The other key is designated the private key and is never revealed to another party. It is straight-forward to send messages under this scheme. Suppose Alice wants to send Bob a message. Alice encrypts some information using Bob's public key; Bob decrypts the ciphertext using his private key.
This method could be also used to prove who sent a message; Alice, for example, could encrypt some plaintext with her private key; when Bob decrypts using Alice's public key, he knows that Alice sent the message authentication and Alice cannot deny having sent the message non-repudiation. Public key cryptography algorithms that are in use today for key exchange or digital signatures include:.
RSA today is used in hundreds of software products and can be used for key exchange, digital signatures, or encryption of small blocks of data. RSA uses a variable size encryption block and a variable size key. The key-pair is derived from a very large number, n , that is the product of two prime numbers chosen according to special rules; these primes may be or more digits in length each, yielding an n with roughly twice as many digits as the prime factors.
The public key information includes n and a derivative of one of the factors of n ; an attacker cannot determine the prime factors of n and, therefore, the private key from this information alone and that is what makes the RSA algorithm so secure. Some descriptions of PKC erroneously state that RSA's safety is due to the difficulty in factoring large prime numbers. In fact, large prime numbers, like small prime numbers, only have two factors!
The ability for computers to factor large numbers, and therefore attack schemes such as RSA, is rapidly improving and systems today can find the prime factors of numbers with more than digits. Nevertheless, if a large number is created from two prime factors that are roughly the same size, there is no known factorization algorithm that will solve the problem in a reasonable amount of time; a test to factor a digit number took 1.
In , Kleinjung et al. Even so, they suggested that bit RSA be phased out by See the Wikipedia article on integer factorization. Regardless, one presumed protection of RSA is that users can easily increase the key size to always stay ahead of the computer processing curve. As an aside, the patent for RSA expired in September which does not appear to have affected RSA's popularity one way or the other.
A detailed example of RSA is presented below in Section 5. Diffie-Hellman is used for secret-key key exchange only, and not for authentication or digital signatures. More detail about Diffie-Hellman can be found below in Section 5. More detail about ECC can be found below in Section 5. It is a PKC-based key authentication system where the public key can be derived from some unique information based upon the user's identity, allowing two users to exchange encrypted messages without having an a priori relationship.
More detail about Identity-Based Encryption can be found below in Section 5. These documents are no longer easily available; all links in this section are from archive. Cramer and V. Shoup of IBM in LUC : A public key cryptosystem designed by P.
Smith and based on Lucas sequences. Can be used for encryption and signatures, using integer factoring. McEliece : A public key cryptosystem based on algebraic coding theory. Menezes, P. Vanstone CRC Press, A digression: Who invented PKC? I tried to be careful in the first paragraph of this section to state that Diffie and Hellman "first described publicly" a PKC scheme.
Although I have categorized PKC as a two-key system, that has been merely for convenience; the real criteria for a PKC scheme is that it allows two parties to exchange a secret even though the communication with the shared secret might be overheard. As shown in Section 5. And, indeed, it is the precursor to modern PKC which does employ two keys. Their method, of course, is based upon the relative ease of finding the product of two large prime numbers compared to finding the prime factors of a large number.
Diffie and Hellman and other sources credit Ralph Merkle with first describing a public key distribution system that allows two parties to share a secret, although it was not a two-key system, per se. A Merkle Puzzle works where Alice creates a large number of encrypted keys, sends them all to Bob so that Bob chooses one at random and then lets Alice know which he has selected. An eavesdropper Eve will see all of the keys but can't learn which key Bob has selected because he has encrypted the response with the chosen key.
In this case, Eve's effort to break in is the square of the effort of Bob to choose a key. While this difference may be small it is often sufficient. Merkle apparently took a computer science course at UC Berkeley in and described his method, but had difficulty making people understand it; frustrated, he dropped the course. Merkle's method certainly wasn't published first, but he is often credited to have had the idea first.
An interesting question, maybe, but who really knows? Because of the nature of the work, GCHQ kept the original memos classified. In , however, the GCHQ changed their posture when they realized that there was nothing to gain by continued silence.
Documents show that a GCHQ mathematician named James Ellis started research into the key distribution problem in and that by , James Ellis, Clifford Cocks, and Malcolm Williamson had worked out all of the fundamental details of PKC, yet couldn't talk about their work. They were, of course, barred from challenging the RSA patent! Hash functions, also called message digests and one-way encryption , are algorithms that, in essence, use no key Figure 1C.
Instead, a fixed-length hash value is computed based upon the plaintext that makes it impossible for either the contents or length of the plaintext to be recovered. Hash algorithms are typically used to provide a digital fingerprint of a file's contents, often used to ensure that the file has not been altered by an intruder or virus.
Hash functions are also commonly employed by many operating systems to encrypt passwords. Hash functions, then, provide a mechanism to ensure the integrity of a file.
Hash functions are also designed so that small changes in the input produce significant differences in the hash value, for example:.
This is an important distinction. Suppose that you want to crack someone's password, where the hash of the password is stored on the server. Indeed, all you then need is a string that produces the correct hash and you're in! However, you cannot prove that you have discovered the user's password, only a "duplicate key. Message Digest MD algorithms: A series of byte-oriented algorithms that produce a bit hash value from an arbitrary-length message.
MD2 has been relegated to historical status, per RFC MD4 has been relegated to historical status, per RFC MD5 RFC : Also developed by Rivest after potential weaknesses were reported in MD4; this scheme is similar to MD4 but is slower because more manipulation is made to the original data.
MD5 has been implemented in a large number of products although several weaknesses in the algorithm were demonstrated by German cryptographer Hans Dobbertin in "Cryptanalysis of MD5 Compress". In , NIST announced that after reviewing 64 submissions, the winner was Keccak pronounced "catch-ack" , a family of hash algorithms based on sponge functions. The NIST version can support hash output sizes of and bits. A root hash is used on peer-to-peer file transfer networks, where a file is broken into chunks; each chunk has its own MD4 hash associated with it and the server maintains a file that contains the hash list of all of the chunks.
The root hash is the hash of the hash list file. Zheng, J. Pieprzyk and J. Seberry, a hash algorithm with many levels of security. HAVAL can create hash values that are , , , , or bits in length. Skein supports internal state sizes of , and bits, and arbitrary output lengths.
SM3 : SM3 is a bit hash function operating on bit input blocks. More information can also be found at the SM3 hash function page. Whirlpool : Designed by V. Rijmen co-inventor of Rijndael and P. Whirlpool operates on messages less than 2 bits in length and produces a message digest of bits. The design of this hash function is very different than that of MD5 and SHA-1, making it immune to the types of attacks that succeeded on those hashes.
A digression on hash collisions. Hash functions are sometimes misunderstood and some sources claim that no two files can have the same hash value. This is in theory, if not in fact, incorrect. Consider a hash function that provides a bit hash value. There are, then, 2 possible hash values. Now, while even this is theoretically correct, it is not true in practice because hash algorithms are designed to work with a limited message size, as mentioned above.
The difficulty is not necessarily in finding two files with the same hash, but in finding a second file that has the same hash value as a given first file. Consider this example. Since there are more than 7 billion people on earth, we know that there are a lot of people with the same number of hairs on their head. Finding two people with the same number of hairs, then, would be relatively simple. The harder problem is choosing one person say, you, the reader and then finding another person who has the same number of hairs on their head as you have on yours.
This is somewhat similar to the Birthday Problem. Alas, researchers as far back as found that practical collision attacks could be launched on MD5, SHA-1, and other hash algorithms and, today, it is generally recognized that MD5 and SHA-1 are pretty much broken.
Readers interested in this problem should read the following:. For historical purposes, take a look at the situation with hash collisions, circa , in RFC In October , the SHA-1 Freestart Collision was announced; see a report by Bruce Schneier and the developers of the attack as well as the paper above by Stevens et al. See also the paper by Stevens et al. Stevens, A. Lenstra, and B. Finally, note that certain extensions of hash functions are used for a variety of information security and digital forensics applications, such as:.
So, why are there so many different types of cryptographic schemes? Why can't we do everything we need with just one? The answer is that each scheme is optimized for some specific cryptographic application s. Hash functions, for example, are well-suited for ensuring data integrity because any change made to the contents of a message will result in the receiver calculating a different hash value than the one placed in the transmission by the sender.
Since it is highly unlikely that two different messages will yield the same hash value, data integrity is ensured to a high degree of confidence. Secret key cryptography, on the other hand, is ideally suited to encrypting messages, thus providing privacy and confidentiality. The sender can generate a session key on a per-message basis to encrypt the message; the receiver, of course, needs the same session key in order to decrypt the message.
Key exchange, of course, is a key application of public key cryptography no pun intended. Asymmetric schemes can also be used for non-repudiation and user authentication; if the receiver can obtain the session key encrypted with the sender's private key, then only this sender could have sent the message.
Public key cryptography could, theoretically, also be used to encrypt messages although this is rarely done because secret key cryptography values can generally be computed about times faster than public key cryptography values. Figure 4 puts all of this together and shows how a hybrid cryptographic scheme combines all of these functions to form a secure transmission comprising a digital signature and digital envelope.
In this example, the sender of the message is Alice and the receiver is Bob. A digital envelope comprises an encrypted message and an encrypted session key. Alice uses secret key cryptography to encrypt her message using the session key , which she generates at random with each session. Alice then encrypts the session key using Bob's public key. The encrypted message and encrypted session key together form the digital envelope.
Upon receipt, Bob recovers the session secret key using his private key and then decrypts the encrypted message. The digital signature is formed in two steps. First, Alice computes the hash value of her message; next, she encrypts the hash value with her private key.
Upon receipt of the digital signature, Bob recovers the hash value calculated by Alice by decrypting the digital signature with Alice's public key. Bob can then apply the hash function to Alice's original message, which he has already decrypted see previous paragraph.
If the resultant hash value is not the same as the value supplied by Alice, then Bob knows that the message has been altered; if the hash values are the same, Bob should believe that the message he received is identical to the one that Alice sent. This scheme also provides nonrepudiation since it proves that Alice sent the message; if the hash value recovered by Bob using Alice's public key proves that the message has not been altered, then only Alice could have created the digital signature.
Bob also has proof that he is the intended receiver; if he can correctly decrypt the message, then he must have correctly decrypted the session key meaning that his is the correct private key. This diagram purposely suggests a cryptosystem where the session key is used for just a single session. Even if this session key is somehow broken, only this session will be compromised; the session key for the next session is not based upon the key for this session, just as this session's key was not dependent on the key from the previous session.
This is known as Perfect Forward Secrecy ; you might lose one session key due to a compromise but you won't lose all of them. In a article in the industry literature, a writer made the claim that bit keys did not provide as adequate protection for DES at that time as they did in because computers were times faster in than in Therefore, the writer went on, we needed 56,bit keys in instead of bit keys to provide adequate protection. The conclusion was then drawn that because 56,bit keys are infeasible true , we should accept the fact that we have to live with weak cryptography false!
The major error here is that the writer did not take into account that the number of possible key values double whenever a single bit is added to the key length; thus, a bit key has twice as many values as a bit key because 2 57 is two times 2 In fact, a bit key would have times more values than a bit key. In cryptography, size does matter. The larger the key, the harder it is to crack a block of encrypted data. The reason that large keys offer more protection is almost obvious; computers have made it easier to attack ciphertext by using brute force methods rather than by attacking the mathematics which are generally well-known anyway.
With a brute force attack, the attacker merely generates every possible key and applies it to the ciphertext. Any resulting plaintext that makes sense offers a candidate for a legitimate key. Until the mids or so, brute force attacks were beyond the capabilities of computers that were within the budget of the attacker community. By that time, however, significant compute power was typically available and accessible. General-purpose computers such as PCs were already being used for brute force attacks.
Distributed attacks, harnessing the power of up to tens of thousands of powerful CPUs, are now commonly employed to try to brute-force crypto keys. This information was not merely academic; one of the basic tenets of any security system is to have an idea of what you are protecting and from whom are you protecting it!
The table clearly shows that a bit key was essentially worthless against even the most unsophisticated attacker. On the other hand, bit keys were fairly strong unless you might be subject to some pretty serious corporate or government espionage.
But note that even bit keys were clearly on the decline in their value and that the times in the table were worst cases. So, how big is big enough? DES, invented in , was still in use at the turn of the century, nearly 25 years later.
If we take that to be a design criteria i. The DES proposal suggested bit keys; by , a bit key would have been required to offer equal protection and an bit key necessary by A or bit SKC key will probably suffice for some time because that length keeps us ahead of the brute force capabilities of the attackers.
Note that while a large key is good, a huge key may not always be better; for example, expanding PKC keys beyond the current or bit lengths doesn't add any necessary protection at this time. Weaknesses in cryptosystems are largely based upon key management rather than weak keys. Blaze, W. Diffie, R. Rivest, B. Schneier, T. Shimomura, E. Thompson, and M. Wiener The most effective large-number factoring methods today use a mathematical Number Field Sieve to find a certain number of relationships and then uses a matrix operation to solve a linear equation to produce the two prime factors.
The sieve step actually involves a large number of operations that can be performed in parallel; solving the linear equation, however, requires a supercomputer. In early , Shamir of RSA fame described a new machine that could increase factorization speed by orders of magnitude. There still appear to be many engineering details that have to be worked out before such a machine could be built. Furthermore, the hardware improves the sieve step only; the matrix operation is not optimized at all by this design and the complexity of this step grows rapidly with key length, both in terms of processing time and memory requirements.
Nevertheless, this plan conceptually puts bit keys within reach of being factored. It is also interesting to note that while cryptography is good and strong cryptography is better, long keys may disrupt the nature of the randomness of data files. Shamir and van Someren "Playing hide and seek with stored keys" have noted that a new generation of viruses can be written that will find files encrypted with long keys, making them easier to find by intruders and, therefore, more prone to attack.
Finally, U. Until the mids, export outside of North America of cryptographic products using keys greater than 40 bits in length was prohibited, which made those products essentially worthless in the marketplace, particularly for electronic commerce; today, crypto products are widely available on the Internet without restriction.
The U. Department of Commerce Bureau of Industry and Security maintains an Encryption FAQ web page with more information about the current state of encryption registration. Without meaning to editorialize too much in this tutorial, a bit of historical context might be helpful.
In the mids, the U. Department of Commerce still classified cryptography as a munition and limited the export of any products that contained crypto. For that reason, browsers in the era, such as Internet Explorer and Netscape, had a domestic version with bit encryption downloadable only in the U.
Many cryptographers felt that the export limitations should be lifted because they only applied to U. Those restrictions were lifted by or , but there is still a prevailing attitude, apparently, that U. On a related topic, public key crypto schemes can be used for several purposes, including key exchange, digital signatures, authentication, and more. The length of the secret keys exchanged via that system have to have at least the same level of attack resistance.
Secure use of cryptography requires trust. While secret key cryptography can ensure message confidentiality and hash codes can ensure integrity, none of this works without trust.
PKC solved the secret distribution problem, but how does Alice really know that Bob is who he says he is? Just because Bob has a public and private key, and purports to be "Bob," how does Alice know that a malicious person Mallory is not pretending to be Bob?
There are a number of trust models employed by various cryptographic schemes. This section will explore three of them:. Each of these trust models differs in complexity, general applicability, scope, and scalability. Pretty Good Privacy described more below in Section 5. A PGP user maintains a local keyring of all their known and trusted public keys. The user makes their own determination about the trustworthiness of a key using what is called a "web of trust.
This is a section of my keychain, so only includes public keys from individuals whom I know and, presumably, trust. Note that keys are associated with e-mail addresses rather than individual names.
In general, the PGP Web of trust works as follows. Suppose that Alice needs Bob's public key. Alice could just ask Bob for it directly via e-mail or download the public key from a PGP key server; this server might a well-known PGP key repository or a site that Bob maintains himself.
In fact, Bob's public key might be stored or listed in many places. Alice is prepared to believe that Bob's public key, as stored at these locations, is valid. Suppose Carol claims to hold Bob's public key and offers to give the key to Alice.
How does Alice know that Carol's version of Bob's key is valid or if Carol is actually giving Alice a key that will allow Mallory access to messages? The answer is, "It depends. And trust is not necessarily transitive; if Dave has a copy of Bob's key and Carol trusts Dave, it does not necessarily follow that Alice trusts Dave even if she does trust Carol.
The point here is that who Alice trusts and how she makes that determination is strictly up to Alice. PGP makes no statement and has no protocol about how one user determines whether they trust another user or not. In any case, encryption and signatures based on public keys can only be used when the appropriate public key is on the user's keyring. Kerberos is a commonly used authentication scheme on the Internet.
Developed by MIT's Project Athena, Kerberos is named for the three-headed dog who, according to Greek mythology, guards the entrance of Hades rather than the exit, for some reason!
In this model, security and authentication will be based on secret key technology where every host on the network has its own secret key. It would clearly be unmanageable if every host had to know the keys of all other hosts so a secure, trusted host somewhere on the network, known as a Key Distribution Center KDC , knows the keys for all of the hosts or at least some of the hosts within a portion of the network, called a realm.
In this way, when a new node is brought online, only the KDC and the new node need to be configured with the node's key; keys can be distributed physically or by some other secure means. While the details of their operation, functional capabilities, and message formats are different, the conceptual overview above pretty much holds for both.
One primary difference is that Kerberos V4 uses only DES to generate keys and encrypt messages, while V5 allows other schemes to be employed although DES is still the most widely algorithm used. Certificates and Certificate Authorities CA are necessary for widespread use of cryptography for e-commerce applications. While a combination of secret and public key cryptography can solve the business issues discussed above, crypto cannot alone address the trust issues that must exist between a customer and vendor in the very fluid, very dynamic e-commerce relationship.
How, for example, does one site obtain another party's public key? How does a recipient determine if a public key really belongs to the sender? How does the recipient know that the sender is using their public key for a legitimate purpose for which they are authorized? When does a public key expire? How can a key be revoked in case of compromise or loss? The basic concept of a certificate is one that is familiar to all of us.
A driver's license, credit card, or SCUBA certification, for example, identify us to others, indicate something that we are authorized to do, have an expiration date, and identify the authority that granted the certificate.
As complicated as this may sound, it really isn't. A beginner's web-page is made available for first-time users to review prior to continuing. Click the 'Create Volume' , button to start the wizard. A standard volume will work just fine. If you wear a tin-foil hat, then a hidden TrueCrypt volume is what you need. The next step would be to select a file location or device for the volume. Choose 'Select File Choose 'Select Device Any data currently on USB flash drive will be removed as a result of this process.
My TrueCrypt volume will masquerade on the hard disk as a backup file and if NTBackup were to try and mount the file, it would come up as invalid. Type any file name and extension you choose and click 'Save'. What type of hashing algorithm and encryption scheme is the next choice to make. There are numerous choices available for both of these options. Feel free to look through them all and the descriptions. AES' job is to secure the data inside a bit shell on the volume's unique file system.
RIPEMD hashes the data and produces a unique digital finger print for validity and integrity purposes. How big do we want the TrueCrypt volume to be? My example of a backup file gives some pretty decent leverage regarding size. That will not be a good idea. This is the binary, symmetrical key VeraCrypt uses to encrypt and decrypt data it writes to or reads from the encrypted volume.
Gaining access to the OTFE key allows decrypting the data directly without knowing or needing the password. There is more than one way to access OTFE keys. While the encrypted volume is mounted, the encryption key is available in all of the following locations:.
This is how the extraction works with Elcomsoft Forensic Disk Decryptor :. It also depends on the encryption settings. Selecting a non-standard combination of an encryption algorithm and hash function e. In our experience, scanning a 16 GB memory dump can take 15 to 30 minutes with default settings and up to several hours with a non-standard combination of encryption and hash.
Elcomsoft Forensic Disk Decryptor offers forensic specialists an easy way to obtain complete real-time access to information stored in popular crypto containers. Supporting desktop and portable versions of BitLocker, FileVault 2, PGP Disk, TrueCrypt and VeraCrypt protection, the tool can decrypt all files and folders stored in crypto containers or mount encrypted volumes as new drive letters for instant, real-time access. Elcomsoft Forensic Disk Decryptor Elcomsoft Forensic Disk Decryptor offers forensic specialists an easy way to obtain complete real-time access to information stored in popular crypto containers.
And for the poor thinkpad I am currently using the answer is: YES. I do notice. But since you asked:. Thats it. Might really depend on your level of paranoia as well as what you have read about the other options. Python Javascript Linux Cheat sheet Contact. As Stephen Touset already answered: The Algorithm might not be as important as you think.
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