What is breakable encryption

In the early nineties it tried to introduce the Clipper chip — an encryption and decryption chip for consumer devices that came with a backdoor for law enforcement. Mathematically, of course, this is ridiculous. It was leaked by the hacker group Shadow Brokers on April 14, and used as part of the worldwide WannaCry ransomware attack in May, the NotPetya cyberattack in June and reportedly part of the Retefe banking Trojan since early September.

Law abiding citizens would be forced to use hobbled encryption while criminals continued to choose the strongest encryption available. Marc Rotenberg, executive director of the Electronic Privacy Information Center, who debated Comey about a year ago at a conference hosted by the American Bar Association, argued that the Fifth Amendment does indeed give American citizens an absolute right to privacy.

And Shahid Buttar, director of grassroots advocacy at the Electronic Frontier Foundation EFF , said encryption is often the only thing protecting journalists in repressive countries, whistleblowers even in the US, and religious minorities such as Christians in Muslim countries. At the root of this is a misapprehension of what security means. Criminals cannot be stopped and punished. But Schneier said the math works the other way.

But he added that he doubts there will be any serious moves in Congress to mandate that government can defeat encryption. Follow NakedSecurity on Twitter for the latest computer security news.

Government is a many-headed hydra. Sometimes i think Government[Law enforcement] is either confused or very misinformed of how certain things work.

On behalf of the world I offer to make a deal with the US government. Open all your books to the public; financial, missions, every single secret. End all exemptions of government workers from US law yes including Congress and Senate excluding themselves from healthcare laws. Eliminate the dumb laws giving companies human rights while not making them accountable for their actions as a human.

Eliminate political parties and make people run on their own merits. Do that, and you can have a backdoor into everything. You are exactly right, and kudos to you. If the government were to truly want breakable encryption for all, all they would have to do is create an encryption solution that works effortlessly in everyday life, similar to https. No encryption process works that smoothly yet, so if they were to introduce it, it would take off, and everybody, including the lazy, and the lazy outlaws, would use it.

Easier written than done. Of course, this is government we are talking about. They have to get contracts with civilian organizations, they have to water it down with endless committee changes, and they have to otherwise make it a waste of taxpayer money.

Probably not terrorists, but you probably have met drug dealers and definitely child molesters. I beg to differ — I consider all of them as types of back doors, and all have risks. Well, that much is true. Ransomware only exists because crypto-currencies allow them to move funds completely independently of oversight. 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.

Now I'm not surprised by the NSA trying anything 1 , but what slightly baffles me is the word "most" - so, what encryption algorithms are known and sufficiently field-tested that are not severely vulnerable to Quantum Computing? Assuming that a true Quantum Computer can be built, then:. This means that a bit AES key would be demoted back to the strength of a bit key -- however, note that these are 2 64 quantum-computing operations; you cannot apply figures from studies with FPGA and GPU and blindly assume that if a quantum computer can be built at all , it can be built and operated cheaply.

Similarly, hash function resistance to various kind of attacks would be similarly reduced. SHA would still be as strong against collisions as a bit hash function nowadays, i. So symmetric cryptography would not be severely damaged if a quantum computer turned out to be built. Even if it could be built very cheaply actual symmetric encryption and hash function algorithms would still offer a very fair bit of resistance. For asymmetric encryption, though, that would mean trouble.

We nonetheless know of several asymmetric algorithms for which no efficient QC-based attack is known, in particular algorithms based on lattice reduction e. These algorithms are not very popular nowadays, for a variety of reasons early versions of NTRU turned out to be weak; there are patents; McEliece's public keys are huge ; and so on , but some would still be acceptable.

Study of cryptography under the assumption that efficient quantum computers can be built is called post-quantum cryptography. Personally I don't believe that a meagre 80 millions dollars budget would get the NSA far. IBM has been working on that subject for decades and spent a lot more than that, and their best prototypes are not amazing. It is highly plausible that NSA has spent some dollars on the idea of quantum computing; after all, that's their job, and it would be a scandal if taxpayer money did not go into that kind of research.

But there is a difference between searching and finding Quantum computing will make most dramatic impact on asymmetric encryption, but symmetric algorithms are considered safe with a large enough key size bits. When Cryptographers speak about quantum computer and post-quantum cryptography,actually they speak about power of Shor's algorithm in factoring numbers,so hard problems based on factoring number that are used for creating cryptosystems are broken with Shor's algorithm quantum computer so RSA,DSA,ELGamal,Diffie-Hellman Key Exchabge,ECC are vulnerable to Quantum Computing!

Just specifying which bit key to use for a particular message works perfectly and is used by the security services. For added protection against the NSA, encrypt using AES chain block cipher mode, then encrypt the cipher text the result from the first encryption again, and repeat as many times as you can afford to repeat.

The NSA would probably try brute force searching to go through the search space, and figure out they've cracked the code by determining the entropy of the result for each of the keys they test.

They know when to stop when they see meaningful text as the result. By encrypting several times, you make it harder for them to determine when they have cracked a code because if they did try the right key, then they would see jumble as the result, almost indistinguishable from the results of the incorrect keys.

As you increase the number of re-encryptions, the difficulty of cracking encrypting content becomes more difficult. The NSA will lose its mind trying to figure out when they have cracked the code.

Software like TrueCrypt can do multiple encryption for you. You will need encryption that runs in one of the more sophisticated modes like "Chain Block Cipher" or "Cipher Feedback. Hopefully this helps you keep your stuff out of the NSA's reach. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question.

Asked 7 years, 10 months ago.