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Invisible ink



 
 
Invisible ink is a substance used for writing, which is either invisible on application or soon thereafter, and which later on can be made visible by some means. Invisible ink is one form of steganography
Steganography

Steganography is the art and science of writing hidden messages in such a way that no-one apart from the sender and intended recipient suspects the existence of the message, a form of security through obscurity....
 and it has been used in espionage
Espionage

Espionage or spying involves an individual obtaining information that is considered secrecy or confidential without the permission of the holder of the information....
. Other uses include anti-counterfeit
Counterfeit

A counterfeit is an imitation made usually with the intent to deceptively represent its content or origins, thus increasing sales appeal due to the reputation of the imitated product....
ing, property marking, hand stamping for readmission, children's games, and marking for the purpose of identification in manufacturing.

Application and use
Invisible ink is applied to a writing surface with a specialty purpose stylus
Stylus

A stylus is a writing utensil. The word is also used for a computer accessory . It usually refers to a narrow elongated staff, similar to a modern ballpoint pen....
, stamp
Stamp

A stamp is a distinctive mark or impression made upon an object, for instance those made on a piece of paper and used to indicate the prepayment of a fee or tax....
, fountain pen
Fountain pen

A fountain pen is a pen that contains a reservoir of water-based liquid Fountain pen inks. If it uses ink cartridges instead of having a built-in ink reservoir, it is often called cartridge pen....
, toothpick
Toothpick

A toothpick is a small stick of wood, plastic, bamboo, metal or other substance used to remove detritus from the teeth, usually after a meal. A toothpick usually has one or two sharp ends to insert between teeth....
 or even a finger dipped in the liquid.






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Encyclopedia


Invisible ink is a substance used for writing, which is either invisible on application or soon thereafter, and which later on can be made visible by some means. Invisible ink is one form of steganography
Steganography

Steganography is the art and science of writing hidden messages in such a way that no-one apart from the sender and intended recipient suspects the existence of the message, a form of security through obscurity....
 and it has been used in espionage
Espionage

Espionage or spying involves an individual obtaining information that is considered secrecy or confidential without the permission of the holder of the information....
. Other uses include anti-counterfeit
Counterfeit

A counterfeit is an imitation made usually with the intent to deceptively represent its content or origins, thus increasing sales appeal due to the reputation of the imitated product....
ing, property marking, hand stamping for readmission, children's games, and marking for the purpose of identification in manufacturing.

Application and use


Invisible ink is applied to a writing surface with a specialty purpose stylus
Stylus

A stylus is a writing utensil. The word is also used for a computer accessory . It usually refers to a narrow elongated staff, similar to a modern ballpoint pen....
, stamp
Stamp

A stamp is a distinctive mark or impression made upon an object, for instance those made on a piece of paper and used to indicate the prepayment of a fee or tax....
, fountain pen
Fountain pen

A fountain pen is a pen that contains a reservoir of water-based liquid Fountain pen inks. If it uses ink cartridges instead of having a built-in ink reservoir, it is often called cartridge pen....
, toothpick
Toothpick

A toothpick is a small stick of wood, plastic, bamboo, metal or other substance used to remove detritus from the teeth, usually after a meal. A toothpick usually has one or two sharp ends to insert between teeth....
 or even a finger dipped in the liquid. Once dry the written surface should appear blank, and of a similar texture and reflectivity as the surrounding surface. With letters, a cover message should be written over the invisible message, as a blank sheet of paper might arouse suspicion that an invisible message is present. This is best done with a ballpoint pen, since fountain pen ink may 'run' when it crosses a line of invisible ink, thus betraying the presence of invisible ink. Invisible ink should not be used on ruled paper as it may similarly alter or streak the colour of the lines.

The ink is later made visible by different methods according to the type of invisible ink used. The ink may be developed by heat or by application of an appropriate chemical, or it may be made visible by viewing under ultraviolet light. Inks which are developed by a chemical reaction
Chemical reaction

A chemical reaction is a process that always results in the interconversion of chemical substances. The substance or substances initially involved in a chemical reaction are called reactants....
 may depend on an acid-base reaction (like litmus paper), reactions similar to the blueprint
Blueprint

A blueprint is a type of paper-based reproduction usually of a technical drawing, documenting an architecture or an engineering design. More generally, the term "blueprint" has come to be used to refer to any detailed plan....
 process, or any of hundreds of others. Developer fluids may be applied using a spray bottle, but some developers are in the form of vapours, e.g. ammonia
Ammonia

Ammonia is a chemical compound with the chemical formula nitrogenhydrogen. It is normally encountered as a gas with a characteristic pungent odor....
 fumes used to develop phenolphthalein
Phenolphthalein

Phenolphthalein is a chemical compound with the chemical formula carbon20hydrogen14oxygen4 . Often used in titrations, it turns colorless in acidic solutions and pink in base solutions....
 ink.

One can obtain toy invisible ink pens which have two tips—one tip for invisible ink writing, and another tip for developing the ink. Also, invisible ink is sometimes used to print parts of pictures or text in book
Book

A book is a set or collection of written, printed, illustrated, or blank sheets, made of paper, parchment, or other material, usually fastened together to hinge at one side....
s for children to play with, particularly while they are travelling. A "decoder pen
Decoder pen

The decoder pen, yes-no pen, yes-know pen or magic pen book is a combination of decoder pen or marker pen specially designed to reveal invisible ink-encoded pictures or writing, in the form of answers to questions or hidden parts of pictures, with specially created children's books with hidden words and pictures....
" is included with these books and children may rub this pen over invisible parts of texts or pictures, thus revealing answers to questions printed in regular ink or completing missing parts of pictures.

Security
Security

Security is the degree of protection against danger, loss, and criminals. Individuals or actions that encroach upon the condition of protection are responsible for a "breach of security."...
 marker pen
Marker pen

A marker pen, marking pen, felt-tip pen, or marker, is a pen which has its own ink-source, and usually a tip made of a porous material, such as felt or nylon....
s with fluorescent ink that glows when illuminated with a UV light may be used to invisibly mark valuable household items in case of burglary
Burglary

Burglary is a crime the essence of which is entry into a building for the purposes of committing an offence. Usually that offence will be theft, but most jurisdictions specify others which fall within the ambit of burglary....
. They may be especially formulated for writing on non-porous surfaces such as glass, plastics, etc. The inks are applied and then identified using a black light or other UV light source. The owner of a recovered, stolen item which has been marked in this way can be traced simply by using an ultraviolet lamp. Security marker pens can be obtained commercially and are widely used as a crime countermeasure.

Some commercially available invisible inks glow very brightly, in a variety of colours, under UV light. This makes them suitable for use in readmissions such as hand stamping.

There is a commercially available red invisible ink which is only invisible when applied to certain types of surfaces, but visible on others.

Some vendors now offer invisible ink for use in computer inkjet printer
Inkjet printer

File:Canon BJ-10v Lite inkjet printer with Scale.JPGInkjet printers operate by propelling variably-sized droplets of liquid or molten material onto almost any sized page....
s. Such inks are usually visible under ultraviolet light. Typical uses include printing information on business forms for use by the form processor, without cluttering up the visible contents of the form. For example, some United States Postal Service
United States Postal Service

The United States Postal Service is an Independent agencies of the United States government responsible for providing postal service in the United States....
 mail sorting stations use UV-visible ink to print bar codes on mailed envelopes giving routing information for use by mail handling equipment further down the line before delivery.

Very rarely, invisible ink has been used in art. It is usually developed, though not always. There are artists who use the effect in conjunction with invisible and other reactive inks and paints to create a variety of effects when used in conjunction with UV lights.

An E2E
End-to-end auditable voting systems

End-to-end auditable or end-to-end voter verifiable systems are voting systems with stringent integrity properties and strong tamper-resistance....
 voting system called Scantegrity II uses invisible ink to enable the voter to obtain a confirmation code only for the voted selection.

Properties of an "ideal" invisible ink


What is an "ideal" invisible ink depends on its intended use. For example, property marking should ideally be done with ink easily read under ultraviolet light, whereas in espionage such an ink would be considered too easily detectable since a large number of letters may be screened relatively quickly using UV light.

Invisible inks are inherently "insecure" against a determined and well-equipped inspector, which must be balanced against the logistical difficulty in carrying out mass-screening of posted mail. It is easier to perform large-scale
ECHELON

ECHELON is a name used in global media and in popular culture to describe a signals intelligence collection and analysis network operated on behalf of the five signatory states to the UK-USA Security Agreement ....
 undetected screening of millions of electronic communications, than to mass-screen even a small fraction of conventional mail. Apart from in dictatorships where large numbers of personnel are employed to spy on fellow nationals, screening of posted mail is only feasible in particular situations, such as letters to and from a particular suspect or facility.

The World War II SOE
Special Operations Executive

The Special Operations Executive , was a United Kingdom World War II organisation. It was initiated by Winston Churchill and Hugh Dalton in July 1940, to conduct warfare by means other than direct military engagement....
 training manual identified the following properties of an "ideal" invisible ink:

  1. Very water soluble, i.e. non-greasy.
  2. Non-volatile, i.e. no pronounced smell.
  3. Not depositing crystals on paper, i.e. not easily seen in glancing light.
  4. Invisible under ultraviolet light.
  5. Does not decompose or discolour the paper e.g. not silver nitrate.
  6. Unreactive with iodine, or with any of the other usual developers.
  7. Potential developers for the ink should be as few as possible.
  8. Should not develop under heat.
  9. Easily obtainable and has at least one plausible innocent use by the holder.
  10. Not a compound of several chemicals, as this would violate "7".


From practical experience "6" and "9" were usually incompatible. SOE
Special Operations Executive

The Special Operations Executive , was a United Kingdom World War II organisation. It was initiated by Winston Churchill and Hugh Dalton in July 1940, to conduct warfare by means other than direct military engagement....
 agents were trained not to risk their lives through reliance on insecure inks, most of which were of World War I vintage. It was known to supply special inks to its field agents, rather than have them depend upon improvisation from obtainable everyday chemicals. When agents were forced to improvise, they were to dilute their invisible ink as much as possible to reduce chances of detection.

Screening letters for secret messages


Any invisible ink can be made visible by someone who is sufficiently determined, but the limitation is generally time available and the fact that one cannot apply hours of effort to every single piece of paper. Thus successful use of invisible ink depends on not arousing suspicion that invisible ink may be present.

Telltale signs of invisible ink, such as pen scratches from a sharp pen, roughness or changed reflectivity of the paper (either more dull or more shiny, usually from using undiluted ink) can be obvious to a careful observer who simply makes use of strong light, a magnifying glass and their nose. Also, key words in the visible letter, such as 'red cabbage' or 'heat', in an odd context may alert a censor to the presence of invisible ink. Invisible ink should not be used with glossy or very smooth paper types, since the sizing
Sizing

Sizing or size is a substance that is applied to materials as a protecting glaze, filler, or lubricant. It is used to change surface properties in papermaking, gilding, and the manufacture of textiles and fiberglass....
 of these papers prevents ink from being absorbed deep into the paper and it is easily visible, especially if the paper is examined under glancing light. There are, however, commercially available inks for non-porous surfaces that are only visible under ultraviolet light and are otherwise virtually invisible on such surfaces.

Using either ultraviolet light or an iodine fume cupboard, messages can be quickly screened for invisible ink and also read without first permanently developing the invisible ink. Thus, if a censor uses this method to intercept messages, he may then let the letter be sent to the intended recipient who will be unaware that the secret message has already been intercepted by a third party.

A "screening station" could theoretically involve visual and olfactory inspection, an examination under ultraviolet light and then the heating of all objects in an oven before finally trying exposure to iodine fumes. In theory, some invisible inks may even show up using a camera sensitive to the infrared light
Infrared

Infrared radiation is electromagnetic radiation whose wavelength is longer than that of visible light , but shorter than that of terahertz radiation and microwaves ....
 spectrum.

Invisible ink types


For practical reasons, the inks are listed here according to their method of development. It must be understood however that some inks - particularly those of organic origin or those consisting of a mixture of several chemicals - may be made visible by several methods. For example, invisible writing with soap water may be made visible either by heat, reaction with phenolphthalein, viewing under ultraviolet light, or by placing the page inside an iodine fume cupboard.

Inks developed by heat


Some of these are organic substances that oxidize when heated, which usually turns them brown. For this type of 'heat fixed' ink, any acidic fluid will work. The most secure way to use any of the following substances for invisible ink is by dilution, usually with water, close to the point when they become difficult to develop.

  • Cola drink
  • Honey solution
  • Lemon, apple, orange or onion juice
  • Milk
  • Bodily fluids such as urine, semen, saliva or blood serum
    Serum

    Serum may refer to:*Blood plasma, with clotting factors removed*Antiserum, for transfer of passive immunity*Serous fluid, any clear bodily fluid...
    .
  • Soap water
  • Sugar solution
  • Wine, or vinegar
  • Cobalt chloride, which turns blue when heated and becomes invisible again after a while (if not overly heated)


The writing is rendered visible by heating
Heating

Heating may refer to:*HVAC: Heating, ventilation and air-conditioningHeating devices, or systems:*Block heater, or headbolt heater, an electric heater that heats the engine of a car to ease starting in cold weather...
 the paper, either on a radiator
Radiator

Radiators are heat exchangers used to transfer thermal energy from one medium to another for the purpose of cooling and heating. The majority of radiators are constructed to function in automobiles, buildings, and electronics....
, by ironing
Ironing

File:Bundesarchiv B 145 Bild-F001163-0012, K?ln, Textilfabrik Bierbaum-Proenen.jpgIroning or smoothing is the work of using a heated tool, or tools, to remove wrinkles from fabric....
 it, or by placing it in an oven
Oven

An oven is an enclosed compartment for heating, baking or drying. It is most commonly used in cooking and pottery. Ovens used in pottery are also known as kilns....
. A 100-Watt light bulb is less likely to damage the paper.

Inks developed by chemical reaction


In most cases, the substance changes color when mixed with an acid or base.

  • Phenolphthalein
    Phenolphthalein

    Phenolphthalein is a chemical compound with the chemical formula carbon20hydrogen14oxygen4 . Often used in titrations, it turns colorless in acidic solutions and pink in base solutions....
    , commonly used as a pH
    PH

    pH is a measure of the Acid or Base of a solution. It is defined as the cologarithm of the Activity of dissolved hydrogen ions . Hydrogen ion activity coefficients cannot be measured experimentally, so they are based on theoretical calculations....
     indicator, turns pink in the presence of a base such as ammonia fumes
    Ammonia

    Ammonia is a chemical compound with the chemical formula nitrogenhydrogen. It is normally encountered as a gas with a characteristic pungent odor....
     or sodium carbonate
    Sodium carbonate

    Sodium carbonate , , is a sodium salt of carbonic acid. It most commonly occurs as a crystalline heptahydrate, which readily efflorescence to form a white powder, the monohydrate....
    .
  • Vinegar
    Vinegar

    Vinegar is an acidic liquid processed from the fermentation of ethanol in a process that yields its key ingredient, acetic acid . It also may come in a diluted form....
    , is revealed by . Vinegar contains acetic acid
    Acetic acid

    Acetic acid, CH3COOH, also known as ethanoic acid, is an organic acid which gives vinegar its sour taste and pungent smell. Pure, water-free acetic acid is a colourless liquid that absorbs water from the environment , and freezes at 16.7 Celsius to a colourless crystalline solid....
     that affects the pH indicator in red cabbage water. Vinegar may also be developed by heat, as above.
  • Ammonia
    Ammonia

    Ammonia is a chemical compound with the chemical formula nitrogenhydrogen. It is normally encountered as a gas with a characteristic pungent odor....
    , developed by red cabbage water.
  • Copper sulfate, developed by sodium iodide
    Sodium iodide

    Sodium iodide is a white, crystalline salt with chemical formula SodiumIodine used in radiation detection, treatment of iodine deficiency, and as a reactant in the Finkelstein reaction....
    , sodium carbonate
    Sodium carbonate

    Sodium carbonate , , is a sodium salt of carbonic acid. It most commonly occurs as a crystalline heptahydrate, which readily efflorescence to form a white powder, the monohydrate....
      ammonium hydroxide
    Ammonium hydroxide

    Ammonium hydroxide, also known as ammonia water, ammonical liquor, ammonia liquor, aqua ammonia, or aqueous ammonia, is a solution of ammonia in water....
     or potassium ferricyanide
    Potassium ferricyanide

    Potassium ferricyanide is the chemical compound with the formula K3[Fe6]. This bright red salt consists of the coordination compound ferricyanide....
    .
  • Lead(II) nitrate
    Lead(II) nitrate

    Lead nitrate is an inorganic compound with the chemical formula lead2. It commonly occurs as a colourless crystal or white powder and, unlike most other lead salt , is solubility in water ....
    , developed by sodium iodide
    Sodium iodide

    Sodium iodide is a white, crystalline salt with chemical formula SodiumIodine used in radiation detection, treatment of iodine deficiency, and as a reactant in the Finkelstein reaction....
    .
  • Iron sulfate
    Iron sulfate

    Iron sulfate may refer to:*Ferrous sulfate, Iron sulfate, FeSO4*Ferric sulfate, Iron sulfate, Fe23...
    , developed by sodium carbonate
    Sodium carbonate

    Sodium carbonate , , is a sodium salt of carbonic acid. It most commonly occurs as a crystalline heptahydrate, which readily efflorescence to form a white powder, the monohydrate....
     or potassium ferricyanate.
  • Cobalt chloride, developed by potassium ferricyanide
    Potassium ferricyanide

    Potassium ferricyanide is the chemical compound with the formula K3[Fe6]. This bright red salt consists of the coordination compound ferricyanide....
    .
  • Iron sulfate
    Iron sulfate

    Iron sulfate may refer to:*Ferrous sulfate, Iron sulfate, FeSO4*Ferric sulfate, Iron sulfate, Fe23...
    , developed by sodium sulfide
    Sodium sulfide

    Sodium sulfide is the name used to refer to the chemical compound Na2S but more commonly its hydrate Na2S.9H2O....
    .
  • Starch
    Starch

    File:Amylose2.svgFile:Amylopektin Sessel.svgStarch or amylum is a polysaccharide carbohydrate consisting of a large number of glucose units joined together by glycosidic bonds....
    , developed by iodine
    Iodine

    Iodine , is a chemical element that has the symbol I and atomic number 53. Naturally-occurring iodine is a single isotope with 74 neutrons....
     solution which turns starch dark blue and the paper light blue.
  • Lemon juice
    Lemon

    The lemon is the common name for Citrus limon. The reproductive tissue surrounds the seed of the angiosperm lemon tree. The lemon is used for culinary and nonculinary purposes throughout the world....
    , developed by iodine
    Iodine

    Iodine , is a chemical element that has the symbol I and atomic number 53. Naturally-occurring iodine is a single isotope with 74 neutrons....
     solution (ink turns white, paper turns light blue).
  • Sodium chloride
    Sodium chloride

    Sodium chloride, also known as common salt, table salt, or halite, is a chemical compound with the chemical formula SodiumChlorine....
     (common table salt), developed by silver nitrate
    Silver nitrate

    Silver nitrate, also known as lunar caustic, is a soluble chemical compound with chemical formula silverNitrogenOxygen3. This compound is a versatile precursor to many other silver compounds, such as those used in photography....
    .


Inks visible under ultraviolet light


Some inks glow faintly (fluoresce
Fluorescence

Fluorescence is a luminescence that is mostly found as an optical phenomenon in cold bodies, in which the molecular absorption of a photon triggers the emission of a photon with a longer wavelength....
) when under an ultraviolet
Ultraviolet

Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than x-rays, in the range 400 nanometer to 10 nm, and energies from 3 Electron volt to 124 eV....
 lamp. This is a property of many substances, particularly organic substances and body fluids.

Other inks work in a near opposite way by absorbing ultraviolet light but without fluoresceing. When these are used on fluorescent
Fluorescence

Fluorescence is a luminescence that is mostly found as an optical phenomenon in cold bodies, in which the molecular absorption of a photon triggers the emission of a photon with a longer wavelength....
 paper, the inked areas fluoresce less than the surrounding paper area when under an ultraviolet lamp. This is especially a property of inks with a yellow tint.

Some UV-visible inks may be detected on a photocopy, due to the relatively strong ultraviolet component in light from the photocopier scanning head.

Examples of inks revealed by ultraviolet light are:

  • laundry detergent
    Laundry detergent

    Laundry detergent, or washing powder, is a substance which is a type of detergent that is added when one is washing laundry to aid in getting the laundry cleaner....
    s containing optical brightener
    Optical brightener

    Optical brighteners, optical brightening agents , fluorescent brightening agents or fluorescent whitening agents are dyes that absorb light in the ultraviolet and violet region of the electromagnetic spectrum, and re-emit light in the blue region ....
    s.
  • soap
    SOAP

    SOAP, originally defined as Simple Object Access Protocol, is a protocol specification for exchanging structured information in the implementation of Web Services in computer networks....
    .
  • Body fluids, such as semen
    Semen

    Semen is an organic fluid, also known as seminal fluid, that usually contains spermatozoon....
    , serum
    Serum

    Serum may refer to:*Blood plasma, with clotting factors removed*Antiserum, for transfer of passive immunity*Serous fluid, any clear bodily fluid...
    , saliva
    Saliva

    Saliva is the watery and usually frothy substance produced in the mouths of humans and most other animals. Saliva is produced in and secreted from the salivary glands....
    , milk
    Milk

    Milk is an opaque white liquid produced by the mammary glands of female mammals . It provides the primary source of nutrition for newborn mammals before they are able to digestion other types of food....
     or urine
    Urine

    Urine is a liquid waste product of the body secreted by the kidneys by a process of filtration from blood called urination and excreted through the urethra....
    .


Inks which disturb the surface of paper


This includes virtually all invisible inks, but pure distilled water can also be used in this way. Application of any fluid will disturb the paper surface fibers or sizing.

Fumes created from heating iodine crystals will develop the writing, which will appear brown because the iodine sticks preferentially to the disturbed areas of the paper. Exposing the paper to strong sunlight will return the writing to its invisible state, as will using a bleach solution.

Slightly dampening paper with a sponge or by steam and then drying it before writing a message, will prevent writing from being developed by this method. But overdoing dampening will result in telltale paper cockling.

Disappearing inks


Inks that are visible for a period of time without the intention of being made visible again are called disappearing inks. Disappearing inks typically rely on the chemical reaction between thymolphthalein
Thymolphthalein

Thymolphthalein is an acid-base PH indicator. Its transition range is at approximately pH 9.3-10.5. Below this pH, it is colorless; above this pH, it is blue....
 and a basic substance such as sodium hydroxide. Thymolphthalein, which is normally colorless, turns blue in solution with the base. As the base reacts with carbon dioxide (always present in the air), the pH drops below 10.5 and the color disappears. Pens are now also available that can be erased simply by swiping a special pen over the original text. Disappearing inks have been used in gag squirtguns, for limited-time secret messages, for security reasons on non-reusable passes, and for fraudulent purposes.

Modern relevance of invisible ink messages


As an indication of security, most inks mentioned above were already known by the end of World War I
World War I

World War I, or the First World War , was a global military conflict which involved the Great powers, organized into two opposing military alliances: the Allies of World War I and the Central Powers....
. However, in 1999 the U.S. Central Intelligence Agency
Central Intelligence Agency

The Central Intelligence Agency is a civilian intelligence agency of the Federal government of the United States. It is the successor of the Office of Strategic Services formed during World War II to coordinate espionage activities between the branches of the US military services....
 successfully requested that a 1940's technical report on invisible ink remained exempt from mandatory declassification
Declassification

Declassification is the process of documents that formerly were Classified information becoming available to the public, under the principle of freedom of information....
, based on the claim that invisible ink was still relevant to national security
National security

The late political scientist Hans Morgenthau, author of Politics Among Nations, defines national security as the integrity of the national territory and its institutions....
. The report thus remains classified.

Former MI-6 agent Richard Tomlinson alleges that Pentel Rolling Writer rollerball pens were extensively used by MI-6 agents to produce secret writing (invisible messages) while on missions.

In 2002, a racist gang was indicted for spreading a riot between federal penitentaries using coded telephone messages, and messages in invisible ink.

In 2008 a British Muslim, Rangzieb Ahmed
Rangzieb Ahmed

Rangzieb Ahmed is a British Pakistani who was the highest ranking Al-Qaeda operative in the United Kingdom. Ahmed, who was a key link between British recruits and al-Qaeda leaders, was responsible for setting up a terrorist cell in Manchester, and had contacts with one of the terrorists responsible for the failed 21 July 2005 London bombings....
, was alleged to have a contact book with Al-Qaeda
Al-Qaeda

Al-Qaeda, alternatively spelled al-Qaida and sometimes al-Qa'ida, is an international Sunni Islam Islamist Extremism movement founded sometime between August 1988 and late 1989/early 1990....
 telephone numbers, written in invisible ink.