principal and the other not pass the check for the other principal. If A, B, and C all share a single key, then B or C could create a MAC that appears to come from A.

So, shared keys between more than two principals lose some properties. First, they lose their binding to identities. Second, authentication for different principals cannot be guaranteed. Third, they complicate open systems, in which new principals can appear at any time, since new principals must be given a key shared with each other principal.

To get around this problem, recall the example of the stock broker. The client published a pair M₁ and M₂ of numbers. It happened that the stock broker was the principal that used these numbers and checked them, but any principal could have performed the stock broker's actions, since M₁ and M₂ were published by the client. We say that key information published like M₁ and M₂ is a public key and m₁ and m₂ are the corresponding private key.

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MOHD IMRAN SHAFIQ BIN NIAMAT [O3DDT16F1096]

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MOHD IMRAN SHAFIQ BIN NIAMAT [O3DDT16F1096]

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-Introduction
Asymmetric Encryption

Asymmetric encryption is a much stronger form of encryption. In this method when an encryption is created, two keys are produced. One is a private key that the creator holds on to and the other is a public key that is released into the public domain. SSL certificates are an example of asymmetric encryption
Each key can only open messages that have been encrypted by the other. So the private key can open public key encrypted messages and the public key can open messages encrypted with the private key. This is beneficial in a number of ways:

If you wish to send encrypted data to someone, you can use their public key to encrypt it and send it to them knowing that only the person with the private key can open it.

The person with the private key can send a message, and whilst anyone with the public key can open it, it confirms the message has come from the correct location.

A very secure way of sending a message is to encrypt it first with your private key and then with the other person's public key. This means that someone with just your public key can now not open it. Only the intended recipient can open it - first using their private key and then your public key to read the information.It is virtually impossible to work out someone's private key from their public key. This is due to the complex algorithm and the use of 1024-bit keys. However as computers improve the number of bits used will likely have to increase. The greatest fear for our current encryption is quantum computers - they could potentially process data at incredible speeds making all our current types of encryption breakable.

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Digital signatures and asymmetric cryptography

Digital signatures are based on asymmetric cryptography and can provide assurances of evidence to origin, identity and status of an electronic document, transaction or message, as well as acknowledging informed consent by the signer. To create a digital signature, signing software (such as an email program) creates a one-way hash of the electronic data to be signed. The user's private key is then used to encrypt the hash, returning a value that is unique to the hashed data. The encrypted hash, along with other information such as the hashing algorithm, forms the digital signature. Any change in the data, even to a single bit, results in a different hash value. This attribute enables others to validate the integrity of the data by using the signer's public key to decrypt the hash. If the decrypted hash matches a second computed hash of the same data, it proves that the data hasn't changed since it was signed. If the two hashes don't match, the data has either been tampered with in some way (indicating a failure of integrity) or the signature was created with a private key that doesn't correspond to the public key presented by the signer (indicating a failure of authentication).

A digital signature also makes it difficult for the signing party to deny having signed something (the property of non-repudiation). If a signing party denies a valid digital signature, their private key has either been compromised, or they are being untruthful. In many countries, including the United States, digital signatures have the same legal weight as more traditional forms of signatures.

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MOHAMAD AMIRUL SALIHIN BIN KHAIRUL ANUAR (03DDT16F1100

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MOHAMAD AMIRUL SALIHIN BIN KHAIRUL ANUAR (03DDT16F1100

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ASYMETRIC ENCRYPTION

INTRODUCTION
We have now defined two functions that are hard to perform: computing the inverse of a one-way function and distinguishing the output of a pseudo-random function from a random function. We then gave high-level definitions of more useful operations: cryptographic hash functions and encryption, which can be based on one-way functions and pseudo-random functions, respectively. But shared keys are inherently limiting; these keys must be shared between each pair of principals and complicate the process of adding new principals to the system. Similarly, shared key operations are not easily applicable to cases where one principal performs an operation that affects many principals. An asymmetric key setup would solve both of these problems: each principal has its own key information that it does not need to share in secret with other principals.

For an example of how problems arise in symmetric-key settings, consider how we might perform some of our shared-key operations in a context with, say, three principals, A, B, and C. Principal A wants to send a message to B and C in such a way that both know that it came from A. If A and B share key kAB and A and C share key kAC, then it's not obvious how to send a bit string that guarantees this property (though such schemes exist); the naive solution of computing a pair (MAC(m, kAB), MAC(m, kAC)) and sending it as an authenticator doesn't work if B and C don't trust each other or don't trust A, since one element of the pair might pass the check for one principal and the other not pass the check for the other principal. If A, B, and C all share a single key, then B or C could create a MAC that appears to come from A.

So, shared keys between more than two principals lose some properties. First, they lose their binding to identities. Second, authentication for different principals cannot be guaranteed. Third, they complicate open systems, in which new principals can appear at any time, since new principals must be given a key shared with each other principal.

To get around this problem, recall the example of the stock broker. The client published a pair M₁ and M₂ of numbers. It happened that the stock broker was the principal that used these numbers and checked them, but any principal could have performed the stock broker's actions, since M₁ and M₂ were published by the client. We say that key information published like M₁ and M₂ is a public key and m₁ and m₂ are the corresponding private key.

HOW IT WORKS
In the most common, Alice and Bob each own two keys, one for encryption and one for decryption. In a secure asymmetric key encryption scheme, the private key should not be deducible from the public key. ... In the alternative, when a message is encrypted with the public key, only the private key can decrypt it.

ORGANIZATION THAT IMPLEMENT THIS ENCRYPTION

Asymmetric Encryption Algorithms, Diffie-Hellman, RSA, ECC, ElGamal, DSA. The following are the major asymmetric encryption algorithms used for encrypting or digitally signing data. Diffie-Hellman key agreement: Diffie-Hellman key agreement algorithm was developed by Dr. Whitfield Diffie and Dr. Martin Hellman in 1976.

LINK
https://www.youtube.com/watch?v=E5FEqGYLL0o