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7.2 Symmetric Key Algorithms

Symmetric key algorithms are used primarily for the bulk encryption of data or data streams. These algorithms are designed to be very fast and have a large number of possible keys. The best symmetric key algorithms offer excellent secrecy; once data is encrypted with a given key, there is no fast way to decrypt the data without possessing the same key.

Symmetric key algorithms can be divided into two categories: block and stream. Block algorithms encrypt data a block (many bytes) at a time, while stream algorithms encrypt byte by byte (or even bit by bit).

7.2.1 Cryptographic Strength of Symmetric Algorithms

Different encryption algorithms are not equal. Some systems are not very good at protecting data, allowing encrypted information to be decrypted without knowledge of the requisite key. Others are quite resistant to even the most determined attack. The ability of a cryptographic system to protect information from attack is called its strength. Strength depends on many factors, including:

  • The secrecy of the key.

  • The difficulty of guessing the key or trying out all possible keys (a key search). Longer keys are generally more difficult to guess or find.

  • The difficulty of inverting the encryption algorithm without knowing the encryption key (breaking the encryption algorithm).

  • The existence (or lack) of back doors, or additional ways by which an encrypted file can be decrypted more easily without knowing the key.

  • The ability to decrypt an entire encrypted message if you know how a portion of it decrypts (called a known plaintext attack).

  • The properties of the plaintext and knowledge of those properties by an attacker. For example, a cryptographic system may be vulnerable to attack if all messages encrypted with it begin or end with a known piece of plaintext. These kinds of regularities were used by the Allies to crack the German Enigma cipher during World War II.

In general, cryptographic strength is not proven; it is only disproven. When a new encryption algorithm is proposed, the author of the algorithm almost always believes that the algorithm offers "perfect" security[6]that is, the author believes there is no way to decrypt an encrypted message without possession of the corresponding key. After all, if the algorithm contained a known flaw, then the author would not propose the algorithm in the first place (or at least would not propose it in good conscience).

[6] This is not to be confused with the formal term "perfect secrecy."

As part of proving the strength of an algorithm, a mathematician can show that the algorithm is resistant to specific kinds of attacks that have been previously shown to compromise other algorithms. Unfortunately, even an algorithm that is resistant to every known attack is not necessarily secure, because new attacks are constantly being developed.

From time to time, some individuals or corporations claim that they have invented new symmetric encryption algorithms that are dramatically more secure than existing algorithms. Generally, these algorithms should be avoided. As there are no known attack methods against the encryption algorithms that are in wide use today, there is no reason to use new, unproven encryption algorithms that might have flaws lurking in them.

7.2.2 Key Length with Symmetric Key Algorithms

Among those who are not entirely familiar with the mathematics of cryptography, key length is a topic of continuing confusion. As we have seen, short keys can significantly compromise the security of encrypted messages because an attacker can merely decrypt the message with every possible key to decipher the message's content. But while short keys provide comparatively little security, extremely long keys do not necessarily provide significantly more practical security than keys of moderate length. That is, while keys of 40 or 56 bits are not terribly secure, a key of 256 bits does not offer significantly more real security than a key of 168 bits, or even a key of 128 bits.

To understand this apparent contradiction, it is important to understand what is really meant by the words key length, and how a brute force attack actually works.

Inside a computer, a cryptographic key is represented as a string of binary digits. Each binary digit can be a 0 or a 1. Thus, if a key is 1 bit in length, there are two possible keys: 0 and 1. If a key is 2 bits in length, there are four possible keys: 00, 01, 10, and 11. If a key is 3 bits in length, there are eight possible keys: 000, 001, 010, 011, 100, 101, 110, and 111. In general, each added key bit doubles the number of keys. The mathematical equation that relates the number of possible keys to the number of bits is:

number of keys = 2(number of bits)

If you are attempting to decrypt a message and do not have a copy of the key, the simplest way to decrypt the message is to do a brute force attack. These attacks are also called key search attacks, because they involve trying every possible key to see if a specific key decrypts the message. If the key is selected at random, then on average, an attacker will need to try half of all the possible keys before finding the actual decryption key.

Fortunately, for those of us who depend upon symmetric encryption algorithms, it is a fairly simple matter to use longer keys. Each time a bit is added, the difficulty for an attacker attempting a brute force attack doubles.

The first widely used encryption algorithm, the DES, used a key that was 56 bits long. At the time that the DES was adopted, many academics said that 56 bits was not sufficient: they argued for a key that was twice as long. But it has been conjectured that the U.S. National Security Agency did not want a cipher with a longer key length widely deployed, most likely because such a secure cipher would significantly complicate its job of international surveillance.[7] To further reduce the impact that the DES would have on its ability to collect international intelligence, U.S. corporations were forbidden from exporting products that implemented the DES algorithm.

[7] The NSA operates a worldwide intelligence surveillance network. This network relies, to a large extent, on the fact that the majority of the information transmitted electronically is transmitted without encryption. The network is also used for obtaining information about the number of messages exchanged between various destinations, a technique called traffic analysis. Although it is widely assumed that the NSA has sufficient computer power to forcibly decrypt a few encrypted messages, not even the NSA has the computer power to routinely decrypt all of the world's electronic communications.

In the early 1990s, a growing number of U.S. software publishers demanded the ability to export software that offered at least a modicum of security. As part of a compromise, a deal was brokered between the U.S. Department of Commerce, the National Security Agency, and the Software Publisher's Association. Under the terms of that agreement, U.S. companies were allowed to export mass-market software that incorporated encryption, provided that the products used a particular encryption algorithm and the length of the key was limited to 40 bits. At the same time, some U.S. banks started using an algorithm called Triple-DES (basically, a threefold application of the DES algorithm) to encryp some financial transactions. It has a key size of 168 bits. Triple-DES is described in the following section.

In October 2000, the National Institute of Standards and Technology (NIST) approved the Rijndael encryption algorithm as the new U.S. Advanced Encryption Standard. Rijndael can be used with keys of 128, 192, or 256 bits. The algorithm's extremely fast speed, combined with its status as the government-chosen standard, means that it will likely be preferable to the DES, Triple-DES, and other algorithms in the future.

So how many bits is enough? That depends on how fast the attacker can try different keys and how long you wish to keep your information secure. As Table 7-1 shows, if an attacker can try only 10 keys per second, then a 40-bit key will protect a message for more than 3,484 years. Of course, today's computers can try many thousands of keys per secondand with special-purpose hardware and software, they can try hundreds of thousands. Key search speed can be further improved by running the same program on hundreds or thousands of computers at a time. Thus, it's possible to search a million keys per second or more using today's technology. If you have the ability to search a million keys per second, you can try all 40-bit keys in only 13 days.

If a key that is 40 bits long is clearly not sufficient to keep information secure, how many bits are necessary? In April 1993, the Clinton Administration introduced the Clipper encryption chip as part of its Escrowed Encryption Initiative (EEI). This chip used a key that was 80 bits long. As Table 7-1 shows, an 80-bit key is more than adequate for many applications. If you could search a billion keys per second, trying all 80-bit keys would still require 38 million years! Clipper was widely criticized not because of the key length, but because the Clipper encryption algorithm was kept secret by the National Security Agency, and because each Clipper chip came with a "back door" that allowed information encrypted by each Clipper chip to be decrypted by the U.S. government in support of law enforcement and intelligence needs.

Table 7-1. Estimated success of brute force attacks (for different numbers of bits in the key and number of keys that can be tried per second)

Length of key

Keys searched per second

Postulated key-searching technology[8]

Approximate time to search all possible keys

40 bits[9]

10

10-year-old desktop computer

3,484 years

40 bits

1,000

Typical desktop computer today

35 years

40 bits

1 million

Small network of desktops

13 days

40 bits

1 billion

Medium-sized corporate network

18 minutes

56 bits

1 million

Desktop computer a few years from now

2,283 years

56 bits

1 billion

Medium-sized corporate network

2.3 years

56 bits[10]

100 billion

DES-cracking machine

8 days

64 bits

1 billion

Medium-sized corporate network

585 years

80 bits

1 million

Small network of desktops

38 billion years

80 bits

1 billion

Medium-sized corporate network

38 million years

128 bits

1 billion

Medium-sized corporate network

1022 years

128 bits

1 billion billion (1 x 1018)

Large-scale Internet project in the year 2005

10,783 billion years

128 bits

1 x 1023

Special-purpose quantum computer in the year 2015?

108 million years

192 bits

1 billion

Medium-sized corporate network

2 x 1041 years

192 bits

1 billion billion

Large-scale Internet project in the year 2005

2 x 1032 years

192 bits

1 x 1023

Special-purpose quantum computer in the year 2015?

2 x 1027 years

256 bits

1 x 1023

Special-purpose quantum computer in the year 2015?

3.7 x 1046 years

256 bits

1 x 1032

Special-purpose quantum computer in the year 2040?

3.7 x 1037 years

[8] Computing speeds assume that a typical desktop computer in the year 2003 can execute approximately 1 billion instructions per second. This is roughly the speed of a 1 Ghz Pentium III computer.

[9] In 1997, a 40-bit RC4 key was cracked in only 3.5 hours.

[10] In 2000, a 56-bit DES key was cracked in less than 4 days.

Increasing the key size from 80 bits to 128 bits dramatically increases the amount of effort to guess the key. As the table shows, if there were a computer that could search a billion keys per second, and if you had a billion of these computers, it would still take 10,783 billion years to search all possible 128-bit keys. As our Sun is likely to become a red giant within the next 4 billion years and, in so doing, destroy the Earth, a 128-bit encryption key should be sufficient for most cryptographic uses, assuming that there are no other weaknesses in the algorithm used.

Lately, there has been considerable interest in the field of quantum computing. Scientists postulate that it should be possible to create atomic-sized computers specially designed to crack encryption keys. But while quantum computers could rapidly crack 56-bit DES keys, it's unlikely that a quantum computer could make a dent in a 128-bit encryption key within a reasonable time: even if you could crack 1 x 1023 keys per second, it would still take 108 million years to try all possible 128-bit encryption keys.

It should be pretty clear at this point that there is no need, given the parameters of cryptography and physics as we understand them today, to use key lengths that are larger than 128 bits. Nevertheless, there seems to be a marketing push towards increasingly larger and larger keys. The Rijndael algorithm can be operated with 128-bit, 192-bit, or 256-bit keys. If it turns out that there is an as-yet hidden flaw in the Rijndael algorithm that gives away half the key bits, then the use of the longer keys might make sense. Why you would want to use those longer key lengths isn't clear, but if you want them, they are there for you to use.

7.2.3 Common Symmetric Key Algorithms

There are many symmetric key algorithms in use today, as shown in Table 7-2.

Table 7-2. Common symmetric encryption algorithms

Algorithm

Description

Key Length

Rating

Blowfish

Block cipher developed by Schneier

1-448 bits

L

DES

DES adopted as a U.S. government standard in 1977

56 bits

§

IDEA

Block cipher developed by Massey and Xuejia

128 bits

L

MARS

AES finalist developed by IBM

128-256 bits

RC2

Block cipher developed by Rivest

1-2048 bits

W

RC4

Stream cipher developed by Rivest

1-2048 bits

L, §

RC5

Block cipher developed by Rivest and published in 1994

128-256 bits

RC6

AES finalist developed by RSA Labs

128-256 bits

Rijndael

NIST selection for AES, developed by Daemen and Rijmen

128-256 bits

W

Serpent

AES finalist developed by Anderson, Biham, and Knudsen

128-256 bits

Triple-DES

A three-fold application of the DES algorithm

168 bits

L

Twofish

AES candidate developed by Schneier

128-256 bits

Key to ratings:

W) Excellent algorithm. This algorithm is widely used and is believed to be secure, provided that keys of sufficient length are used.

L) Algorithm appears strong but is being phased out for other algorithms that are faster or thought to be more secure.

) Algorithm appears to be strong but will not be widely deployed because it was not chosen as the AES standard.

§) Use of this algorithm is no longer recommended because of short key length or mathematical weaknesses. Data encrypted with this algorithm should be reasonably secure from casual browsing, but would not withstand a determined attack by a moderately-funded attacker.

Some of the algorithms that are commonly encountered in the field of computer security are summarized in the following list:

DES

The Data Encryption Standard was adopted as a U.S. government standard in 1977 and as an ANSI standard in 1981. The DES is a block cipher that uses a 56-bit key and has several different operating modes depending on the purpose for which it is employed. The DES is a strong algorithm, but today the short key length limits its use. Indeed, in 1998 a special-purpose machine for "cracking DES" was created by the Electronic Frontier Foundation (EFF) for under $250,000. In one demonstration, it found the key to an encrypted message in less than a day in conjunction with a coalition of computer users around the world.

Triple-DES

Triple-DES is a way to make the DES dramatically more secure by using the DES encryption algorithm three times with three different keys, for a total key length of 168 bits. Also called "3DES," this algorithm has been widely used by financial institutions and by the Secure Shell program (ssh). Simply using the DES twice with two different keys does not improve its security to the extent that one might at first suspect because of a theoretical plaintext attack called meet-in-the-middle, in which an attacker simultaneously attempts encrypting the plaintext with a single DES operation and decrypting the ciphertext with another single DES operation until a match is made in the middle. Triple-DES avoids this vulnerability.

Blowfish

Blowfish is a fast, compact, and simple block encryption algorithm invented by Bruce Schneier. The algorithm allows a variable-length key, up to 448 bits, and is optimized for execution on 32- or 64-bit processors. The algorithm is unpatented and has been placed in the public domain. Blowfish is used in the Secure Shell and other programs.

IDEA

The International Data Encryption Algorithm (IDEA) was developed in Zurich, Switzerland, by James L. Massey and Xuejia Lai and published in 1990. IDEA uses a 128-bit key. IDEA is used by the popular program PGP to encrypt files and electronic mail. Unfortunately, wider use of IDEA has been hampered by a series of software patents on the algorithm, which are currently held by Ascom-Tech AG in Solothurn, Switzerland.[11]

[11] Although we are generally in favor of intellectual property protection, we are opposed to the concept of software patents, in part because they hinder the development and use of innovative software by individuals and small companies. Software patents also tend to hinder some forms of experimental research and education.

RC2

This block cipher was originally developed by Ronald Rivest and kept as a trade secret by RSA Data Security. The algorithm was revealed by an anonymous Usenet posting in 1996 and appears to be reasonably strong (although there are some particular keys that are weak). RC2 allows keys between 1 and 2,048 bits. The RC2 key length was traditionally limited to 40 bits in software that was exported to allow for decryption by the U.S. National Security Agency.[12]

[12] The 40-bit "exportable" implementation of SSL actually uses a 128-bit RC2 key, in which 88 bits are revealed, producing a "40-bit secret." Netscape claimed that the 88 bits provided protection against codebook attacks, in which all 240 keys would be precomputed and the resulting encryption patterns stored. Other SSL implementors have suggested that using a 128-bit key in all cases and simply revealing 88 bits of the key in exportable versions of Navigator made Netscape's SSL implementation easier to write.

RC4

This stream cipher was originally developed by Ronald Rivest and kept as a trade secret by RSA Data Security. This algorithm was also revealed by an anonymous Usenet posting in 1994 and appears to be reasonably strong. RC4 allows keys between 1 and 2,048 bits. The RC4 key length was traditionally limited to 40 bits in software that was exported.

RC5

This block cipher was developed by Ronald Rivest and published in 1994. RC5 allows a user-defined key length, data block size, and number of encryption rounds.

Rijndael (AES)

This block cipher was developed by Joan Daemen and Vincent Rijmen, and was chosen in October 2000 by the National Institute of Standards and Technology to be the U.S.'s new Advanced Encryption Standard. Rijndael is an extraordinarily fast and compact cipher that can use keys that are 128, 192, or 256 bits long.[13]

[13] In September 2002, Bruce Schneier's Crypto-Gram Newsletter reported on a series of academic papers that have found weaknesses or points of attack in the Rijndael cipher (as well as several others). Although Schneier takes pains to point out that these attacks are currently highly theoretical and potentially impossible to implement, the history of cryptography suggests that AES may not be remembered as the last best cryptosystem. For details, see http://www.counterpane.com/crypto-gram-0209.html and the references it contains.

7.2.4 Attacks on Symmetric Encryption Algorithms

If you are going to use cryptography to protect information, then you must assume that people who you do not wish to access your information will be recording your data, and, if they determine it is encrypted, may try to decrypt it forcibly.[14] To be useful, your cryptographic system must be resistant to this kind of direct attack.

[14] Whitfield Diffie has pointed out that if your data is not going to be subjected to this sort of direct attack, then there is no need to encrypt it.

Attacks against encrypted information fall into three main categories. They are:

  • Key search (brute force) attacks

  • Cryptanalysis

  • Systems-based attacks

7.2.4.1 Key search (brute force) attacks

As we saw earlier, the simplest way to attack an encrypted message is simply to attempt to decrypt the message with every possible key. Most attempts will fail, but eventually one of the tries will succeed and either allow the cracker into the system or permit the ciphertext to be decrypted. These attacks, illustrated in Figure 7-3, are called key search or brute force attacks.

There's no way to defend against a key search attack because there's no way to keep an attacker from trying to decrypt your message with every possible key.

Figure 7-3. A key search attack
figs/puis3_0703.gif

Key search attacks are not very efficient. And, as we showed earlier, if the chosen key is long enough, a key search attack is not even feasible. For example, with a 128-bit key and any conceivable computing technology, life on Earth will cease to exist long before even a single key is likely to be cracked!

On the other hand, many key search attacks are made considerably simpler because most users pick keys based on small passwords with printable characters. For a 128-bit key to be truly secure, all 128 bits must be randomly chosen. That is, there must be 2128 distinct keys that could possibly be used to encrypt the data. If a "128-bit key" is actually derived from a password of four lower-case letters, then even though the key appears to be 128 bits long, there are really only 26 x 26 x 26 x 26, or 456,976 different keys that could actually be used. Instead of a 128-bit key, a key that is chosen from four lower-case letters has an effective key length between 18 bits and 19 bits! (This is because 218 = 262,144, while 219 = 524,288.)

From this simple analysis, it would appear that any of the strong algorithms described earlier with a 128-bit key length should be sufficient for most cryptographic needsboth now and forever more. Unfortunately, there are a number of factors that make this solution technically, legally, or politically unsuitable for many applications, as we'll see later in this chapter.

7.2.4.2 Cryptanalysis

If key length were the only factor determining the security of a cipher, everyone interested in exchanging secret messages would simply use codes with 128-bit keys, and all cryptanalysts (people who break codes) would have to find new jobs. Cryptography would be a resolved branch of mathematics, similar to simple addition.

What keeps cryptography interesting is the fact that most encryption algorithms do not live up to our expectations. Key search attacks are seldom required to divulge the contents of an encrypted message. Instead, most encryption algorithms can be defeated by using a combination of sophisticated mathematics and computing power. The result is that many encrypted messages can be deciphered without knowing the key. A skillful cryptanalyst can sometimes decipher encrypted text without even knowing the encryption algorithm.

A cryptanalytic attack can have two possible goals. The cryptanalyst might have ciphertext and want to discover the plaintext, or might have ciphertext and want to discover the encryption key that was used to encrypt it. (These goals are similar but not quite the same.) The following attacks are commonly used when the encryption algorithm is known, and these may be applied to encrypted files or Internet traffic:

Known plaintext attack

In this type of attack, the cryptanalyst has a block of plaintext and a corresponding block of ciphertext. Although this may seem an unlikely occurrence, it is actually quite common when cryptography is used to protect electronic mail (with standard headers at the beginning of each message), standard forms, or hard disks (with known structures at predetermined locations on the disk). The goal of a known plaintext attack is to determine the cryptographic key (and possibly the algorithm), which can then be used to decrypt other messages.

Chosen plaintext attack

In this type of attack, the cryptanalyst has the subject of the attack (unknowingly) encrypt chosen blocks of data, creating a result that the cryptanalyst can then analyze. Chosen plaintext attacks are simpler to carry out than they might appear. (For example, the subject of the attack might be a radio link that encrypts and retransmits messages received by telephone.) The goal of a chosen plaintext attack is to determine the cryptographic key, which can then be used to decrypt other messages.

Differential cryptanalysis

This attack, which is a form of chosen plaintext attack, involves encrypting many texts that are only slightly different from one another and comparing the results.

Differential fault analysis

This attack works against cryptographic systems that are built in hardware. The device is subjected to environmental factors (heat, stress, radiation) designed to coax the device into making mistakes during the encryption or decryption operation. These faults can be analyzed, and from them the device's internal state, including the encryption key or algorithm, can possibly be learned.

Differential power analysis

This is another attack against cryptographic hardwarein particular, smart cards. By observing the power that a smart card uses to encrypt a chosen block of data, it is possible to learn a little bit of information about the structure of the secret key. By subjecting the smart card to a number of specially chosen data blocks and carefully monitoring the power used, it is possible to determine the secret key.

Differential timing analysis

This attack is similar to differential power analysis, except that the attacker carefully monitors the time that the smart card takes to perform the requested encryption operations.

The only reliable way to determine if an algorithm is strong is to hire a stable of the world's best cryptographers and pay them to find a weakness. This is the approach used by the U.S. National Security Agency. Unfortunately, this approach is beyond the ability of most cryptographers, who instead settle on an alternative known as peer review.

Peer review is the process by which most mathematical and scientific truths are verified. First, a person comes up with a new idea or proposes a new theory. Next, the inventor attempts to test his idea or theory on his own. If the idea holds up, it is then published in an academic journal or otherwise publicized within a community of experts. If the experts are motivated, they might look at the idea and see if it has any worth. If the idea stands up over the passage of time, especially if many experts try and fail to disprove the idea, it gradually comes to be regarded as truth.

Peer review of cryptographic algorithms and computer security software follows a similar process. As individuals or organizations come up with a new algorithm, the algorithm is published. If the algorithm is sufficiently interesting, cryptographers or other academics might be motivated to find flaws in it. If the algorithm can stand the test of time, it might be secure, pending some new mathematical discovery or technique being developed.

It's important to realize that simply publishing an algorithm or a piece of software does not guarantee that flaws will be found. The Wireless Encryption Protocol (WEP) encryption algorithm used by the 802.11 networking standard was published for many years before a significant flaw was found in the algorithmthe flaw had been there all along, but no one had bothered to look for it.

The peer review process isn't perfect, but it's better than the alternative: no review at all. Do not trust people who say they've developed a new encryption algorithm but also say that they don't want to disclose how the algorithm works because such disclosure would compromise the strength of the algorithm. In practice, there is no way to keep an algorithm secret: if the algorithm is being used to store information that is valuable, an attacker will purchase (or steal) a copy of a program that implements the algorithm, disassemble the program, and figure out how it works.[15] True cryptographic security lies in openness and peer review, not in algorithmic secrecy.

[15] In the case of the RC2 and RC4 encryption algorithms, the attackers went further and published source code for the reverse-engineered algorithms!

7.2.4.3 Systems-based attacks

Another way of breaking a code is to attack the cryptographic system that uses the cryptographic algorithm, without actually attacking the algorithm itself.

One of the most spectacular cases of a systems-based attack was the VC-I video encryption algorithm used for early satellite TV broadcasts. For years, video pirates sold decoder boxes that could intercept the transmissions of keys and use them to decrypt the broadcasts. The VC-I encryption algorithm was sound, but the system as a whole was weak. (This case also demonstrates the fact that when a lot of money is at stake, people will often find the flaws in a weak encryption system, and those flaws will be exploited.)

Many of the early attacks against Netscape's implementation of SSL were actually attacks on Netscape Navigator's implementation, rather than on the SSL protocol itself. In one published attack, researchers David Wagner and Ian Goldberg at the University of California at Berkeley discovered that Navigator's random number generator was not really random. It was possible for attackers to closely monitor the computer on which Navigator was running, predict the random number generator's starting configuration, and determine the randomly chosen key using a fairly straightforward method. In another attack, the researchers discovered that they could easily modify the Navigator program itself so that the random number generator would not be executed. This entirely eliminated the need to guess the key.

Covert channels are another concern. The U.S. Department of Defense's 1985 Trusted Computer System Evaluation Criteria define a covert channel as "any communication channel that can be exploited by a process to transfer information in a manner that violates the system's security policy." For example, even if an attacker cannot decrypt encrypted email messages, he may be able to gain information by examining the message sender, recipient, timing, path through the network, character set encoding, or other features that are often overlooked by those concerned about message confidentiality or integrity alone.

Show Me the Keys!

For most people, the idea of an encryption key is a pretty abstract concept. It's important to remember that an encryption key is nothing more than a sequence of numbers. A variety of different encryption keys are shown here:

Typical PGP public key
-----BEGIN PGP PUBLIC KEY BLOCK-----
Version: PGPfreeware 7.0.3 for non-commercial use <http://www.pgp.com>

mQGiBDO4bV0RBADlPi7V0LvQ8d16s4YniLyvacbbn6FwypNA952/4AkDe5qxmLfP
kmw8f8tEoTP+Piw78tNmiv+uwNF+A1Iyj5fMVfMWa1Orre70+dXaMhkulaIbyWUy
... 80 lines omitted ...
NaIfOdAlN1KNJ9sepaGYzUAbpVL9glGu4+rw9U07Mw+GkokATAQYEQIADAUCOoNi
IgUbDAAAAAAKCRAez+Vw96uNVJI9AKDvOPeiLjDKyLSDYXi6Go3ws6wYnQCfVlUX
8seFcPFUEgML7lOF4WgpKxw=
=iA0+
-----END PGP PUBLIC KEY BLOCK-----
Typical SSH public key
1024 37 
1298522689083978590489119516791918925941302538262159337002014444456770676008980
5486695356867123381954013079461244685564737310556304949543707542699596363093219
0115016916159882829116322269907996865140268688181016886624185740592018258548746
149448320062974219266512791102992871147404824830689301813453230087636727 
simsong@walden
Typical DES key
05674317

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