LNCS, vol. Springer, Heidelberg In: PODC, pp. List of Bitcoin Heists Accessed 11 Feb Bitcoin wiki: Transactions. Accessed 11 Feb Accessed 11 feb In: Christin, N. FC In: Joux, A. In: Lee, D. In: Wiener, M. In: Kim, K. PKC In: Pfitzmann, B. SIAM J. In: Kaliski, B. In: Franklin, M. In: Manulis, M. ACNS Springer, Cham In: Maurer, U. In: Stern, J. In: Bugliesi, M. ICALP In: Preneel, B.
Financial cyber threats in Part 2: malware In: Cachin, C. ACM Meiklejohn, S. ACM 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 6. 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. TABLE 2. Contents of an X. 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:. 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 8.
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. Although DES has been deprecated and replaced by the Advanced Encryption Standard AES because of its vulnerability to a modestly-priced brute-force attack, many applications continue to rely on DES for security, and many software designers and implementers continue to include DES in new applications.
In some cases, use of DES is wholly appropriate but, in general, DES should not continue to be promulgated in production software and hardware. 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; at the destination, the sender's e-mail address yields the public key from the receiver's keyring. Figure 9 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. At the destination side, the receiver uses their own private key.
Figure 10 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 The AH is merely an additional header in a packet, more or less representing another protocol layer above IP this is shown in Figure 14 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:.
HMAC uses a shared secret key between two parties rather than public key methods for message authentication. In HMAC, both parties share a secret key. The secret key will be employed with the hash algorithm in a way that provides mutual authentication without transmitting the key on the line. IPsec key management procedures will be used to manage key exchange between the two parties. Recall that hash functions operate on a fixed-size block of input at one time; MD5 and SHA-1, for example, work on 64 byte blocks.
These functions then generate a fixed-size hash value; MD5 and SHA-1, in particular, produce 16 byte bit and 20 byte bit output strings, respectively. 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 18 , 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.
But that wasn't the only problem with SSL. Weeks later, an SSL vulnerability in the bash Unix command shell was discovered, aptly named Shellshock. Here's a nice overview of the SSL problems! You might have read above that SSLv2 fell out of use by the early s and was formally deprecated in This is true. In general, public key cryptography systems use hard-to-solve problems as the basis of the algorithm.
The most predominant public key cryptography algorithm for many years was RSA, based on the prime factors of very large integers. While RSA can be successfully attacked, the mathematics of the algorithm have not been compromised, per se; instead, computational brute-force has broken the keys. The first thing to note about elliptic curves is that they are neither elliptic i.
Elliptic curves are a part of number theory and algebraic geometry, and can be defined over any field of numbers i. In cryptography, we normally use elliptic curves over a finite field of prime numbers, which we denote F P.
This is one reason that we use the modulo function; modulo arithmetic defines a finite range of numbers e. So, given this preamble, an elliptic curve in F P consists of the set of real numbers x,y that satisfies the equation:. In addition, the curve has to be non-singular sometimes stated as "not containing any singularities" , which means that the curve has no cusps, self-intersections, or isolated points. To ensure this, there is one more condition, namely, the values of a and b must satisfy the requirement that:.
The set of all of the solutions to the equation forms the elliptic curve. Changing a and b changes the shape of the curve, and small changes in these parameters can result in major changes in the set of x,y solutions. Elliptic curves have the interesting property that adding two points on the elliptic curve yields a third point on the curve. Therefore, adding two points, P and Q, gets us to point R.
Small changes in P or Q can cause a large change in the position of R. Now, the astute reader will notice that the line above went through a point labelled -R and that, in the Cartesian coordinate system, we've merely changed the sign of the y coordinate to get the point labelled R; i. Stated another, slightly more rigorous way, the curve is symmetric about the x-axis. Meanwhile, if it doesn't matter, why do it?
So, to get there, we need to define a number of operations on P, including doubling P and multiplying P by some number. At this point, we leave the area of simple scalar arithmetic and enter into group law and algebraic geometry. There are a bunch of good explanations about why we do this reflection that I am not going to replicate but I will give one key thing to keep in mind.
While the sign doesn't matter when squaring a number, it does matter in other types of arithmetic. When adding points on the elliptic curve, we need to maintain the associative law, which says:. Working with elliptic curves gets us into group laws and the operations often reflect about the x-axis in order to maintain the associative principle. So let's go back to the original problem statement from above.
An attacker might know P and Q but finding the integer, n , is a difficult problem to solve. See Bernstein and Lange's SafeCurves: choosing safe curves for elliptic-curve cryptography site for a review and analysis of various ECC curve standard specifications.
ECC has emerged as a replacement in many environments because it provides similar levels of security compared to RSA but with significantly reduced key sizes and, therefore, reduced processing demands. Since the ECC key sizes are so much shorter than comparable RSA keys, the length of the public key and private key is much shorter in elliptic curve cryptosystems. This results into faster processing times, and lower demands on memory and bandwidth; some studies have found that ECC is faster than RSA for signing and decryption, but slower for signature verification and encryption.
There are a number of exceptional ECC tutorials online at various levels of detail and complexity to which readers are referred:. In September of that year, they put out a formal Call for Algorithms and in August announced that 15 candidate algorithms were being considered Round 1. The remarkable thing about this entire process has been the openness as well as the international nature of the "competition.
Their Overview of the AES Development Effort has full details of the process, algorithms, and comments so I will not repeat everything here. With the report came the recommendation that Rijndael be named as the AES standard. AES contains a subset of Rijndael's capabilities e. The day comment period ended on May 29, and the U. Rijndael pronounced as in "rain doll" or "rhine dahl" is a block cipher designed by Joan Daemen and Vincent Rijmen, both cryptographers in Belgium.
Rijndael can operate over a variable-length block using variable-length keys; the specification submitted to NIST describes use of a , , or bit key to encrypt data blocks that are , , or bits long; note that all nine combinations of key length and block length are possible.
The design of Rijndael was strongly influenced by the block cipher called Square , also designed by Daemen and Rijmen. Rijndael is an iterated block cipher, meaning that the initial input block and cipher key undergoes multiple rounds of transformation before producing the output. Each intermediate cipher result is called a State. For ease of description, the block and cipher key are often represented as an array of columns where each array has 4 rows and each column represents a single byte 8 bits.
An array representing a State will have Nb columns, where Nb values of 4, 6, and 8 correspond to a , , and bit block, respectively. Similarly, an array representing a Cipher Key will have Nk columns, where Nk values of 4, 6, and 8 correspond to a , , and bit key, respectively.
The number of transformation rounds Nr in Rijndael is a function of the block length and key length, and is given by the table below:. Now, having said all of this, the AES version of Rijndael does not support all nine combinations of block and key lengths, but only the subset using a bit block size.
The paragraphs below will describe the operations mentioned above. The nomenclature used below is taken from the AES specification although references to the Rijndael specification are made for completeness. The arrays s and s' refer to the State before and after a transformation, respectively NOTE: The Rijndael specification uses the array nomenclature a and b to refer to the before and after States, respectively.
The subscripts i and j are used to indicate byte locations within the State or Cipher Key array. The SubBytes transformation The substitute bytes called ByteSub in Rijndael transformation operates on each of the State bytes independently and changes the byte value. An S-box, or substitution table , controls the transformation. The characteristics of the S-box transformation as well as a compliant S-box table are provided in the AES specification; as an example, an input State byte value of 0x6b will be replaced with a 0x7f in the output State and an input value of 8 0x08 would be replaced with a 48 0x One way to think of the SubBytes transformation is that a given byte in State s is given a new value in State s' according to the S-box.
The S-box, then, is a function on a byte in State s so that:. The ShiftRows transformation The shift rows called ShiftRow in Rijndael transformation cyclically shifts the bytes in the bottom three rows of the State array. According to the more general Rijndael specification, rows 2, 3, and 4 are cyclically left-shifted by C1, C2, and C3 bytes, respectively, per the table below:. The diagram below shows the effect of the ShiftRows transformation on State s:.
The MixColumns transformation The mix columns called MixColumn in Rijndael transformation uses a mathematical function to transform the values of a given column within a State, acting on the four values at one time as if they represented a four-term polynomial. In essence, if you think of MixColumns as a function, this could be written:. The column position doesn't change, merely the values within the column. The Cipher Key is used to derive a different key to be applied to the block during each round of the encryption operation.
These keys are called the Round Keys and each will be the same length as the block, i. Consider that AES uses a bit block and either 10, 12, or 14 iterative rounds depending upon key length. Similarly, a bit key would require bits of key material x13 , or 52 bit words, while a bit key would require bits of key material x15 , or 60 bit words. The key expansion mechanism, then, starts with the , , or bit Cipher Key and produces a , , or bit Expanded Key, respectively.
The original Cipher Key occupies the first portion of the Expanded Key and is used to produce the remaining new key material. The result is an Expanded Key that can be thought of and used as 11, 13, or 15 separate keys, each used for one AddRoundKey operation.
These, then, are the Round Keys. Recall that each Round Key is the same length as the block. Recall from the beginning of the AES overview that the cipher itself comprises a number of rounds of just a few functions:. In the code:. One of the encryption schemes employed by Cisco routers to encrypt passwords is a stream cipher.
It uses the following fixed keystream thanks also to Jason Fossen for independently extending and confirming this string :. When a password is to be encrypted, the password function chooses a number between 0 and 15, and that becomes the offset into the keystream. Password characters are then XORed byte-by-byte with the keystream according to:. Consider the following example.
Suppose we have the password abcdefgh. The keystream characters and hex code that supports an offset from 0 to 15 bytes and a password length up to 24 bytes is:. Let's say that the function decides upon a keystream offset of 6 bytes. We then start with byte 6 of the keystream start counting the offset at 0 and XOR with the password:. Decryption is pretty trivial so that exercise is left to the reader.
TrueCrypt is an open source, on-the-fly crypto system that can be used on devices supports by Linux, MacOS, and Windows. First released in , TrueCrypt can be employed to encrypt a partition on a disk or an entire disk. On May 28, , the TrueCrypt. Although this paper is intended as a crypto tutorial and not a news source about crypto controversy, the sudden withdrawal of TrueCrypt cannot go without notice.
Readers interested in using TrueCrypt should know that the last stable release of the product is v7. The TrueCrypt Wikipedia page and accompanying references have some good information about the "end" of TrueCrypt as we knew it. While there does not appear to be any rush to abandon TrueCrypt, it is also the case that you don't want to use old, unsupported software for too long.
A replacement was announced almost immediately upon the demise of TrueCrypt: " TrueCrypt may live on after all as CipherShed. One final editorial comment. TrueCrypt was not broken or otherwise compromised. It was withdrawn by its developers for reasons that have not yet been made public but there is no evidence to assume that TrueCrypt has been damaged in any way; on the contrary, two audits, completed in April and April , found no evidence of backdoors or malicious code.
A TrueCrypt volume is stored as a file that appears to be filled with random data, thus has no specific file signature. An additional clue is that a TrueCrypt container will also appear on a disk as a file that is some increment of bytes in size. While these indicators might raise a red flag, they don't rise to the level of clearly identifying a TrueCrypt volume. When a user creates a TrueCrypt volume, a number of parameters need to be defined, such as the size of the volume and the password.
To access the volume, the TrueCrypt program is employed to find the TrueCrypt encrypted file, which is then mounted as a new drive on the host system. Consider this example where an encrypted TrueCrypt volume is stored as a file named James on a thumb drive.
On a Windows system, this thumb drive has been mounted as device E:. If one were to view the E: device, any number of files might be found. TrueCrypt mounts the encrypted file, James , and it is now accessible to the system Figure A standard volume has a single password, while a hidden volume is created within a standard volume and uses a second password. As shown in Figure 23, the unallocated free space in a TrueCrypt volume is always filled with random data, thus it is impossible to differentiate a hidden encrypted volume from a standard volume's free space.
To access the hidden volume, the file is mounted as shown above and the user enters the hidden volume's password. When under duress, the user would merely enter the password of the standard i. An active area of research in the digital forensics community is to find methods with which to detect hidden TrueCrypt volumes.
Most of the methods do not detect the presence of a hidden volume, per se, but infer the presence by left over forensic remnants. As an example, both MacOS and Windows systems usually have a file or registry entry somewhere containing a cached list of the names of mounted volumes. This list would, naturally, include the name of TrueCrypt volumes, both standard and hidden. If the user gives a name to the hidden volume, it would appear in such a list.
If an investigator were somehow able to determine that there were two TrueCrypt volume names but only one TrueCrypt device, the inference would be that there was a hidden volume. Having nothing to do with TrueCrypt, but having something to do with plausible deniability and devious crypto schemes, is a new approach to holding password cracking at bay dubbed Honey Encryption.
With most of today's crypto systems, decrypting with a wrong key produces digital gibberish while a correct key produces something recognizable, making it easy to know when a correct key has been found. Honey Encryption produces fake data that resembles real data for every key that is attempted, making it significantly harder for an attacker to determine whether they have the correct key or not; thus, if an attacker has a credit card file and tries thousands of keys to crack it, they will obtain thousands of possibly legitimate credit card numbers.
EFS can be used to encrypt individual files, directories, or entire volumes. While off by default, EFS encryption can be easily enabled via File Explorer aka Windows Explorer by right-clicking on the file, directory, or volume to be encrypted, selecting Properties, Advanced, and Encrypt contents to secure data Figure Note that encrypted files and directories are displayed in green in Windows Explorer. The Windows command prompt provides an easy tool with which to detect EFS-encrypted files on a disk.
There are weaknesses with the system, most of which are related to key management. As an example, the RSA private key can be stored on an external device such as a floppy disk yes, really! In practice, however, this is rarely done; the user's private RSA key is often stored on the hard drive. A more serious implementation issue is that a backup file named esf0. For this reason, it is best to use encrypted directories because the temporary backup file is protected by being in an encrypted directory.
This information includes Figure 26 :. Files in an NTFS file system maintain a number of attributes that contain the system metadata e. RC4 works in output-feedback OFB mode, so that the key stream is independent of the plaintext. RC4 employs an 8x8 substitution box S-box.
A permutation of the S-box is then performed as a function of the key. The K array is a byte structure that holds the key possibly supplemented by an Initialization Vector , repeating itself as necessary so as to be bytes in length obviously, a longer key results in less repetition. The CipherSaber IV is a byte sequence of random numbers between the value of The IV is placed in the first bytes of the encrypted file and is appended to the user-supplied key which, in turn, can only be up to bytes in length.
The main operation of Spritz is similar to the main operation of RC4, except that a new variable, w , is added:. As seen above, RC4 has two pointers into the S-box, namely, i and j ; Spritz adds a third pointer, k. Pointer i move slowly through the S-box; note that it is incremented by 1 in RC4 and by a constant, w , in Spritz. Spritz allows w to take on any odd value, ensuring that it is always relatively prime to In essence, RC4 sets w to a value of 1.
Both ciphers have a single swap of entries in the S-box. Both also produce an output byte, z , as a function of the other parameters. Spritz, additionally, includes the previous value of z as part of the calculation of the new value of z. Assume that the Client is logging on to a remote Server across the Internet. The Client needs to prove to the Server that it knows the password but doesn't want to reveal the password in any form that an eavesdropper can decrypt.
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|Localbitcoins escrow shortage||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. While stream ciphers do not propagate transmission errors, they are, by their nature, periodic so that the keystream will eventually repeat. CAs, in turn, form trust relationships with other CAs. The model, however, is limited; just how many public keys can a single user reliably store and maintain? Although the details of the algorithm were never made public, Skipjack was a block cipher using an bit key and 32 iteration cycles per bit block.|
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Although ECDSA has not taken off on the web, it has become the digital signature scheme of choice for new cryptographic non-web applications. As we described in a previous blog post , the security of a key depends on its size and its algorithm. Some algorithms are easier to break than others and require larger keys for the same level of security. Breaking an RSA key requires you to factor a large number. We are pretty good at factoring large numbers and getting better all the time.
The mathematical community has not made any major progress in improving algorithms to solve this problem since is was independently introduced by Koblitz and Miller in Smaller keys are better than larger keys for several reasons. Smaller keys have faster algorithms for generating signatures because the math involves smaller numbers. Smaller public keys mean smaller certificates and less data to pass around to establish a TLS connection.
This means quicker connections and faster loading times on websites. Typical RSA keys in website certificates are bits. On our servers, using an ECDSA certificate reduces the cost of the private key operation by a factor of 9. This is an image taken from the Chrome browser under the green lock icon for this page under the connection tab:. This blog post is our first experiment using an SSL certificate based on elliptic curves. In the near future we will enable code that will allow sites to have a fallback certificate so that visitors with old browsers without ECDSA support can still view their site over HTTPS.
We can be relatively confident about the mathematical security of ECDSA save for some questions about the choice of curve. The history of cryptography shows us that good cryptography has been repeatedly defeated not because of bad math, but because of bad implementations of good math. One interesting quirk of the ECDSA algorithm is that every signature requires some random or unpredictable data as input. If the source of randomness is predictable to an attacker, then they can figure out the private key.
Hackers have exploited this vulnerability in several high-profile incidents. More recently, some Android devices were found to be incorrectly generating random values, resulting in a massive theft of Bitcoins from devices running Bitcoin software. Luckily, this attack is not a threat against busy remote servers. The danger of key leakage via poor random data or side channel attacks is a concern but is manageable with proper preparation.
At CloudFlare we ensure that the system random number generator has enough entropy. Cryptography is hard to implement correctly, especially in the context of a complex protocol like TLS as evidenced in some famous recent bug fixes.
That said, the benefits seem to outweigh the risks in this case. On a personal note, Dr. Vanstone was one of my professors at the University of Waterloo. He was passionate about mathematics and cryptography and he was one of the reasons I decided to pursue security engineering as a career.
The book he co-authored, The Handbook of Applied Cryptography , is still one of the classics in the field. Elliptic curve cryptography is a powerful technology that can enable faster and more secure cryptography across the Internet. Vanstone hoped. It's no secret that Cloudflare has been a big proponent of TLS 1. Additionally, the dashboard will be moved from www. Everybody has secrets. What this amounts to is that if the implementation of a signature algorithm is bogus, well, it may leak important data, including the private key.
This is true of any cryptographic algorithm, and RSA is not exempt. Singling out DSA is unwarranted. What can be said in all neutrality is that DSA and ECDSA require a source of randomness for each signature, which is a relatively heavy requirement for embedded systems such as smartcards. Solutions exist; when I have time, I work on the issue. Edit: this is now a published RFC. As for key size , the current standard specifies sizes of , and bits that's the size of p.
An older version of the standard allowed only bits, while an even older allowed all sizes multiple of 64 from to bits. A number of deployed implementations of DSA are a bit lagging behind the standard, and thus allow only bit keys. A bit DSA key is not a critical risk. As far as we know, DSA appears to be at least as strong as RSA with the same key size, and in practice a bit stronger.
DSA relies on discrete logarithm and the current DL-break record is for bits, while the current record for factorization RSA is bits. Best known algorithms for factorization and DL have a lot of similarities, but the final step where a lot of fast RAM is needed appears to be more expensive with DL than with factorization. Thus, right now, a bit DSA key is not a true security risk. Especially since, for signatures, we have less to worry about future break than for encryption; and DSA is signature-only.
The main issue with DSA is that it is not as widely supported as RSA; when it is supported, it may have limitations e. These limitations are not intrinsic to the algorithm, but reflect the state of the market, which is dominated by RSA. However, it is currently quite fashionable to switch to elliptic curve variants of DSA and, correspondingly, the market is slowly very slowly shifting towards more support for EC DSA.
You can implement DSA deterministically avoiding this problem. I think it's a flaw in typical implementations, and should be fixed. But apparently those who work on these implementations disagree, or want to follow some flawed standard procedures. Systems with a broken RNG are a big problem, no matter which crypto you use. For example it will often totally break confidentiality of your encrypted connections because the session keys are bad.
Avoid these systems at all cost. Some older standards FIPS mandate bit keys, and some implementations might be limited to that size. But the newer standard FIPS allows them, and many implementations support bit keys. They have similar performance at similar security levels.
So there are reasons for using it, despite weakness to broken RNGs. Sign up to join this community. The best answers are voted up and rise to the top. Is the use of DSA keys a security risk? Ask Question. Asked 8 years ago. Active 7 years ago. Viewed 3k times. What is the truth? Is the use of DSA really reducing security as much as it appears to me?
Improve this question. The second one says "on a system with a flawed pRNG ". It's also possible to implement DSA in a way that doesn't suffer from this , while remaining compatible with normal implementations. It says "just using it on a system with a flawed pRNG".
Sounds to me forgive the extreme metaphor!
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