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On Public-key Steganography in the Presence of an Active Warden

On Public-key Steganography in the Presence of an Active Warden
On Public-key Steganography in the Presence of an Active Warden

On Public-key Steganography in the Presence of an Active

Warden

Scott Craver

Intel Corporation

Microcomputer Research Labs

2200Mission College Blvd.,Santa Clara,CA95052-8119

Department of Mathematical Sciences

Northern Illinois University

DeKalb,IL60115

Abstract.The so-called prisoners’problem,in which two individuals attempt to

communicate covertly without alerting a“warden”who controls the communications

channel,has taken a number of forms,adorned with various assumptions or require-

ments which make the problem more or less dif?cult.One assumption which makes

the problem considerably more managable is that the participants are allowed to share

some secret information(such as an encryption key)prior to imprisonment.Another

assumption,which makes the problem much more dif?cult,is that the warden be al-

lowed to modify messages sent between the prisoners as well as read them.This paper

describes techniques for pure steganography,in which no secret information needs to

be shared before imprisonment.First,a modi?cation of an existing protocol will be

shown to admit pure steganography if the warden is not allowed to modify the contents

of the channel.Then,a technique will be described that allows pure steganography be-

tween two prisoners in the presence in the presence of an active(content-modifying)

warden.

This technique is possible through the use of two distinct channels rather than one:the

subliminal channel for steganographic communication is augmented by a supralimi-

nal channel,one in which information is not hidden from the warden but cannot be

modi?ed.

1The prisoners’problem

The prisoners’problem was?rst posed by G.J.Simmons in1983,and is generally con-sidered to be the de facto model of covert communication.In this problem,two people, usually named Alice and Bob,are thrown in prison and intend to co-author an escape plan.The problem is that all communication between them is arbitrated by a warden,here named Wendy,who will place both parties in solitary con?nement at the?rst sign of any suspicious communication.Alice and Bob must trade inconspicuous-seeming transmissions which contain hidden information that,they hope,Wendy will not notice.

Using terminology agreed upon in[6],the inconspicuous data that is used to hide the real message is usually referred to as cover-data or cover-objects:a letter is often called a cover-text,for instance,while an image may be called a cover-image.The hidden or embedded message is placed therein,turning the cover-object into a stego-object.Alice’s and Bob’s goal,then,is to trade stego-objects without Wendy realizing that they are in fact stego-objects.

Fig.1.The prisoners’problem,illustrated

Further complications may hinder Alice’s and Bob’s escape.Wendy the warden may,in certain situations,be allowed to slightly modify messages as they are passed between the prisoners,to foil any hidden codes depending on the exact wording of the communication between them.In this case we call Wendy an active warden;without this ability she is considered a passive warden.One real-world example of an active warden is the censoring of telegrams by the United States government during World War II:the semantic content of telegrams could not be changed,but censors would slightly alter their exact wording, replacing words with close synonyms to foil possible secret codes[1].

It may be bene?cial at this point to describe some common variations of the prisoners’

problem.First,the warden’s power to alter the transmissions between the prisoners affects the dif?culty of the problem:

–A passive warden can do nothing but spy on the communications channel between the prisoners.

–An active warden is allowed to modify(slightly)the data being sent between the https://www.doczj.com/doc/387359843.html,d modi?cation of text which does not alter its semantic content(say,replacing words with close synonyms)is an example of an active warden being active.The active warden must not modify data so much that innocent communication would be foiled.–The case of a malicious warden is not often addressed.A malicious warden would be one who may alter the prisoners’messages with impunity,perhaps composing entire messages for one prisoner while pretending to be the other.In this environment the pris-oners can not hope to do much of anything!Fortunately,real-world situations prevent a warden from grossly altering the content of messages.Imagine the confusion if a large number of telegrams sent during World War II were altered in meaning,suppressed,or entirely fabricated by crafty censors on the lookout for spies!

As for the prisoners themselves,it should be pointed out that in the best case,they would not have to communicate prior to imprisonment,so as to(say)trade an encryption key.This best-case scenario,here called pure steganography,is very dif?cult to engineer. Current steganographic protocols generally assume that some information is shared between the prisoners prior to imprisonment.If this assumption was not allowed,little progress in information hiding could have been made to date.

The remainder of this paper is organized in the following fashion.In section2it will be shown how steganographers have managed to send information covertly in the presence of an active(and in some cases malicious)warden,provided that information such as secret and public keys can be traded beforehand.In section3,we will see how a protocol,described by Ross Anderson in[1],allows steganography in the presence of a passive warden with only one prisoner knowing the other’s public key.A modi?cation of this protocol will be shown to admit pure steganography in the presence of a passive warden.Finally,section4 will describe what are here called supraliminal channels,which allow pure steganography in the presence of an active warden.The paper will close with a discussion of the feasibility of supraliminal channels.

2Private-key steganography

Let us assume that Alice and Bob are allowed to share a secret key prior to imprisonment, or even to trade public keys.This gives them the opportunity not only to communicate covertly,but to defeat an active warden.In the former case,steganography consists merely of encrypting a message in such a way that the ciphertext appears statistically random,and embedding the bits of the text in a known subliminal channel.The embedded information, of course,must be made to have the same distribution as the channel noise in order to foil statistical tests.

In the presence of an active warden,it is not enough to embed a message in a known place.If Alice can subtly alter the bits in an image,it follows that Wendy could scramble those same bits with as little impact,erasing whatever was being sent via the subliminal channel.In this case it is possible to use what is referred to in[1]as a“selection channel.”

Essentially,the secret information shared between Alice and Bob is used to determine where the message is hidden.A cryptographically secure pseudo-random generator,seeded by a secret key,can be used to pick a subset of pixels in an image,for instance,to be used to conceal the data.If Wendy attempts to make subtle changes to the image,she may only be able to scramble a small percentage of the actual channel bits,since she doesn’t know exactly where they are.This scrambling can then be?xed using an error-correcting code.

The sharing of keys before imprisonment,however,is a requirement that we would ultimately like to see removed.It allows a great deal of freedom on the part of Alice and Bob —indeed,if they share public keys before imprisonment,they can even defeat a malicious warden by signing their secret messages to prevent impersonation—but it is not reassuring to think that if two people ever need to communicate covertly,they must know so far in advance that they can trade secret keys before a real-world“warden”starts listening in.

3Public-key steganography

3.1Boiling out the impurities

In public-key cryptography,it is not necessary for two people to share a secret key to estab-lish a secure channel.One only needs to know the the other’s public key.This suggests a possible approach to steganography in which a secret key does not have to be agreed upon by Alice and Bob prior to imprisonment.Some information must still be known a priori—one prisoner must know the other’s public key—but from a practical perspective this is a much more reasonable requirement.

A protocol which allows public-key steganography in the presence of a passive warden is described by Ross Anderson in[1].It relies on the fact that an encrypted message can be random enough to hide“in plain sight:”

1.Alice,knowing Bob’s public key,encrypts her message with it to obtain an apparently

meaningless ciphertext.

2.Alice embeds in a channel known to Bob(and,hence,to Wendy).The resulting

stego-object is sent to Bob.

3.Bob has no idea if any message is hidden in the channel or not,but we can assume that

the technique is standard enough that if he suspects a message,he will look for it.He retrieves a random-seeming string,attempts to decrypt it with his private key,and out pops Alice’s message.

One problem with this approach is that Bob has no idea if anything is being sent:he may not even know Alice,and certainly does not know if she intends to use a steganographic channel.If the two traded a private key before imprisonment,at least Bob would know that some secret transmission was pending.In this case,Bob will just have to suspect that a hidden message might be present in any cover object he receives.

This is not too serious a problem,however:it is already assumed(as it usually is in cryptography)that the information-hiding technique used by Alice is known to all,and standard enough that Wendy would suspect its use.Certainly Bob can,too.As long as hidden content is suspected and can be easily extracted by a known method if it does exist, it is not unfair to assume that it will be discovered.

A more practical,related problem is that in a large group of possible recipients every single recipient must suspect hidden content in each object.Only the intended recipient will ?nd it,of course;but in an environment such as a USENET newsgroup,where a large num-ber of people may send stego-objects,each of which may be targeted toward an unspeci?ed recipient,all the parties involved may spend the better part of each day looking inside every object.This is related to the previous problem,since it is the result of the message sender not being able to give the intended recipient any warning that a message is being sent.

3.2Pure steganography using the Anderson protocol

The assumption made above is not to be taken lightly,for it suggests that the protocol described in[1]is actually more powerful than may initially be suspected.If we can assume that Bob will attempt to decode what might or might not be a hidden message,then we can also assume(at least in the two-prisoner case)that Bob may attempt to participate in what might or might not be an ongoing steganography protocol.For example,suppose that Alice and Bob are astronomers residing on separate planets,each searching for signs of intelligent life in the universe.Bob receives from Alice’s planet what might be a message, or what might be noise.He may decide to treat the signal as if it were a message,send one back in the same“language,”and wait for a second signal to con?rm his suspicion.

In the context of steganography,the situation is complicated by the fact that the signals being traded must be meaningless to everyone but Alice and Bob.We can imagine that if the search for extra-terrestrial Alice ends up beaming a meaningful signal to the nearby warlike Wendy,Bob may give away that his planet is inhabitable and ripe for colonization. On the other hand,the situation is made less complicated by the cryptologic assumption that whatever data-hiding or encryption algorithm is used is known to all.

In any case,the possibility that Bob may participate in a protocol on suspicion of a steganographic message suggests a method by which Alice may send Bob her public key while they are both imprisoned,entirely eliminating the need for prior communication.A passive warden is still required for this to happen,but this too can be relaxed,as will be demonstrated in the next section.

Protocol1A modi?cation of the protocol described in[1]

This is essentially Anderson’s protocol with an extra step at the beginning.It is assumed that a method of information-hiding is known to all,as well as a public-key encryption algorithm.Wendy is assumed to be passive.

1.Alice generates a random public key/private key pair.If she is using RSA,for instance,

she could generate the large prime numbers used for the key by picking cryptographi-cally pseudo-random strings and testing for primality until one is found.She then selects another pseudo-random string for the public key.This is usually the way RSA keys are created.

2.Alice embeds the key in the subliminal channel,viewable by both Bob and Wendy,and

sends the resultant stego-object to Bob.Neither Bob nor Wendy can determine if the channel contains noise or a key.If Wendy can only snoop,then Bob can attempt to communicate:

3.Bob suspects that the data in question is a public key,uses it to encrypt a short note of

acknowledgement with a randomly chosen secret key for future covert transmissions, and sends this back to Alice embedded in a stego-object.

4.Alice suspects that the returned data is an encrypted key,decrypts it with her private key,

and out pops a message from Bob.Now the two can communicate by an appropriate secret-key protocol.

At no point in the protocol does Wendy have any idea that the randomness means any-thing:Alice alone can deduce content from Bob’s reply.As long as she is not allowed to insert her own information(and thus either foil the transmission or maliciously insert her own key to catch the two in the act),she can not conclude that communication has taken place.

If Wendy is capable of writing to the channel,then there is no way communication can take place:if Wendy does not utterly destroy the“in plain sight”bits,she can attempt a man-in-the-middle attack by overwriting Alice’s key with her own.A more malicious warden could entirely spoof either Alice’s or Bob’s response.In that case,however,the original protocol would not work either,since in neither case would Bob have any way of identifying the author of the original message.

4Public-key steganography in the presence of an active warden Cover-plots and Supraliminal Channels

If we assume that the Warden can only make minor modi?cations to the possible stego-objects sent between Alice and Bob,then we can assume that there is some amount of per-ceptually signi?cant information that the warden cannot change whatsoever.For instance,if Alice sends Bob a picture of a cow and Wendy can only modify1bit in every100,we can assume that Wendy will not be able to turn the cow into a pig.In a novel,there could be ex-plicit states of affairs or descriptions of characters so relevant to the plot that no information about those states can be changed without a signi?cant rewrite of a number of portions of the book.If we develop some formal encoding of object and state-of-affairs descriptions,we have the makings for a channel through which Alice can send a small amount of information to Bob out in the open,but with high integrity.What we are describing here is a supralimi-nal channel rather than a subliminal one:information is hidden in plain sight,so obviously, in fact,that it is impossible to modify without gross modi?cations to the transmitted object.

Formally,we can de?ne a cover-plot function,where is a set of pos-sible encodings of state-of-affairs descriptions,or“cover-plots”—so called because they can be considered the plot,or content,of a cover-object.A cover-plot is simply a formal description of content appropriate to the medium of the cover-object.Such a description could be used by an author or content-creator to compose a covertext containing an em-bedding of,and hence an embedding of the bit-string.The cover-plot function would have the following properties:

–The function would be known to both Bob and Alice(and hence we must assume that it is also known to Wendy).

–A member of the inverse image under of any particular bitstring is feasible to com-pute,as is itself.

–is onto.It is not necessary for to be one-to-one—indeed,if is many-to-one Alice’s job will be signi?cantly easier,since she will have more freedom in choosing a cover-object which embeds a particular bit-string.

–A cover-object can be created to contain a state-of-affairs description such that an active warden cannot signi?cantly change the encoding of(that is,she cannot change to such that)without making unreasonable,wide-sweeping changes to the entire cover-object.

–A human being(or,ideally,a computer program)can deduce the exact state-of-affairs description embedded within a cover-object.The composer of the covertext can fa-cilitate this deduction by making the embedding very clear,but this should not be so necessary that an object with an easy-to-interpret embedding is conspicuous.

–Clarifying the last property,an innocent cover-object without an explicitly embedded state-of-affairs description can yet be interpreted as having one.That is,innocent cover-objects should have clearly deducible cover-plot descriptions(which map under to random garbage)so that the presence of a clearly deducible cover-plot description is not indicative of a hidden message,unless the bit string possesses some meaning.

This can be summarized as a channel that is robust,blatant and inconspicuous.Here, a robust channel is one whose content cannot be altered without making unreasonably drastic changes to the stego-object(i.e.,requiring a malicious,instead of an active,warden).

A blatant channel is one whose content is publicly accessible,a necessity if Alice is to send Bob information when no key is shared between them prior to transmission.For a channel to be inconspicuous as well as blatant may sound like a contradiction,but it is not:an inconspicuous channel is one whose existence alone is not indicative of a hidden message.A perfectly innocent image,containing no covert information,will seem to the warden to contain random cover-plot bits.If Alice sends Bob a cover-object with an obvious message in this supraliminal channel(“Bob:here is the secret plan to break of out of jail. Love,Alice”)then Wendy can throw the two into solitary con?nement.However,if Alice sends Bob apparently random cover-plot bits,perhaps a random session key to be used later, Wendy cannot conclude that the message is anything other than innocent,since innocent messages also contain random cover-plot bits.Only when that key is later used can Wendy know that covert communication is taking place.

One cannot help but notice the connection to digital watermarking,a form of informa-tion hiding in which the hidden data is required to be robust to signi?cant modi?cation of an image.In particular,a recent approach to watermarking,advocated by Ingemar Cox,et al in [2],has resulted in robust watermarking schemes using what largely resembles a subliminal channel with supraliminal aspirations.Cox,et al emphasize the importance of hiding a wa-termark in perceptually signi?cant components of an image,such as high-magnitude DCT matrix coef?cients,so that an ownership label can survive a signi?cant amount of abuse by a forger.Further,the watermark can still be made invisible,as the technique presented in[2]demonstrates.One may wonder if a similar scheme would allow the embedding of a supraliminal channel invisibly in an existing image,so that Alice and Bob need not compose a new image for each message for the explicit purpose of embedding a particular string of cover-plot bits.

Unfortunately,conceptual differences between robust watermarking and embedding bits in a supraliminal channel prevent the application of one to the other.In the former case,some sort of secret key is often used to embed a watermark,so that only those who know the key

can detect or remove the watermark.A cover-plot,on the other hand,must be readable by all but removable by none.Also,the purpose of a supraliminal channel(and,indeed, steganography in general)is to hide a speci?c message of some meaning to the recipient;In the case of invisible watermarking,the embedded labels need not have any semantic content at all,or may be a function of the image.The scheme described in[2],for instance,embeds a vector of pseudo-random numbers picked from a normal distribution.In[3],it is discovered that in order for this scheme to become secure it may be necessary for the vector to be a function of a one-way hash of the image itself.In short,we have a difference of priorities: in watermarking,an ownership label can be meaningless,or picked to?t the cover-object, while the cover-object’s content is given beforehand and is important.In steganography, the image can be meaningless,or picked to?t the embedded message,while the hidden message’s content is given beforehand and is important.

Finally,if it was possible to embed a supraliminal channel in an existing image(for ex-ample)without signi?cantly altering it,it would be equally possible for a warden to scram-ble the channel without signi?cantly altering the image,since everybody knows where the information is and how to bury cover-plot bits inside.Hence the content of the cover-object should itself be a function of the information embedded within it.It may be hasty to declare it impossible for a supraliminal channel to be subliminal,but the two concepts seem to have irreconcilable differences.

Example1.A rudimentary supraliminal channel for audio/video clips

In this example,the cover-object may be an audio-video clip in which people are speak-ing.The noise within the clip could be used to embed a subliminal channel.The set of cover-plots is the set of all texts which can be spoken by Alice and unambiguously under-stood by Bob.The cover-plot function is computed by hashing the text of each suf?ciently long word,assigning each a numeric value.

For instance,suppose that each letter of the alphabet is assigned some agreed-upon numeric value.When an audio clip is received by Bob,he types into his computer all words of(say)at least six letters.For each word the computer calculates the product of the letters’numeric values,modulo some small prime.These values can then be arranged left-to-right and treated as the base-p representation of an integer.

Alice must be able to compose a convincing body of text which hashes to a desired array of values.She has some?exibility in that smaller words can be used with impunity to generate a context for the larger words.She can then use a dictionary(or,more likely,a thesaurus)which can be searched by cover-plot values.Notice that the larger the number of values to which a word can hash(the larger the value of in the above example),the harder Alice’s job will be,and the more conspicuous a cover-plot might be given a small amount of time to create one.On the other hand,if the number of possible hash values is made small, the ease in composition on Alice’s part is offset by a lower bandwidth.

Once this composition step is complete,Alice turns on a video camera and records herself(or other people)reciting the body of text she composed.

This channel is blatant,as long as the technique is made publicly available and the letters’numeric values are a known standard.The channel is inconspicuous,since every text

document,innocent or not,has a cover-plot.Finally,the channel is robust unless Wendy is capable of seamlessly altering both the sound of Alice’s voice and her lip movements so as to change the text of her speech.While this is possible with today’s technology,there exist real-world domains where Wendy does not possess the time to do this(say,where she has to monitor hundreds of such transmissions per day or per hour),or where the cost in time and computation is too high to justify the altering of video clips on the mere suspicion that their text may have some future steganographic signi?cance.Alternatively,she could completely re-record the message herself,hoping that Bob does not know what Alice looks or sounds like,but this would likely classify her as a malicious warden.

A formalized method for describing the plot,characters,etc.of a letter or book,or a describing the overall content of an image may also serve as good cover-plot functions;one could use details so central to a cover-object’s content that to change them would require signi?cant changes throughout the object.Perceptually signi?cant components of certain transforms of the cover-object may also do the trick,provided one can feasibly compose a cover-object when given particular transform components that it must contain.This could make Alice’s job much more dif?cult,but Bob’s would be so simple that it could be com-pletely automated.If a robust supraliminal channel can be entirely automated,requiring no (or negligible)human intervention in composing or interpreting a work,it could be quite a signi?cant contribution to the?eld of steganography.

Public-key steganography with a supraliminal channel

Of course,a supraliminal channel is not appropriate for subliminal communication between Alice and Bob,for a number of reasons.First,the bandwidth will likely be very small,since the channel is engineered to be highly robust.The number of deducible states-of-affairs may be larger for a novel than for an image or video clip,but in either case it is unlikely that a single object could hold a reasonably sized message.A robust channel of this kind is more appropriate for transmission of a session key,as it will be used below.

Secondly,it is expected that Wendy also knows how to compute,so any information passed through the channel is available to her.Unless the cover-plot bits have no apparent meaning,Alice and Bob are in serious trouble(or at least more serious than what previously got them thrown in prison).

With public-key cryptography,however,such a channel could be used to defeat an active https://www.doczj.com/doc/387359843.html,ually it is assumed that Alice and Bob share a secret key.With a supraliminal channel,however,a secret key can be exchanged covertly with no prior information,right in front of an active warden.The protocol is described below and in?gures2and3.

Protocol2Key exchange in the presence of an active warden

In this protocol,Alice and Bob have no information prior to imprisonment.It is assumed that a public-domain cover-plot algorithm(as well as this protocol)is known to all,including Wendy.Alice and Bob perform the following steps:

1.Alice generates a random public key and a private key.

2.Alice then?nds a cover-plot within the inverse image of.

Wendy

Bob Alice

1100110..possibly altered object Cover-Object (embedding)Fig.2.How a cover-plot function is used to establish a supralminal channel.

3.Alice composes a cover-object

containing an embedding of the cover-plot S,and sends this to Bob.At this point,Wendy can inspect the channel,and will ?nd a random-looking string of cover-plot bits.There is no reason to expect anything unless the data is later used in some way,say as a session key.The cover-plot bits pass unmolested through the channel to Bob.

4.Bob extracts the cover-plot bits,suspecting that they represent a public key.He cre-ates a pseudo-random secret key ,which he will later use to embed information in a

hide information in a

Wendy can see:The string E(r)Alice possesses:

Wendy can see:Bob now possesses:Her public key E

Her private key D The string E Alice’s public key E

Alice now possesses:

The session key r=D(E(r)

(Optionally) the message T Bob possesses:A session key r, used to

(optionally) A message T subliminal channel

Fig.3.Protocol using supraliminal and subliminal channels.Beneath each character is listed the in-formation he or she knows once the illustrated step has taken place.subliminal channel,and encrypts it with the purported public key to get a pseudo-random string Alice .He then ?nds a cover-plot ,and creates a cover-object containing an embedding of .5.

Bob now uses his secret key to securely embed a message in the subliminal channel of the image,using an existing secret-key-based technique which the active warden cannot defeat.If the medium used to implement the supraliminal channel is not rich enough to support a subliminal channel,Alice and Bob can always postpone this step and embed their secret messages in the subliminal channels of subsequent cover-objects.6.

Bob sends to Alice.Now,Wendy can again snoop the channel,and now has (what she might suspect is)both and .Even if she does suspect this,there is no indi-cation that the strings are related in this way,and no way she can determine the value of ,and thus no way she can determine the existence of any subliminal message.Fur-ther,both strings are random-seeming enough that there is no indication that any covert communication is occurring.She sends the message through the channel to Alice.7.

Alice decrypts what she assumes to be to get ,and,optionally,snoops the subliminal channel using the secret key to ?nd a message.8.Alice and Bob now communicate with impunity using a secure secret-key based scheme,with the random key that they now both share.Wendy has no reason to suspect that a key exchange has occurred.

Statistical tests on the cover-plot bits may yield some deviation from what would be

expected in an innocent object.However,the strings Alice and Bob share are already the product of cryptographically secure pseudo-random generators,and if the cover-plot bits of a certain medium typically fall into a non-uniform distribution,the bits can always be encoded in a manner that matches this distribution.Further,the strings transmitted via this channel are very short,and only two transmissions are needed to share a key.This may make statistical tests dif?cult.

5Are supraliminal channels“fair?”

There are a number of possible objections that may be made to the protocols presented here.First,just how fair is it to assume that the warden is not malicious?Why not imper-sonate Alice or Bob,or grossly modify their work for the purpose of foiling the possible covert communication?After all,Bob has no idea what cover-object to expect from Al-ice.He would not necessarily know if Wendy completely changed the transmitted object to something else.

The reason why Wendy can not be malicious in real-world situations is quite clear,but is sometimes forgotten when we focus entirely on the situation of two prisoners whose very names indicate that they intend to communicate covertly.A real-world warden,be she a postal censor or a system administrator,may deal with communications between a large number of people.At best she can suspect that trading of secret information is taking place,and may not be sure where or between whom.To signi?cantly alter the meaning of large number of e-mail documents or telegrams is simply unacceptible behavior.Even if the recipients of those documents have no idea what content to expect,all subsequent communication would either give away the ruse or need to be intercepted and modi?ed as well.David Kahn in[5]describes the concept of a“semagram,”a secret communication not in written form:

For example,during World War2,censors intercepted a shipment of watches.Fear-ing that the position of the hands of the watches could be spelling out a secret message,they changed the position of the hands.

If no secret message existed in those watch-hands,the recipient would likely not care about the modi?cation.On the other hand,if the recipient ultimately recieved a shipment of radial tires instead of watches,he or she would have legitimate reason to complain,as would everyone else who received a package subjected to a similar censoring methodology. Even if the recipient had no idea what content to expect,the resulting“thank you”note would be confusing indeed.Unless the United States could intercept all future transmissions from the recipient which allude to the shipment’s content,the censorship will ultimately be discovered.In any case,such wide-scale modi?cation of potentially innocent content is unreasonable.As Einstein may have put it,“Raf?niert ist der V orsteher,aber boshaft ist er nicht.”

The big question-marks,however,regard the very feasibility of the supraliminal channel: can it be done ef?ciently?Further,is it fair to allow the cover-object to be a function of the information being sent?It is often assumed that the cover-object is given,and any message

could be inserted therein.But the cover-object is assumed to be meaningless to Alice and Bob anyway,a mere front for the real message;we might as well use the opportunity to hide actual content.

Ef?ciency is the real problem,in this author’s opinion.Cover-plot functions mapping plot descriptions of stories or other high-level content would probably require a human being to perform both the composition and interpretation steps,and quite possibly the generation step as well(see?gure2.)One could develop a scheme which makes the interpretation step easy enough for a computer to manage,but in order to automate the entire process it may not help to turn a cryptographic problem into an arti?cial intelligence problem.If a supraliminal channel could be based on perceptually signi?cant information that a computer is suited to both interpret and convincingly compose,this hurdle would seem much less daunting.

6Conclusion

The prisoners’problem exists in many variations,often assuming that the prisoners share some information prior to imprisonment.Pure steganography,without any a priori secret knowledge between the communicating parties,is very dif?cult,but not necessarily impos-sible:a public-key steganography protocol has been described in[1]which requires only that one party’s public key be known to the other.Furthermore,certain assumptions allow this protocol to be modi?ed so as to allow pure steganography in the presence of a passive warden.Finally,if a supraliminal channel as described in this paper can be feasibly imple-mented,secret key exchange and hence pure steganography can take place in the presence of an active warden.

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tomorrowmorning明天早晨 allday/morning/night整天/整个早晨/整晚(等于thewholeday/morning/night)mostofthetime(在)大多数时间 3、一般规则 除了前两点特殊用法之外,其他≤一天,用on,>一天用in,在具体时刻或在某时用at(不强调时间范围) 关于 On 1 2) 3) (注意:节日里有表人的词汇先复数再加s’所有格,如 onChildren’sDay,onWomen’sDay,onTeachers’Day有四个节日强调单数之意思,onMother’sDay,onFather’sDay,onAprilFool’sDay,onValentine’sDay) 星期、onSunday在周日,onSundaymorning在周日早晨onthelastFridayofeachmonth在每个月的最后一个星期五

日期、onJune2nd在六月二日 onthesecond(ofJune2nd)在六月的第二天即在六月二日onthemorningofJune2nd在六月二日的早晨,onarainymorning在一个多雨的早晨 onacertainday在某天 onthesecondday在第二天(以过去某天为参照) 关于 In 1 2) InJune在六月 inJune,2010在2010年六月 in2010在2010年 inamonth/year在一个月/年里(在将来时里翻译成一个月/年之后) inspring在春天

微课的类型介绍

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结语: 但在实际微课的设计与拍摄时,老师还得根据课程的性质、教学的要求、学校的实际硬件条件及自身的技术能力来选择微课的类型,只有这样,微课才能真正与课堂教学相结合,并能通过翻转课堂教学来提升课程教学的质量。 创作编号:BG7531400019813488897SX 创作者:别如克*

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inonat的时间用法和地点用法版

i n o n a t的时间用法和 地点用法版 集团档案编码:[YTTR-YTPT28-YTNTL98-UYTYNN08]

i n,o n,a t的时间用法和地点用法 一、in,on,at的时间用法 1、固定短语: inthemorning/afternoon/evening在早晨/下午/傍晚, atnoon/night在中午/夜晚,(不强调范围,强调的话用duringthenight)earlyinthemorning=intheearlymorning在大清早, lateatnight在深夜 ontheweekend在周末(英式用attheweekend在周末,atweekends每逢周末)onweekdays/weekends在工作日/周末, onschooldays/nights在上学日/上学的当天晚上, 2、不加介词 this,that,last,next,every,one,yesterday,today,tomorrow,tonight,all,most等之前一般不加介词。如, thismorning今天早晨 (on)thatday在那天(thatday更常用些) lastweek上周 nextyear明年 thenextmonth第二个月(以过去为起点的第二个月,nextmonth以现在为起点的下个月) everyday每天 onemorning一天早晨 yesterdayafternoon昨天下午 tomorrowmorning明天早晨

allday/morning/night整天/整个早晨/整晚(等于 thewholeday/morning/night) mostofthetime(在)大多数时间 3、一般规则 除了前两点特殊用法之外,其他≤一天,用on,>一天用in,在具体时刻或在某时用at(不强调时间范围) 关于on On指时间表示: 1)具体的时日和一个特定的时间,如某日,某节日,星期几等。Hewillcometomeetusonourarrival. OnMay4th(OnSunday,OnNewYear’sday,OnChristmasDay),therewillbeacelebra tion. 2)在某个特定的早晨,下午或晚上。 Hearrivedat10o’clocko nthenightofthe5th. Hediedontheeveofvictory. 3)准时,按时。 Iftherainshouldbeontime,Ishouldreachhomebeforedark. 生日、onmyninthbirthday在我九岁生日那天 节日、onTeachers’Day在教师节 (注意:节日里有表人的词汇先复数再加s’所有格,如 onChildren’sDay,onWomen’sDay,onTeachers’Day有四个节日强调单数之意思, onMother’sDay,onFather’sDay,onAprilFool’sDay,onValentine’sDay)星期、onSunday在周日,onSundaymorning在周日早晨

(完整版)微课亮点介绍

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精华版+in,+at,+on表时间的用法

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引号“”‘’括号[] 破折号——省略号……书名号 着重号· 间隔号· 连接号— 专名号____ 备注占两格左上角

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位置,它们的前一半可以放在一行的开头,但不出现在一行的末尾,后一半不出现在一行的开头。 破折号和省略号都占两个字的位置,可以放在一行的开头,也可以放在一行的末尾,但不可以把一个符号分成两段。这两种符号的位置都写在行次中间。) 引用之语未独立,标点符号引号外;引用之语能独立,标点符号引号里。 注意事项: 冒号 表示提示性话语之后的停顿,用来提引下文。 ①同志们,朋友们:现在开会了。 ②他十分惊讶地说:“啊,原来是你!” ③北京紫禁城有四座城门:午门、神武门、东华门和西华门。 注意:“某某说”在引语前,用冒号;在引语中或引语后,则不用冒号。如: ⑴老师说:“李白是唐代的大诗人,中学课本有不少李白的诗。” ⑵“李白是唐代的大诗人,”老师说,“中学课本里有不少李白的诗。” ⑶“李白是唐代的大诗人,中学课本里有不少李白的诗。”老师说。

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