The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: Download conference paper PDF. Choi, S. Information Processing Letters to appear, Google Scholar.
Cramer, R. In: Krawczyk, H. LNCS, vol. Springer, Heidelberg CrossRef Google Scholar. In: Knudsen, L. In: Feigenbaum, J. In: Coppersmith, D. Desmedt, Y. In: CANS In: ProvSec Dolev, D. El Gamal, T. In: Blakely, G. Gennaro, R. In: Pointcheval, D. CT-RSA Hofheinz, D. In: Menezes, A. In: Joux, A. Kiltz, E. Kurosawa, K. In: Franklin, M. Lipmaa, H. Naor, M. 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 algorithms can generally be executed up to times faster than public key cryptography algorithms. 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. The system described here is one where we basically encrypt the secret session key with the receiver's public key. While this generic scheme works well, it causes some incompatibilities in practice.
HPKE was designed specifically to be simple, reusable, and future-proof. 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. Consider driver's licenses. I have one issued by the State of Florida. The license establishes my identity, indicates the type of vehicles that I can operate and the fact that I must wear corrective lenses while doing so, identifies the issuing authority, and notes that I am an organ donor.
When I drive in other states, the other jurisdictions throughout the U. When I leave the U. When I am in Aruba, Australia, Canada, Israel, and many other countries, they will accept not the Florida license, per se, but any license issued in the U. This analogy represents the certificate trust chain, where even certificates carry certificates.
For purposes of electronic transactions, certificates are digital documents. The specific functions of the certificate include:. A sample abbreviated certificate is shown in Figure 7. While this is a certificate issued by VeriSign, many root-level certificates can be found shipped with browsers.
When the browser makes a connection to a secure Web site, the Web server sends its public key certificate to the browser. The browser then checks the certificate's signature against the public key that it has stored; if there is a match, the certificate is taken as valid and the Web site verified by this certificate is considered to be "trusted.
Most certificates today comply with X. Certificate authorities are the repositories for public keys and can be any agency that issues certificates. When a sender needs an intended receiver's public key, the sender must get that key from the receiver's CA. That scheme is straight-forward if the sender and receiver have certificates issued by the same CA.
If not, how does the sender know to trust the foreign CA? One industry wag has noted, about trust: "You are either born with it or have it granted upon you. CAs, in turn, form trust relationships with other CAs. Thus, if a user queries a foreign CA for information, the user may ask to see a list of CAs that establish a "chain of trust" back to the user.
One major feature to look for in a CA is their identification policies and procedures. When a user generates a key pair and forwards the public key to a CA, the CA has to check the sender's identification and takes any steps necessary to assure itself that the request is really coming from the advertised sender. Different CAs have different identification policies and will, therefore, be trusted differently by other CAs.
Verification of identity is just one of many issues that are part of a CA's Certification Practice Statement CPS and policies; other issues include how the CA protects the public keys in its care, how lost or compromised keys are revoked, and how the CA protects its own private keys. As a final note, CAs are not immune to attack and certificates themselves are able to be counterfeited.
Problems have continued over the years; good write-ups on this can be found at " Another Certification Authority Breached the 12th! The paragraphs above describe three very different trust models. It is hard to say that any one is better than the others; it depends upon your application.
One of the biggest and fastest growing applications of cryptography today, though, is electronic commerce e-commerce , a term that itself begs for a formal definition. PGP's web of trust is easy to maintain and very much based on the reality of users as people. The model, however, is limited; just how many public keys can a single user reliably store and maintain?
And what if you are using the "wrong" computer when you want to send a message and can't access your keyring? How easy it is to revoke a key if it is compromised? PGP may also not scale well to an e-commerce scenario of secure communication between total strangers on short-notice. Kerberos overcomes many of the problems of PGP's web of trust, in that it is scalable and its scope can be very large.
In the early days of the Internet, every host had to maintain a list of every other host; the Domain Name System DNS introduced the idea of a distributed database for this purpose and the DNS is one of the key reasons that the Internet has grown as it has. While certificates and the benefits of a PKI are most often associated with electronic commerce, the applications for PKI are much broader and include secure electronic mail, payments and electronic checks, Electronic Data Interchange EDI , secure transfer of Domain Name System DNS and routing information, electronic forms, and digitally signed documents.
A single "global PKI" is still many years away, that is the ultimate goal of today's work as international electronic commerce changes the way in which we do business in a similar way in which the Internet has changed the way in which we communicate.
The paragraphs above have provided an overview of the different types of cryptographic algorithms, as well as some examples of some available protocols and schemes. The paragraphs below will show several real cryptographic applications that many of us employ knowingly or not everyday for password protection and private communication. Some of the schemes described below never were widely deployed but are still historically interesting, thus remain included here.
But passwords are not typically kept on a host or server in plaintext, but are generally encrypted using some sort of hash scheme. Note that each password is stored as a byte string. The first two characters are actually a salt , randomness added to each password so that if two users have the same password, they will still be encrypted differently; the salt, in fact, provides a means so that a single password might have different encryptions.
The remaining 11 bytes are the password hash, calculated using DES. This fact, coupled with the weak encryption of the passwords, resulted in the development of the shadow password system where passwords are kept in a separate, non-world-readable file used in conjunction with the normal password file. In the NT case, all passwords are hashed using the MD4 algorithm, resulting in a bit byte hash value they are then obscured using an undocumented mathematical transformation that was a secret until distributed on the Internet.
The password password , for example, might be stored as the hash value in hexadecimal b22d73c34bd4aa79c8b09f Passwords are not saved in plaintext on computer systems precisely so they cannot be easily compromised. For similar reasons, we don't want passwords sent in plaintext across a network. But for remote logon applications, how does a client system identify itself or a user to the server? One mechanism, of course, is to send the password as a hash value and that, indeed, may be done.
A weakness of that approach, however, is that an intruder can grab the password off of the network and use an off-line attack such as a dictionary attack where an attacker takes every known word and encrypts it with the network's encryption algorithm, hoping eventually to find a match with a purloined password hash. In some situations, an attacker only has to copy the hashed password value and use it later on to gain unauthorized entry without ever learning the actual password.
An even stronger authentication method uses the password to modify a shared secret between the client and server, but never allows the password in any form to go across the network. As suggested above, Windows NT passwords are stored in a security file on a server as a byte hash value.
When a user logs on to a server from a remote workstation, the user is identified by the username, sent across the network in plaintext no worries here; it's not a secret anyway! The server then generates a bit random number and sends it to the client also in plaintext. This number is the challenge. Recall that DES employs a bit key, acts on a bit block of data, and produces a bit output.
In this case, the bit data block is the random number. The client actually uses three different DES keys to encrypt the random number, producing three different bit outputs. The first key is the first seven bytes 56 bits of the password's hash value, the second key is the next seven bytes in the password's hash, and the third key is the remaining two bytes of the password's hash concatenated with five zero-filled bytes.
So, for the example above, the three DES keys would be b22d73c34 , bd4aa79c8b0 , and 9f Each key is applied to the random number resulting in three bit outputs, which comprise the response. Thus, the server's 8-byte challenge yields a byte response from the client and this is all that would be seen on the network. The server, for its part, does the same calculation to ensure that the values match. There is, however, a significant weakness to this system.
Specifically, the response is generated in such a way as to effectively reduce byte hash to three smaller hashes, of length seven, seven, and two, respectively. Thus, a password cracker has to break at most a 7-byte hash. One Windows NT vulnerability test program that I used in the past reported passwords that were "too short," defined as "less than 8 characters.
This was, in fact, not the case at all; all the software really had to do was to look at the last eight bytes of the Windows NT LanMan hash to see that the password was seven or fewer characters. Consider the following example, showing the LanMan hash of two different short passwords take a close look at the last 8 bytes :.
MS-CHAP assumes that it is working with hashed values of the password as the key to encrypting the challenge. Diffie and Hellman introduced the concept of public key cryptography. The mathematical "trick" of Diffie-Hellman key exchange is that it is relatively easy to compute exponents compared to computing discrete logarithms. Diffie-Hellman works like this. Alice and Bob start by agreeing on a large prime number, N. There is actually another constraint on G, namely that it must be primitive with respect to N.
As an example, 2 is not primitive to 7 because the set of powers of 2 from 1 to 6, mod 7 i. The definition of primitive introduced a new term to some readers, namely mod. The phrase x mod y and read as written! Read more about the modulo function in the appendix.
Anyway, either Alice or Bob selects N and G; they then tell the other party what the values are. Alice and Bob then work independently Figure 9 :. Perhaps a small example will help here. In this example, then, Alice and Bob will both find the secret key 1 which is, indeed, 3 6 mod 7 i. A short digression on modulo arithmetic. This can be confirmed, of course, by noting that:. Diffie-Hellman can also be used to allow key sharing amongst multiple users.
Note again that the Diffie-Hellman algorithm is used to generate secret keys, not to encrypt and decrypt messages. Unlike Diffie-Hellman, RSA can be used for key exchange as well as digital signatures and the encryption of small blocks of data. Today, RSA is primarily used to encrypt the session key used for secret key encryption message integrity or the message's hash value digital signature. RSA's mathematical hardness comes from the ease in calculating large numbers and the difficulty in finding the prime factors of those large numbers.
Although employed with numbers using hundreds of digits, the math behind RSA is relatively straight-forward. The public key is the number pair n,e. Although these values are publicly known, it is computationally infeasible to determine d from n and e if p and q are large enough. Now, this might look a bit complex and, indeed, the mathematics does take a lot of computer power given the large size of the numbers; since p and q may be digits decimal or more, d and e will be about the same size and n may be over digits.
Nevertheless, a simple example may help. In this example, the values for p, q, e, and d are purposely chosen to be very small and the reader will see exactly how badly these values perform, but hopefully the algorithm will be adequately demonstrated:. I choose this trivial example because the value of n is so small in particular, the value M cannot exceed n. But here is a more realistic example using larger d, e, and n values, as well as a more meaningful message; thanks to Barry Steyn for permission to use values from his How RSA Works With Examples page.
Now suppose that our message M is the character string "attack at dawn" which has the numeric value after converting the ASCII characters to a bit string and interpreting that bit string as a decimal number of This more realistic example gives just a clue as to how large the numbers are that are used in the real world implementations. RSA keylengths of and bits are considered to be pretty weak.
The minimum suggested RSA key is bits; and bits are even better. It employs dc , an arbitrary precision arithmetic package that ships with most UNIX systems:. Despite all of these options, ECB is the most commonly deployed mode of operation. Although other block ciphers have replaced DES, it is still interesting to see how DES encryption is performed; not only is it sort of neat, but DES was the first crypto scheme commonly seen in non-governmental applications and was the catalyst for modern "public" cryptography and the first public Feistel cipher.
DES uses a bit key. In fact, the bit key is divided into eight 7-bit blocks and an 8th odd parity bit is added to each block i. By using the 8 parity bits for rudimentary error detection, a DES key is actually 64 bits in length for computational purposes although it only has 56 bits worth of randomness, or entropy See Section A.
DES then acts on bit blocks of the plaintext, invoking 16 rounds of permutations, swaps, and substitutes, as shown in Figure The standard includes tables describing all of the selection, permutation, and expansion operations mentioned below; these aspects of the algorithm are not secrets. The basic DES steps are:. At any given step in the process, then, the new L block value is merely taken from the prior R block value.
K n is a bit value derived from the bit DES key. Each round uses a different 48 bits according to the standard's Key Schedule algorithm. The cipher function, f, combines the bit R block value and the bit subkey in the following way. First, the 32 bits in the R block are expanded to 48 bits by an expansion function E ; the extra 16 bits are found by repeating the bits in 16 predefined positions.
The bit expanded R-block is then ORed with the bit subkey. The result is a bit value that is then divided into eight 6-bit blocks. These are fed as input into 8 selection S boxes, denoted S 1 , Each 6-bit input yields a 4-bit output using a table lookup based on the 64 possible inputs; this results in a bit output from the S-box.
The 32 bits are then rearranged by a permutation function P , producing the results from the cipher function. Observe that we start with a byte input message. DES acts on eight bytes at a time, so this message is padded to 24 bytes and provides three "inputs" to the cipher algorithm we don't see the padding here; it is appended by the DES code.
Since we have three input blocks, we get 24 bytes of output from the three bit eight byte output blocks. An excellent step-by-step example of DES can also be found at J. The mainstream cryptographic community has long held that DES's bit key was too short to withstand a brute-force attack from modern computers.
Remember Moore's Law: computer power doubles every 18 months. Given that increase in power, a key that could withstand a brute-force guessing attack in could hardly be expected to withstand the same attack a quarter century later. DES is even more vulnerable to a brute-force attack because it is often used to encrypt words, meaning that the entropy of the bit block is, effectively, greatly reduced.
That is, if we are encrypting random bit streams, then a given byte might contain any one of 2 8 possible values and the entire bit block has 2 64 , or about If we are encrypting words, however, we are most likely to find a limited set of bit patterns; perhaps 70 or so if we account for upper and lower case letters, the numbers, space, and some punctuation.
Despite this criticism, the U. It was completed in 84 days by R. Verser in a collaborative effort using thousands of computers on the Internet. This problem was solved by distributed. The distributed. Information about the hardware design and all software can be obtained from the EFF. This is widely considered to have been the final nail in DES's coffin. The Deep Crack algorithm is actually quite interesting. The general approach that the DES Cracker Project took was not to break the algorithm mathematically but instead to launch a brute-force attack by guessing every possible key.
A bit key yields 2 56 , or about 72 quadrillion, possible values. So the DES cracker team looked for any shortcuts they could find! First, they assumed that some recognizable plaintext would appear in the decrypted string even though they didn't have a specific known plaintext block. They then applied all 2 56 possible key values to the bit block I don't mean to make this sound simple! The system checked to see if the decrypted value of the block was "interesting," which they defined as bytes containing one of the alphanumeric characters, space, or some punctuation.
This dropped the number of possible keys that might yield positive results to about 2 40 , or about a trillion. They then made the assumption that an "interesting" 8-byte block would be followed by another "interesting" block.
So, if the first block of ciphertext decrypted to something interesting, they decrypted the next block; otherwise, they abandoned this key. Only if the second block was also "interesting" did they examine the key closer. Looking for 16 consecutive bytes that were "interesting" meant that only 2 24 , or 16 million, keys needed to be examined further. This further examination was primarily to see if the text made any sense. And even a slow laptop today can search through lists of only a few million items in a relatively short period of time.
It is well beyond the scope of this paper to discuss other forms of breaking DES and other codes. Nevertheless, it is worth mentioning a couple of forms of cryptanalysis that have been shown to be effective against DES. Differential cryptanalysis , invented in by E.
Biham and A. Shamir of RSA fame , is a chosen-plaintext attack. By selecting pairs of plaintext with particular differences, the cryptanalyst examines the differences in the resultant ciphertext pairs. Linear plaintext , invented by M. Matsui, uses a linear approximation to analyze the actions of a block cipher including DES.
Both of these attacks can be more efficient than brute force. Once DES was "officially" broken, several variants appeared. But none of them came overnight; work at hardening DES had already been underway. In the early s, there was a proposal to increase the security of DES by effectively increasing the key length by using multiple keys with multiple passes.
But for this scheme to work, it had to first be shown that the DES function is not a group , as defined in mathematics. If DES were a group, it wouldn't matter how many keys and passes we applied to some plaintext; we could always find a single bit key that would provide the same result. As it happens, DES was proven to not be a group so that as we apply additional keys and passes, the effective key length increases.
One obvious choice, then, might be to use two keys and two passes, yielding an effective key length of bits. Let's call this Double-DES. The two keys, Y1 and Y2, might be applied as follows:. So far, so good. But there's an interesting attack that can be launched against this "Double-DES" scheme.
First, notice that the applications of the formula above can be thought of with the following individual steps where C' and P' are intermediate results :. That leaves us vulnerable to a simple known plaintext attack sometimes called "Meet-in-the-middle" where the attacker knows some plaintext P and its matching ciphertext C.
To obtain C', the attacker needs to try all 2 56 possible values of Y1 applied to P; to obtain P', the attacker needs to try all 2 56 possible values of Y2 applied to C. So "Double-DES" is not a good solution. Generation of the ciphertext C from a block of plaintext P is accomplished by:. For obvious reasons, this is sometimes referred to as an encrypt-decrypt-encrypt mode operation. The use of three, independent bit keys provides 3DES with an effective key length of bits.
Given the relatively low cost of key storage and the modest increase in processing due to the use of longer keys, the best recommended practices are that 3DES be employed with three keys. Developed in , DESX is a very simple algorithm that greatly increases DES's resistance to brute-force attacks without increasing its computational complexity. As it happens, DESX is no more immune to other types of more sophisticated attacks, such as differential or linear cryptanalysis, but brute-force is the primary attack vector on DES.
After DES was deprecated and replaced by the Advanced Encryption Standard AES because of its vulnerability to a modestly-priced brute-force attack, many applications continued to rely on DES for security, and many software designers and implementers continued to include DES in new applications. Pretty Good Privacy PGP is one of today's most widely used public key cryptography programs and was the first open cryptosystem that combined hashing, compression, SKC, and PKC into a method to protect files, devices, and e-mail.
Public keys were shared via a concept known as a Web of Trust; individuals would directly exchange their public keyrings and then share their keyrings with other trusted parties. PGP secret keys, however, were bits or larger, making it a "strong" cryptography product. Yet, in , perhaps as a harbinger of the mixed feelings that this technology engendered, the Electronic Frontier Foundation EFF awarded Zimmermann the Pioneer Award and Newsweek Magazine named him one of the 50 most influential people on the Internet.
PGP can be used to sign or encrypt e-mail messages with the mere click of the mouse. When PGP is first installed, the user has to create a key-pair. One key, the public key, can be advertised and widely circulated. The private key is protected by use of a passphrase. The passphrase has to be entered every time the user accesses their private key. The sender uses their private key to sign the message; at the destination, the sender's e-mail address yields the public key from the receiver's keyring in order to validate the signature.
Figure 12 shows a PGP signed message. This message will not be kept secret from an eavesdropper, but a recipient can be assured that the message has not been altered from what the sender transmitted. In this instance, the sender signs the message using their own private key.
The receiver uses the sender's public key to verify the signature; the public key is taken from the receiver's keyring based on the sender's e-mail address. Note that the signature process does not work unless the sender's public key is on the receiver's keyring. The receiver's e-mail address is the pointer to the public key in the sender's keyring with which to encrypt the message. At the destination side, the receiver uses their own private key to decrypt the message.
Figure 13 shows a PGP encrypted message PGP compresses the file, where practical, prior to encryption because encrypted files have a high degree of randomness and, therefore, cannot be efficiently compressed. In this example, public key methods are used to exchange the session key for the actual message encryption that employs secret-key cryptography. In this case, the receiver's e-mail address is the pointer to the public key in the sender's keyring; in fact, the same message can be sent to multiple recipients and the message will not be significantly longer since all that needs to be added is the session key encrypted by each receiver's public key.
When the message is received, the recipient will use their private key to extract the session secret key to successfully decrypt the message Figure PGP went into a state of flux in In March , NAI announced that they were dropping support for the commercial version of PGP having failed to find a buyer for the product willing to pay what they wanted. NOTE: The information in this section assumes that the reader is familiar with the Internet Protocol IP , at least to the extent of the packet format and header contents.
IPsec is not a single protocol, in fact, but a suite of protocols providing a mechanism to provide data integrity, authentication, privacy, and nonrepudiation for the classic Internet Protocol IP. The latter requires more processing than the former, but will probably end up being the preferred usage for applications such as VPNs and secure electronic commerce.
Central to IPsec is the concept of a security association SA. An SA is a simplex one-way or unidirectional logical connection between two communicating IP endpoints that provides security services to the traffic carried by it using either AH or ESP procedures. Providing security to the more typical scenario of two-way bi-directional communication between two endpoints requires the establishment of two SAs one in each direction. See also RFC Figure 15 shows the format of the IPsec AH.
The AH is merely an additional header in a packet, more or less representing another protocol layer above IP this is shown in Figure 17 below. The contents of the AH are:. The ESP header i. The contents of the ESP packet are:. A transport mode SA is a security association between two hosts. This mode of operation is only supported by IPsec hosts. A tunnel mode SA is a security association applied to an IP tunnel. In this mode, there is an "outer" IP header that specifies the IPsec destination and an "inner" IP header that specifies the destination for the IP packet.
This mode of operation is supported by both hosts and security gateways. Initially, an IPv4 packet contains a normal IPv4 header which may contain IP options , followed by the higher layer protocol header e. An IPv6 packet is similar except that the packet starts with the mandatory IPv6 header followed by any IPv6 extension headers, and then followed by the higher layer data. Note that in both transport and tunnel modes, the entire IP packet is covered by the authentication except for the mutable fields.
A field is mutable if its value might change during transit in the network; IPv4 mutable fields include the fragment offset, time to live, and checksum fields. Note, in particular, that the address fields are not mutable. AH authenticates the entire packet transmitted on the network whereas ESP only covers a portion of the packet transmitted on the network the higher layer data in transport mode and the entire original packet in tunnel mode.
But the ramifications are significant. The third component of IPsec is the establishment of security associations and key management. These tasks can be accomplished in one of two ways. The simplest form of SA and key management is manual management. In this method, a security administer or other individual manually configures each system with the key and SA management data necessary for secure communication with other systems. Manual techniques are practical for small, reasonably static environments but they do not scale well.
Several protocols have defined for these functions:. The client and server then agree upon an encryption scheme. SSL v2. SSL v3. In , SSL v3 was found to be breakable. In , the theoretical became practical when a CBC proof-of-concept exploit was released. Meanwhile, TLS v1. In , TLS v1. The client i. The communication between the client and server comprises the TLS protocol handshake Figure 20 , which has three phases, followed by actual data exchange.
The first phase of the protocol handshake is Key Exchange , used to establish the shared key and select the encryption method. This is the only phase of TLS communication that is not encrypted. During this phase:. From this point forward, all communication is encrypted. The second step of the protocol handshake is the Server Parameters phase, where the server specifies other, additional handshake parameters.
The server accomplishes this task by the use of two messages:. The third, and final phase, of the TLS protocol handshake is Authentication , during which the server is authenticated and, optionally, the client , keys are confirmed, and the integrity of the handshake assured. The messages exchanged during this phase include:.
During this phase, the server sends its authentication messages followed by the client sending its authentication messages. Once the Finished messages have been exchanged, the protocol handshake is complete, and the client and server now start to exchange encrypted Application Data. Most of us have used SSL to engage in a secure, private transaction with some vendor.
The steps are something like this. During the SSL exchange with the vendor's secure server, the server sends its certificate to our client software. The certificate includes the vendor's public key and a validation of some sort from the CA that issued the vendor's certificate signed with the CA's private key. Our browser software is shipped with the major CAs' certificates containing their public keys; in that way, the client software can authenticate the server's certificate.
Note that the server generally does not use a certificate to authenticate the client. Instead, purchasers are generally authenticated when a credit card number is provided; the server checks to see if the card purchase will be authorized by the credit card company and, if so, considers us valid and authenticated!
The reason that only the server is authenticated is rooted in history. SSL was developed to support e-commerce by providing a trust mechanism so that customers could have faith in a merchant. In the real world, you "trust" a store because you can walk into a brick-and-mortar structure. The store doesn't know who the customer is; they check to see if the credit card is valid and, if so, a purchase goes through.
In addition, how many people would have been willing to purchase an individual certificate and install it on their browser merely so that they shop online? This latter requirement, if implemented, could have killed e-commerce before it ever got started. See E. For several decades, it had been illegal to generally export products from the U.
By the lates, products using strong SKC has been approved for the worldwide financial community. As mentioned earlier, SSL was designed to provide application-independent transaction security for the Internet. DTLS v1. Known as Heartbleed , this vulnerability had apparently been introduced into OpenSSL in late with the introduction of a feature called heartbeat.
Heartbleed exploited an implementation flaw in order to exfiltrate keying material from an SSL server or some SSL clients, in what is known at reverse Heartbleed ; the flaw allowed an attacker to grab 64 KB blocks from RAM. Heartbleed is known to only affect OpenSSL v1. In addition, the OpenSSL 0. Note also that Heartbleed affects some versions of the Android operating system , notably v4.
As more ICOs take place and more alternate cryptocurrencies are developed, this program aims to protect our traders from potentially depreciating or scam projects. Our platform facilitates the creation and digitisation of certain types of assets like trade agreements and bank instruments. This improves the turnaround time with low transaction cost.
This allows for automated settlements and trades based on predefined conditions, which will trigger the self-execution of these smart contracts. All tradable assets that can be represented via a digital token and publicly traded can be used in these smart contracts, subject to regulatory requirements. The content provided in this document and any accompanying material is for informational purposes only.
It should not be considered legal or financial advice. The recipient should consult with an attorney or other professional to determine what may be best for their individual needs. Calfin Fintex Pte Ltd does not make any guarantee or other promise as to any results that may be obtained from using our content. No one should make any investment decision without first consulting his or her own financial advisor and conducting his or her own research and due diligence.
The contents of this this document and on our website is not intended to and does not constitute legal advice or investment advice. Your use of this information is completely at your risk. If you are located in a jurisdiction where the contents of this document are regulated or prohibited, you must ignore this document and discard it.
Whitepage: Whitepage. Facebook: CGCX official. Telegram: CGCX official. Twitter: CGCX offical. Forgot password? Please enter your email address below and we'll email you a link to a page where you can easily create a new password. More Informations Website: www. Your email or username. Password Forgot password? Remember me. New to Newbium? Sign up now.
Domain parameters must be the same. MarekKlein Than you! This solved the problem. I though that domain parameters should be different for each client. What are they exactly? They can't be any secret if every client knows them. I can just recommend you to have a look at Diffie-Hellman. If you have a look at the "Cryptographic explanation" section, then domain parameters are p and g.
Add a comment. Sorted by: Reset to default. Highest score default Date modified newest first Date created oldest first. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.
Post as a guest Name. Email Required, but never shown. The Overflow Blog. Will chatbots ever live up to the hype? The Authorization Code grant in excruciating detail Part 2 of 2. Featured on Meta. Question Close Reasons project - Introduction and Feedback. Related 4. Hot Network Questions. Question feed. Accept all cookies Customize settings.
Hybrid encryption uses public-key cryptography to exchange a secret Basically, the DH key exchange is one of the tools used in the first. Discrete logarithm integrated encryption scheme, hybrid authenticated encryption scheme based on DH in F∗ p. E. ECIES. Elliptic curve integrated encryption. In cryptography, the Double Ratchet Algorithm is a key management algorithm that was As a hybrid of DH and KDF ratchets, it combines several desired features.