For many years, cryptographers attempted to hide the telltale frequencies by using several different substitutions for common letters, but this technique was unable to fully hide patterns in the substitutions for plaintext letters.

For current cryptographic purposes, an elliptic curve is a plane curve which consists of the points satisfying the equation

For cryptography, this is very bad: we want typical instances of a cryptographic problem to be hard.

For cryptographic applications, only generators meeting the K3 or K4 standard are acceptable.

For example, thermite can be used for the emergency destruction of cryptographic equipment when there is a danger that it might be captured by enemy troops.

For example, a cryptographic algorithm may be implemented by hardware and software that is widely distributed among users.

For example, Shafi Goldwasser, a noted female computer scientist — computer science being a field largely dominated by men — uses the pronoun " she " exclusively in her Lecture Notes on Cryptography in reference to cryptographic adversaries.

For example, CTS is ciphertext stealing mode and available in many popular cryptographic libraries.

For instance, in Europe during and after the Renaissance, citizens of the various Italian states — the Papal States and the Roman Catholic Church included — were responsible for rapid proliferation of cryptographic techniques, few of which reflect understanding ( or even knowledge ) of Alberti's polyalphabetic advance.

For this reason, the md5sum and sha1sum utilities are often preferred in Unix operating systems, which use the MD5 and SHA-1 cryptographic hash functions respectively.

For example, Transport Layer Security ( TLS ) is a cryptographic protocol that is used to secure web ( HTTP ) connections.

For instance, TLS employs what is known as the Diffie-Hellman key exchange, which although it is only a part of TLS per se, Diffie-Hellman may be seen as a complete cryptographic protocol in itself for other applications.

For this purpose, cryptographic hash functions are employed often.

For an example of a cryptographic signature, a proposed purchase order accepted by a vendor and returned via email to the purchaser after being digitally signed.

For attacks on computer systems themselves ( which are often used to perform cryptography and thus contain cryptographic keys or plaintexts ), see computer security.

For example, FIPS 140-3 requires power analysis countermeasures for cryptographic devices bought to the U. S. government.

For this reason, care should be taken to ensure there are no secret values which affect the conditional branches within cryptographic software implementations.

For instance, the BIS must be notified before open-source cryptographic software is made publicly available on the Internet, though no review is required.

For other areas that do not provide for different levels of security, a cryptographic module receives a rating that reflects fulfillment of all of the requirements for that area.

For example, digital certificates are protected within tamper-proof cryptographic processors.

For classification of keys according to their usage see cryptographic key types.

* For its use in data structure, database and cryptographic applications, see hash function or unique key.

For example, the quintessential cryptographic system has Alice wanting to send a message to Bob without Eve being able to eavesdrop on them.

For example, each encryption key can be generated from the underlying key material using a cryptographic hash function or other key derivation function.

For example, cryptographic keys are often quite large and cumbersome to compare, so a user who

For the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.

For further protection, climbers typically put a bouldering mat ( crash pad ) on the ground to break their fall.

For example, a scene may be improved by cutting a few frames out of an actor's pause ; a brief view of a listener can help conceal the break.

For a period of time the Chinese attempted to become self-reliant, but found that in doing so the country could not break even economically, especially when attempting to maintain a communist vision when it came to economics.

For instance, high range voltmeters don't break at predictable moments in time, but rather at unpredictable moments.

For " many Marxian libertarian socialists, the political bankruptcy of socialist orthodoxy necessitated a theoretical break.

For 37 years beginning in 1967, Albert was the voice of the New York Knicks on radio and television ( getting his start by being a ball boy for the Knicks before getting his first break on New York radio by sportscaster Marty Glickman ) before being let go by the chairman of the MSG Network and Cablevision after Albert criticized the Knicks ' poor play on-air in 2004.

For some prominent communists such as Bertram Wolfe, Jay Lovestone, Arthur Koestler, and Heinrich Brandler, the Bukharin trial marked their final break with communism and even turned the first three into fervent anti-Communists eventually.

For full discussion of degrees of correspondence between spelling and pronunciation in alphabetic orthographies, including reasons why such correspondence may break down, see Phonemic orthography.

For seventy years, the CPSU had been the cohesive force that kept the union together ; without the authority of the party in the Soviet center, the nationalities of the constituent republics pulled harder than ever to break away from the union.

For example, if an estimate of how long it takes to break an encryption scheme is one thousand years, and it were used to encrypt details which are obsolete a few weeks after being sent, then this could be deemed a reasonable risk and trade-off.

For my littlest finger is thicker than my father's loins ; and your backs, which bent like reeds at my father's touch, shall break like straws at my own touch.

For example, all salts of sodium, potassium and ammonium are soluble in water, as are all nitrates and many sulfate salts except barium sulfate, calcium sulfate ( sparingly soluble ) and Lead ( 2 ) sulfate However, ions that bind tightly to each other and form highly stable lattices would be less soluble, because it would be harder for these structures to break apart for the compounds to dissolve.

For extra speed a swimmer wears a body suit, which has rubber or plastic bumps that break up the water close to the body and provides a small amount of thrust — just barely enough to help a swimmer swim faster.

For example, schools may extend the remaining school days later into the afternoon, shorten spring break, or delay the start of summer vacation.

For his second triumph, his donatives were said to break all records, though the amounts in Plutarch's account are implausibly high: Pompey ’ s lowest ranking soldiers each received 6000 sesterces ( about six times their annual pay ) and his officers around 5 million sesterces each.

For a stone greater that 10 mm, ESWL may not help break the stone in one treatment ; instead, two or three treatments may be needed.

For example, line break has an escape sequence of

For this reason, the faithful do not yet break their fast nor exchange the paschal kiss.

For example in the Northern Hemisphere beginning in late August / September of year one and continuing until May of year two, with a three to four month summer break in between years one and two.

For example, there is no three to four month summer break, and between semesters there might be seven to ten days off rather than three to five weeks vacation.

For example, the Ford Excursion could net the company $ 18, 000, while they could not break even with the Ford Focus unless the buyer chose options, leading Detroit's big three automakers to focus on SUVs over small cars.

For some prominent former communists, such as Bertram Wolfe, Jay Lovestone, Arthur Koestler, and Heinrich Brandler, the Bukharin trial marked their final break with communism and turned the first three into fervent anti-communists.

For example, at the microwave frequency, the microwave field causes the periodic rotation of water molecules, sufficient to break hydrogen bonds.