Get 2^d intermediate states and 2^d ciphertexts, then compute the keys that maps between them. This requires 2^{2d} key-recoveries, since each intermediate state needs to be linked to all ciphertexts.
|
|
Chosen-ciphertext attacks, like other attacks, may be adaptive or non-adaptive. In an adaptive chosen- ciphertext attack, the attacker can use the results from prior decryptions to inform their choices of which ciphertexts to have decrypted. In a non-adaptive attack, the attacker chooses the ciphertexts to have decrypted without seeing any of the resulting plaintexts. After seeing the plaintexts, the attacker can no longer obtain the decryption of additional ciphertexts.
|
|
Deterministic encryption can leak information to an eavesdropper, who may recognize known ciphertexts. For example, when an adversary learns that a given ciphertext corresponds to some interesting message, they can learn something every time that ciphertext is transmitted. To gain information about the meaning of various ciphertexts, an adversary might perform a statistical analysis of messages transmitted over an encrypted channel, or attempt to correlate ciphertexts with observed actions (e.g., noting that a given ciphertext is always received immediately before a submarine dive).
|
|
Nevertheless, not all nomenclators were broken; today, cryptanalysis of archived ciphertexts remains a fruitful area of historical research.
|
|
This has significant advantages, as it prevents an adversary from recognizing intercepted messages by comparing them to a dictionary of known ciphertexts.
|
|
In a chosen-plaintext attack the adversary can (possibly adaptively) ask for the ciphertexts of arbitrary plaintext messages. This is formalized by allowing the adversary to interact with an encryption oracle, viewed as a black box. The attacker’s goal is to reveal all or part of the secret encryption key. It may seem infeasible in practice that an attacker could obtain ciphertexts for given plaintexts.
|
|
One way to do this is to deploy data compression techniques prior to encryption, for example by removing redundant vowels while retaining readability. This is a good idea anyway, as it reduces the amount of data to be encrypted. Ciphertexts greater than the unicity distance can be assumed to have only one meaningful decryption. Ciphertexts shorter than the unicity distance may have multiple plausible decryptions.
|
|
This algorithm first generates a new pair of public and secret keys for the homomorphic encryption scheme, and then uses these keys with the homomorphic scheme to encrypt the correct input wires, represented as the secret key of the garbled circuit. The produced ciphertexts represent the public encoding of the input (σx) that is given to the worker, while the secret key (τx) is kept private by the client. After that, the worker applies the computation steps of the Yao's protocol over the ciphertexts generated by the problem generation algorithm. This is done by recursively decrypting the gate ciphertexts until arriving to the final output wire values (σy).
|
|
Cover of The Beale Papers The Beale ciphers (or Beale Papers) are a set of three ciphertexts, one of which allegedly states the location of a buried treasure of gold, silver and jewels estimated to be worth over US$43 million Comprising three ciphertexts, the first (unsolved) text describes the location, the second (solved) ciphertext the content of the treasure, and the third (unsolved) lists the names of the treasure's owners and their next of kin. The story of the three ciphertexts originates from an 1885 pamphlet detailing treasure being buried by a man named Thomas J. Beale in a secret location in Bedford County, Virginia, in the 1820s. Beale entrusted a box containing the encrypted messages to a local innkeeper named Robert Morriss and then disappeared, never to be seen again. According to the story, the innkeeper opened the box 23 years later, and then decades after that gave the three encrypted ciphertexts to a friend before he died.
|
|
In its full generality, partitioning cryptanalysis works by dividing the sets of possible plaintexts and ciphertexts into efficiently-computable partitions such that the distribution of ciphertexts is significantly non-uniform when the plaintexts are chosen uniformly from a given block of the partition. Partitioning cryptanalysis has been shown to be more effective than linear cryptanalysis against variants of DES and CRYPTON. A specific partitioning attack called mod n cryptanalysis uses the congruence classes modulo some integer for partitions.
|
|
The operator selects one of the first 7 columns using the key digit and then finds the row in which the key letter occurs. That row in the second set of columns is used to encipher and decipher BATCO messages. The scrambled alphabet in the selected row defines the correspondence between plaintext symbols in the column headings and ciphertext symbols in the individual cells. Note that there are two possible ciphertexts for each plaintext symbol, except for 0, which has four possible ciphertexts.
|
|
In the history of cryptography, early ciphers, implemented using pen-and-paper, were routinely broken using ciphertexts alone. Cryptographers developed statistical techniques for attacking ciphertext, such as frequency analysis. Mechanical encryption devices such as Enigma made these attacks much more difficult (although, historically, Polish cryptographers were able to mount a successful ciphertext-only cryptanalysis of the Enigma by exploiting an insecure protocol for indicating the message settings). More advanced ciphertext-only attacks on the Enigma were mounted in Bletchley Park during World War II, by intelligently guessing plaintexts corresponding to intercepted ciphertexts.
|
|
In cryptography, the term ciphertext expansion refers to the length increase of a message when it is encrypted. Many modern cryptosystems cause some degree of expansion during the encryption process, for instance when the resulting ciphertext must include a message-unique Initialization Vector (IV). Probabilistic encryption schemes cause ciphertext expansion, as the set of possible ciphertexts is necessarily greater than the set of input plaintexts. Certain schemes, such as Cocks Identity Based Encryption, or the Goldwasser- Micali cryptosystem result in ciphertexts hundreds or thousands of times longer than the plaintext.
|
|
For public-key systems, adaptive-chosen-ciphertexts are generally applicable only when they have the property of ciphertext malleability -- that is, a ciphertext can be modified in specific ways that will have a predictable effect on the decryption of that message.
|
|
Gentry's scheme supports both addition and multiplication operations on ciphertexts, from which it is possible to construct circuits for performing arbitrary computation. The construction starts from a somewhat homomorphic encryption scheme, which is limited to evaluating low-degree polynomials over encrypted data; it is limited because each ciphertext is noisy in some sense, and this noise grows as one adds and multiplies ciphertexts, until ultimately the noise makes the resulting ciphertext indecipherable. Gentry then shows how to slightly modify this scheme to make it bootstrappable, i.e., capable of evaluating its own decryption circuit and then at least one more operation.
|
|
For an asymmetric key encryption algorithm cryptosystem to be semantically secure, it must be infeasible for a computationally bounded adversary to derive significant information about a message (plaintext) when given only its ciphertext and the corresponding public encryption key. Semantic security considers only the case of a "passive" attacker, i.e., one who generates and observes ciphertexts using the public key and plaintexts of her choice. Unlike other security definitions, semantic security does not consider the case of chosen ciphertext attack (CCA), where an attacker is able to request the decryption of chosen ciphertexts, and many semantically secure encryption schemes are demonstrably insecure against chosen ciphertext attack.
|
|
This concern is particularly serious in the case of public key cryptography, where any party can encrypt chosen messages using a public encryption key. In this case, the adversary can build a large "dictionary" of useful plaintext/ciphertext pairs, then observe the encrypted channel for matching ciphertexts.
|
|
Similar to format- preserving encryption, FTE can be used to control the format of ciphertexts. The canonical example is a credit card number, such as `1234567812345670` (16 bytes long, digits only). However, FTE does not enforce that the input format must be the same as the output format.
|
|
If a ciphertext is created this way, its creator would be aware, in some sense, of the plaintext. However, many cryptosystems are not plaintext-aware. As an example, consider the RSA cryptosystem without padding. In the RSA cryptosystem, plaintexts and ciphertexts are both values modulo N (the modulus).
|
|
The sub-group hiding assumption is a computational hardness assumption used in elliptic curve cryptography and pairing-based cryptography. It was first introduced inDan Boneh, Eu-Jin Goh, Kobbi Nissim: Evaluating 2-DNF Formulas on Ciphertexts. TCC 2005: 325-341 to build a 2-DNF homomorphic encryption scheme.
|
|
In the case of symmetric-key algorithm cryptosystems, an adversary must not be able to compute any information about a plaintext from its ciphertext. This may be posited as an adversary, given two plaintexts of equal length and their two respective ciphertexts, cannot determine which ciphertext belongs to which plaintext.
|
|
Alexander (c. 1945) p. 96 If the two messages were in depth, then the matches occur just as they did in the plaintexts. However, if the messages were not in depth, then the two ciphertexts will compare as if they were random, giving a repeat rate of about 1 in 26.
|
|
RSA Security, which had a patent on the algorithm,Rivest, R. L, "Block Encryption Algorithm With Data Dependent Rotation", , issued on 3 March 1998. offered a series of US$10,000 prizes for breaking ciphertexts encrypted with RC5, but these contests have been discontinued as of May 2007. As a result, distributed.
|
|
Data compression can be achieved by building SEAL with Zlib support. By default, data is compressed using the DEFLATE algorithm which achieves significant memory footprint savings when serializing objects such as encryption parameters, ciphertexts, plaintexts, and all available keys: Public, Secret, Relin (relinearization), and Galois. Compression can always be disabled.
|
|
More generally, format-preserving encryption requires a keyed permutation on some finite language. This makes format-preserving encryption schemes a natural generalization of (tweakable) block ciphers. In contrast, traditional encryption schemes, such as CBC, are not permutations because the same plaintext can encrypt to multiple different ciphertexts, even when using a fixed key.
|
|
However, as the RSA decryption exponent is randomly distributed, modular exponentiation may require a comparable number of squarings/multiplications to BG decryption for a ciphertext of the same length. BG has the advantage of scaling more efficiently to longer ciphertexts, where RSA requires multiple separate encryptions. In these cases, BG may be significantly more efficient.
|
|
Then, of course, the monoalphabetic ciphertexts that result must be cryptanalyzed. # A cryptanalyst looks for repeated groups of letters and counts the number of letters between the beginning of each repeated group. For instance, if the ciphertext were , the distance between groups is 10. The analyst records the distances for all repeated groups in the text.
|
|
The mode is susceptible to traffic analysis, replay and randomization attacks on sectors and 16-byte blocks. As a given sector is rewritten, attackers can collect fine-grained (16 byte) ciphertexts, which can be used for analysis or replay attacks (at a 16-byte granularity). It would be possible to define sector-wide block ciphers, unfortunately with degraded performance (see below).
|
|
A chosen-ciphertext attack (CCA) is an attack model for cryptanalysis where the cryptanalyst can gather information by obtaining the decryptions of chosen ciphertexts. From these pieces of information the adversary can attempt to recover the hidden secret key used for decryption. For formal definitions of security against chosen-ciphertext attacks, see for example: Michael Luby and Mihir Bellare et al.
|
|
The Feistel construction is also used in cryptographic algorithms other than block ciphers. For example, the optimal asymmetric encryption padding (OAEP) scheme uses a simple Feistel network to randomize ciphertexts in certain asymmetric key encryption schemes. A generalized Feistel algorithm can be used to create strong permutations on small domains of size not a power of two (see format-preserving encryption).
|
|
The friend then spent the next twenty years of his life trying to decode the messages, and was able to solve only one of them which gave details of the treasure buried and the general location of the treasure. The unnamed friend then published all three ciphertexts in a pamphlet which was advertised for sale in the 1880s. Since the publication of the pamphlet, a number of attempts have been made to decode the two remaining ciphertexts and to locate the treasure, but all efforts have resulted in failure. There are many arguments that the entire story is a hoax, including the 1980 article "A Dissenting Opinion" by cryptographer Jim Gillogly, and a 1982 scholarly analysis of the Beale Papers and their related story by Joe Nickell, using historical records that cast doubt on the existence of Thomas J. Beale.
|
|
Therefore, RSA is not plaintext aware: one way of generating a ciphertext without knowing the plaintext is to simply choose a random number modulo N. In fact, plaintext- awareness is a very strong property. Any cryptosystem that is semantically secure and is plaintext-aware is actually secure against a chosen-ciphertext attack, since any adversary that chooses ciphertexts would already know the plaintexts associated with them.
|
|
This attack, however, requires both chosen plaintexts and adaptive chosen ciphertexts, so is largely theoretical. Then in 2002, Biham, et al. applied differential-linear cryptanalysis, a purely chosen-plaintext attack, to break the cipher. The same team has also developed what they call a related-key boomerang attack, which distinguishes COCONUT98 from random using one related-key adaptive chosen plaintext and ciphertext quartet under two keys.
|
|
If we line up the plaintext with a 6-character keyword "" (6 does not divide into 20): crypto is short for cryptography. the first instance of "" lines up with "" and the second instance lines up with "". The two instances will encrypt to different ciphertexts and the Kasiski examination will reveal nothing. However, with a 5-character keyword "" (5 divides into 20): crypto is short for cryptography.
|
|
Differential cryptanalysis is usually a chosen plaintext attack, meaning that the attacker must be able to obtain ciphertexts for some set of plaintexts of their choosing. There are, however, extensions that would allow a known plaintext or even a ciphertext-only attack. The basic method uses pairs of plaintext related by a constant difference. Difference can be defined in several ways, but the eXclusive OR (XOR) operation is usual.
|
|
Designers of tamper-resistant cryptographic smart cards must be particularly cognizant of these attacks, as these devices may be completely under the control of an adversary, who can issue a large number of chosen-ciphertexts in an attempt to recover the hidden secret key. It was not clear at all whether public key cryptosystems can withstand the chosen ciphertext attack until the initial breakthrough work of Moni Naor and Moti Yung in 1990, which suggested a mode of dual encryption with integrity proof (now known as the "Naor-Yung" encryption paradigm). This work made understanding of the notion of security against chosen ciphertext attack much clearer than before and open the research direction of constructing systems with various protections against variants of the attack. When a cryptosystem is vulnerable to chosen-ciphertext attack, implementers must be careful to avoid situations in which an adversary might be able to decrypt chosen- ciphertexts (i.e.
|
|
Unpublished manuscript. Biryukov and Kushilevitz (1998) published an improved differential attack requiring only 16 chosen-plaintext pairs, and then demonstrated that it could be converted to a ciphertext-only attack using 212 ciphertexts, under reasonable assumptions about the redundancy of the plaintext (for example, ASCII-encoded English language). A ciphertext-only attack is devastating for a modern block cipher; as such, it is probably more prudent to use another algorithm for encrypting sensitive data.
|
|
The Goldwasser–Micali (GM) cryptosystem is an asymmetric key encryption algorithm developed by Shafi Goldwasser and Silvio Micali in 1982. GM has the distinction of being the first probabilistic public-key encryption scheme which is provably secure under standard cryptographic assumptions. However, it is not an efficient cryptosystem, as ciphertexts may be several hundred times larger than the initial plaintext. To prove the security properties of the cryptosystem, Goldwasser and Micali proposed the widely used definition of semantic security.
|
|
Secondly, BG is efficient in terms of storage, inducing a constant-size ciphertext expansion regardless of message length. BG is also relatively efficient in terms of computation, and fares well even in comparison with cryptosystems such as RSA (depending on message length and exponent choices). However, BG is highly vulnerable to adaptive chosen ciphertext attacks (see below). Because encryption is performed using a probabilistic algorithm, a given plaintext may produce very different ciphertexts each time it is encrypted.
|
|
Faster Bootstrapping with Polynomial Error. In CRYPTO 2014 (Springer) These techniques were further improved to develop efficient ring variants of the GSW cryptosystem: FHEW (2014) and TFHE (2016). The FHEW scheme was the first to show that by refreshing the ciphertexts after every single operation, it is possible to reduce the bootstrapping time to a fraction of a second. FHEW introduced a new method to compute Boolean gates on encrypted data that greatly simplifies bootstrapping, and implemented a variant of the bootstrapping procedure.
|
|
ElGamal encryption is probabilistic, meaning that a single plaintext can be encrypted to many possible ciphertexts, with the consequence that a general ElGamal encryption produces a 2:1 expansion in size from plaintext to ciphertext. Encryption under ElGamal requires two exponentiations; however, these exponentiations are independent of the message and can be computed ahead of time if need be. Decryption requires one exponentiation and one computation of a group inverse which can however be easily combined into just one exponentiation.
|
|
These ciphers can be broken with a brute force attack, that is by simply trying out all keys. Substitution ciphers can have a large key space, but are often susceptible to a frequency analysis, because for example frequent letters in the plaintext language correspond to frequent letters in the ciphertexts. Polyalphabetic ciphers such as the Vigenère cipher prevent a simple frequency analysis by using multiple substitutions. However, more advanced techniques such as the Kasiski examination can still be used to break these ciphers.
|
|
A cryptosystem that supports on ciphertexts is known as fully homomorphic encryption (FHE). Such a scheme enables the construction of programs for any desirable functionality, which can be run on encrypted inputs to produce an encryption of the result. Since such a program need never decrypt its inputs, it can be run by an untrusted party without revealing its inputs and internal state. Fully homomorphic cryptosystems have great practical implications in the outsourcing of private computations, for instance, in the context of cloud computing.
|
|
A general batch chosen-plaintext attack is carried out as follows : # The attacker may choose n plaintexts. (This parameter n is specified as part of the attack model, it may or may not be bounded.) # The attacker then sends these n plaintexts to the encryption oracle. # The encryption oracle will then encrypt the attacker's plaintexts and send them back to the attacker. # The attacker receives n ciphertexts back from the oracle, in such a way that the attacker knows which ciphertext corresponds to each plaintext.
|
|
The homomorphic properties of the encryption scheme enable the worker to obtain an encryption of the correct output wire. Finally, the worker returns the ciphertexts of the output to the client who decrypts them to compute the actual output y = F(x) or ⊥. The definition of the verifiable computation scheme states that the scheme should be both correct and secure. Scheme Correctness is achieved if the problem generation algorithm produces values that enable an honest worker to compute encoded output values that will verify successfully and correspond to the evaluation of F on those inputs.
|
|
A chosen-plaintext attack is more powerful than known- plaintext attack, because the attacker can directly target specific terms or patterns without having to wait for these to appear naturally, allowing faster gathering of data relevant to cryptanalysis. Therefore, any cipher that prevents chosen-plaintext attacks is also secure against known-plaintext and ciphertext-only attacks. However, a chosen-plaintext attack is less powerful than a chosen-ciphertext attack, where the attacker can obtain the plaintexts of arbitrary ciphertexts. A CCA-attacker can sometimes break a CPA-secure system.
|
|
In this attack the intruder intercepts the second message and replies to B using the two ciphertexts from message 2 in message 3. In the absence of any check to prevent it, M (or perhaps M,A,B) becomes the session key between A and B and is known to the intruder. Cole describes both the Gürgens and Peralta arity attack and another attack in his book Hackers Beware. In this the intruder intercepts the first message, removes the plaintext A,B and uses that as message 4 omitting messages 2 and 3.
|
|
The most efficient identity-based encryption schemes are currently based on bilinear pairings on elliptic curves, such as the Weil or Tate pairings. The first of these schemes was developed by Dan Boneh and Matthew K. Franklin (2001), and performs probabilistic encryption of arbitrary ciphertexts using an Elgamal-like approach. Though the Boneh-Franklin scheme is provably secure, the security proof rests on relatively new assumptions about the hardness of problems in certain elliptic curve groups. Another approach to identity-based encryption was proposed by Clifford Cocks in 2001.
|
|
Consequently, semantic security is now considered an insufficient condition for securing a general-purpose encryption scheme. Indistinguishability under Chosen Plaintext Attack (IND-CPA) is commonly defined by the following experiment: # A random pair (pk,sk) is generated by running Gen(1^n). # A probabilistic polynomial time-bounded adversary is given the public key pk , which it may use to generate any number of ciphertexts (within polynomial bounds). # The adversary generates two equal-length messages m_0 and m_1, and transmits them to a challenge oracle along with the public key.
|
|
The IV has to be non-repeating and, for some modes, random as well. The initialization vector is used to ensure distinct ciphertexts are produced even when the same plaintext is encrypted multiple times independently with the same key. Block ciphers may be capable of operating on more than one block size, but during transformation the block size is always fixed. Block cipher modes operate on whole blocks and require that the last part of the data be padded to a full block if it is smaller than the current block size.
|
|
A (full) adaptive chosen-ciphertext attack is an attack in which ciphertexts may be chosen adaptively before and after a challenge ciphertext is given to the attacker, with only the stipulation that the challenge ciphertext may not itself be queried. This is a stronger attack notion than the lunchtime attack, and is commonly referred to as a CCA2 attack, as compared to a CCA1 (lunchtime) attack. Few practical attacks are of this form. Rather, this model is important for its use in proofs of security against chosen-ciphertext attacks.
|
|
Ciphertext indistinguishability is a property of many encryption schemes. Intuitively, if a cryptosystem possesses the property of indistinguishability, then an adversary will be unable to distinguish pairs of ciphertexts based on the message they encrypt. The property of indistinguishability under chosen plaintext attack is considered a basic requirement for most provably secure public key cryptosystems, though some schemes also provide indistinguishability under chosen ciphertext attack and adaptive chosen ciphertext attack. Indistinguishability under chosen plaintext attack is equivalent to the property of semantic security, and many cryptographic proofs use these definitions interchangeably.
|
|
Probabilistic encryption is the use of randomness in an encryption algorithm, so that when encrypting the same message several times it will, in general, yield different ciphertexts. The term "probabilistic encryption" is typically used in reference to public key encryption algorithms; however various symmetric key encryption algorithms achieve a similar property (e.g., block ciphers when used in a chaining mode such as CBC), and stream ciphers such as Freestyle which are inherently random. To be semantically secure, that is, to hide even partial information about the plaintext, an encryption algorithm must be probabilistic.
|
|
OAEP satisfies the following two goals: #Add an element of randomness which can be used to convert a deterministic encryption scheme (e.g., traditional RSA) into a probabilistic scheme. #Prevent partial decryption of ciphertexts (or other information leakage) by ensuring that an adversary cannot recover any portion of the plaintext without being able to invert the trapdoor one-way permutation f. The original version of OAEP (Bellare/Rogaway, 1994) showed a form of "plaintext awareness" (which they claimed implies security against chosen ciphertext attack) in the random oracle model when OAEP is used with any trapdoor permutation.
|
|
To counter this problem, cryptographers proposed the notion of "randomized" or probabilistic encryption. Under these schemes, a given plaintext can encrypt to one of a very large set of possible ciphertexts, chosen randomly during the encryption process. Under sufficiently strong security guarantees the attacks proposed above become infeasible, as the adversary will be unable to correlate any two encryptions of the same message, or correlate a message to its ciphertext, even given access to the public encryption key. This guarantee is known as semantic security or ciphertext indistinguishability, and has several definitions depending on the assumed capabilities of the attacker (see semantic security).
|
|
From these two related ciphertexts, known to cryptanalysts as a depth, the veteran cryptanalyst Brigadier John Tiltman in the Research Section teased out the two plaintexts and hence the keystream. But even almost 4,000 characters of key was not enough for the team to figure out how the stream was being generated, it was just too complex and seemingly random. After three months, the Research Section handed the task to mathematician Bill Tutte. He applied a technique that he had been taught in his cryptographic training, of writing out the key by hand and looking for repetitions.
|
|
The attacker then computes the differences of the corresponding ciphertexts, hoping to detect statistical patterns in their distribution. The resulting pair of differences is called a differential. Their statistical properties depend upon the nature of the S-boxes used for encryption, so the attacker analyses differentials (ΔX, ΔY), where ΔY = S(X ⊕ ΔX) ⊕ S(X) (and ⊕ denotes exclusive or) for each such S-box S. In the basic attack, one particular ciphertext difference is expected to be especially frequent; in this way, the cipher can be distinguished from random. More sophisticated variations allow the key to be recovered faster than exhaustive search.
|
|
Firstly, the ranges of the encryption function under any two distinct keys are disjoint (with overwhelming probability). The second property says that it can be checked efficiently whether a given ciphertext has been encrypted under a given key. With these two properties the receiver, after obtaining the labels for all circuit-input wires, can evaluate each gate by first finding out which of the four ciphertexts has been encrypted with his label keys, and then decrypting to obtain the label of the output wire. This is done obliviously as all the receiver learns during the evaluation are encodings of the bits.
|
|
To avoid these problems, practical RSA implementations typically embed some form of structured, randomized padding into the value m before encrypting it. This padding ensures that m does not fall into the range of insecure plaintexts, and that a given message, once padded, will encrypt to one of a large number of different possible ciphertexts. Standards such as PKCS#1 have been carefully designed to securely pad messages prior to RSA encryption. Because these schemes pad the plaintext m with some number of additional bits, the size of the un-padded message M must be somewhat smaller.
|
|
Kocher described a new attack on RSA in 1995: if the attacker Eve knows Alice's hardware in sufficient detail and is able to measure the decryption times for several known ciphertexts, Eve can deduce the decryption key d quickly. This attack can also be applied against the RSA signature scheme. In 2003, Boneh and Brumley demonstrated a more practical attack capable of recovering RSA factorizations over a network connection (e.g., from a Secure Sockets Layer (SSL)-enabled webserver) This attack takes advantage of information leaked by the Chinese remainder theorem optimization used by many RSA implementations.
|
|
Probabilistic encryption is particularly important when using public key cryptography. Suppose that the adversary observes a ciphertext, and suspects that the plaintext is either "YES" or "NO", or has a hunch that the plaintext might be "ATTACK AT CALAIS". When a deterministic encryption algorithm is used, the adversary can simply try encrypting each of his guesses under the recipient's public key, and compare each result to the target ciphertext. To combat this attack, public key encryption schemes must incorporate an element of randomness, ensuring that each plaintext maps into one of a large number of possible ciphertexts.
|
|
A federal court dismissed the suit in Apple's favor. On March 21, 2016, a group of researchers from Johns Hopkins University published a report in which they demonstrated that an attacker in possession of iMessage ciphertexts could potentially decrypt photos and videos that had been sent via the service. The researchers published their findings after the vulnerability had been patched by Apple. On May 3, 2016, an independent open-source project named "PieMessage" was announced by app developer Eric Chee, consisting of code for OS X that communicates with iMessage and connects to an Android client, allowing the Android client to send and receive messages.
|
|
These attacks leave the intruder with the session key and may exclude one of the parties from the conversation. Boyd and Mao observe that the original description does not require that S check the plaintext A and B to be the same as the A and B in the two ciphertexts. This allows an intruder masquerading as B to intercept the first message, then send the second message to S constructing the second ciphertext using its own key and naming itself in the plaintext. The protocol ends with A sharing a session key with the intruder rather than B. Gürgens and Peralta describe another attack which they name an arity attack.
|
|
Geometric cryptography is an area of cryptology where messages and ciphertexts are represented by geometric quantities such as angles or intervals and where computations are performed by ruler and compass constructions. The difficulty or impossibility of solving certain geometric problems like trisection of an angle using ruler and compass only is the basis for the various protocols in geometric cryptography. This field of study was suggested by Mike Burmester, Ronald L. Rivest and Adi Shamir in 1996. Though the cryptographic methods based on geometry have practically no real life applications, they are of use as pedagogic tools for the elucidation of other more complex cryptographic protocols.
|
|
Integral cryptanalysis is a cryptanalytic attack that is particularly applicable to block ciphers based on substitution–permutation networks. Unlike differential cryptanalysis, which uses pairs of chosen plaintexts with a fixed XOR difference, integral cryptanalysis uses sets or even multisets of chosen plaintexts of which part is held constant and another part varies through all possibilities. For example, an attack might use 256 chosen plaintexts that have all but 8 of their bits the same, but all differ in those 8 bits. Such a set necessarily has an XOR sum of 0, and the XOR sums of the corresponding sets of ciphertexts provide information about the cipher's operation.
|
|
Forms of integral cryptanalysis have since been applied to a variety of ciphers, including Hierocrypt, IDEA, Camellia, Skipjack, MISTY1, MISTY2, SAFER++, KHAZAD, and FOX (now called IDEA NXT). Unlike differential cryptanalysis, which uses pairs of chosen plaintexts with a fixed XOR difference, integral cryptanalysis uses sets or even multisets of chosen plaintexts of which part is held constant and another part varies through all possibilities. For example, an attack might use 256 chosen plaintexts that have all but 8 of their bits the same, but all differ in those 8 bits. Such a set necessarily has an XOR sum of 0, and the XOR sums of the corresponding sets of ciphertexts provide information about the cipher's operation.
|
|
In cryptography, a ciphertext-only attack (COA) or known ciphertext attack is an attack model for cryptanalysis where the attacker is assumed to have access only to a set of ciphertexts. While the attacker has no channel providing access to the plaintext prior to encryption, in all practical ciphertext-only attacks, the attacker still has some knowledge of the plaintext. For instance, the attacker might know the language in which the plaintext is written or the expected statistical distribution of characters in the plaintext. Standard protocol data and messages are commonly part of the plaintext in many deployed systems and can usually be guessed or known efficiently as part of a ciphertext-only attack on these systems.
|
|
The key, which is given as one input to the cipher, defines the mapping between plaintext and ciphertext. If data of arbitrary length is to be encrypted, a simple strategy is to split the data into blocks each matching the cipher's block size, and encrypt each block separately using the same key. This method is not secure as equal plaintext blocks get transformed into equal ciphertexts, and a third party observing the encrypted data may easily determine its content even when not knowing the encryption key. To hide patterns in encrypted data while avoiding the re-issuing of a new key after each block cipher invocation, a method is needed to randomize the input data.
|
|
Herbivore divides a large anonymity network into smaller DC-net groups, enabling participants to evade disruption attempts by leaving a disrupted group and joining another group, until the participant finds a group free of disruptors. This evasion approach introduces the risk that an adversary who owns many nodes could selectively disrupt only groups the adversary has not completely compromised, thereby "herding" participants toward groups that may be functional precisely because they are completely compromised. Dissent implements several schemes to counter disruption. The original protocol used a verifiable cryptographic shuffle to form a DC-net transmission schedule and distribute "transmission assignments", allowing the correctness of subsequent DC-nets ciphertexts to be verified with a simple cryptographic hash check.
|
|
In the Paillier, ElGamal, and RSA cryptosystems, it is also possible to combine several ciphertexts together in a useful way to produce a related ciphertext. In Paillier, given only the public key and an encryption of m_1 and m_2, one can compute a valid encryption of their sum m_1+m_2. In ElGamal and in RSA, one can combine encryptions of m_1 and m_2 to obtain a valid encryption of their product m_1 m_2. Block ciphers in the cipher block chaining mode of operation, for example, are partly malleable: flipping a bit in a ciphertext block will completely mangle the plaintext it decrypts to, but will result in the same bit being flipped in the plaintext of the next block.
|
|
In the most basic form of key recovery through differential cryptanalysis, an attacker requests the ciphertexts for a large number of plaintext pairs, then assumes that the differential holds for at least r − 1 rounds, where r is the total number of rounds. The attacker then deduces which round keys (for the final round) are possible, assuming the difference between the blocks before the final round is fixed. When round keys are short, this can be achieved by simply exhaustively decrypting the ciphertext pairs one round with each possible round key. When one round key has been deemed a potential round key considerably more often than any other key, it is assumed to be the correct round key.
|
|
Indistinguishability under non- adaptive and adaptive Chosen Ciphertext Attack (IND-CCA1, IND-CCA2) uses a definition similar to that of IND-CPA. However, in addition to the public key (or encryption oracle, in the symmetric case), the adversary is given access to a decryption oracle which decrypts arbitrary ciphertexts at the adversary's request, returning the plaintext. In the non-adaptive definition, the adversary is allowed to query this oracle only up until it receives the challenge ciphertext. In the adaptive definition, the adversary may continue to query the decryption oracle even after it has received a challenge ciphertext, with the caveat that it may not pass the challenge ciphertext for decryption (otherwise, the definition would be trivial).
|
|
Adaptive-chosen-ciphertext attacks were perhaps considered to be a theoretical concern but not to be manifested in practice until 1998, when Daniel Bleichenbacher of Bell Laboratories (at the time) demonstrated a practical attack against systems using RSA encryption in concert with the PKCS#1 v1 encoding function, including a version of the Secure Socket Layer (SSL) protocol used by thousands of web servers at the time. The Bleichenbacher attacks, also known as the million message attack, took advantage of flaws within the PKCS #1 function to gradually reveal the content of an RSA encrypted message. Doing this requires sending several million test ciphertexts to the decryption device (e.g., SSL-equipped web server).
|
|
In 2008, an attack was published against a reduced 8-round version of Cryptomeria to discover the S-box in a chosen-key scenario. In a practical experiment, the attack succeeded in recovering parts of the S-box in 15 hours of CPU time, using 2 plaintext-ciphertext pairs. A paper by Julia Borghoff, Lars Knudsen, Gregor Leander and Krystian Matusiewicz in 2009 breaks the full-round cipher in three different scenarios; it presents a 224 time complexity attack to recover the S-box in a chosen-key scenario, a 248 boomerang attack to recover the key with a known S-box using 244 adaptively chosen plaintexts/ciphertexts, and a 253.5 attack when both the key and S-box are unknown.
|
|
Just as there are no proofs that integer factorization is computationally difficult, there are also no proofs that the RSA problem is similarly difficult. By the above method, the RSA problem is at least as easy as factoring, but it might well be easier. Indeed, there is strong evidence pointing to this conclusion: that a method to break the RSA method cannot be converted necessarily into a method for factoring large semiprimes. This is perhaps easiest to see by the sheer overkill of the factoring approach: the RSA problem asks us to decrypt one arbitrary ciphertext, whereas the factoring method reveals the private key: thus decrypting all arbitrary ciphertexts, and it also allows one to perform arbitrary RSA private-key encryptions.
|
|
The eight letters 'OUOSVAVV', framed by the letters 'DM' The Shugborough Inscription is a sequence of letters – O U O S V A V V, between the letters D M – carved on the 18th-century Shepherd's Monument in the grounds of Shugborough Hall in Staffordshire, England, below a mirror image of Nicolas Poussin's painting the Shepherds of Arcadia. It has never been satisfactorily explained, and has been called one of the world's top uncracked ciphertexts. In 1982, the authors of the pseudohistorical The Holy Blood and the Holy Grail suggested that Poussin was a member of the Priory of Sion, and that his Shepherds of Arcadia contained hidden meanings of great esoteric significance. The book makes a passing reference to the Shepherd's monument and the inscription, but offers no solution.
|
|
Indeed, even Roger Bacon knew about ciphers, and the estimated date for the manuscript roughly coincides with the birth of cryptography in Europe as a relatively systematic discipline. The counterargument is that almost all cipher systems consistent with that era fail to match what is seen in the Voynich manuscript. For example, simple substitution ciphers would be excluded because the distribution of letter frequencies does not resemble that of any known language; while the small number of different letter shapes used implies that nomenclator and homophonic ciphers would be ruled out, because these typically employ larger cipher alphabets. Polyalphabetic ciphers were invented by Alberti in the 1460s and included the later Vigenère cipher, but they usually yield ciphertexts where all cipher shapes occur with roughly equal probability, quite unlike the language-like letter distribution which the Voynich manuscript appears to have.
|
|
Though the simple DC-nets protocol uses binary digits as its transmission alphabet, and uses the XOR operator to combine cipher texts, the basic protocol generalizes to any alphabet and combining operator suitable for one-time pad encryption. This flexibility arises naturally from the fact that the secrets shared between the many pairs of participants are, in effect, merely one-time pads combined together symmetrically within a single DC-net round. One useful alternate choice of DC- nets alphabet and combining operator is to use a finite group suitable for public-key cryptography as the alphabet—such as a Schnorr group or elliptic curve—and to use the associated group operator as the DC-net combining operator. Such a choice of alphabet and operator makes it possible for clients to use zero-knowledge proof techniques to prove correctness properties about the DC-net ciphertexts that they produce, such as that the participant is not "jamming" the transmission channel, without compromising the anonymity offered by the DC-net.
|
|
An adaptive chosen-ciphertext attack (abbreviated as CCA2) is an interactive form of chosen-ciphertext attack in which an attacker first sends a number of ciphertexts to be decrypted chosen adaptively, then uses the results to distinguish a target ciphertext without consulting the oracle on the challenge ciphertext, in an adaptive attack the attacker is further allowed adaptive queries to be asked after the target is revealed (but the target query is disallowed). It is extensing the indifferent (non-adaptive) chosen-ciphertext attack (CCA1) where the second stage of adaptive queries is not allowed. Charles Rackoff and Dan Simon defined CCA2 and suggested a system building on the non-adaptive CCA1 definition and system of Moni Naor and Moti Yung (which was the first treatment of chosen ciphertext attack immunity of public key systems). In certain practical settings, the goal of this attack is to gradually reveal information about an encrypted message, or about the decryption key itself.
|
|