Blackjack Rsa Meaning List
Blackjack Rsa Meaning Key
Blackjack Rsa Meaning Synonyms

A reference to the amount of a player's minimum bet and maximum bet while playing blackjack. A 1-4 spread would mean the player's maximum bet is four times the size of the player's minimum bet. If a player spreads to two hands, the bet spread may be described as 1 - 2X4, which would mean one hand at one unit to two hands of four units each. Since the term 'blackjack' also refers to the mineral zincblende, which was often associated with gold or silver deposits, he suggests that the mineral name was transferred by prospectors to the top bonus in the game. He was unable to find any historical evidence for a special bonus for having the combination of an Ace with a black Jack.

The generation of random numbers is too important to be left to chance.

Everything we do to achieve privacy and security in the computer age depends on random numbers.

In February 2012, two groups of researchers revealed that large numbersof RSA encryption keys that are actively used on the Internet can be crackedbecause the random numbers used to generate these keys were not random enough.Here, I offer a puzzle in which you will identifyand crack RSA keys that are vulnerable in the same way — usinga slightly simpler version of the same technique. This should providea clearer understanding of how this problem arises and how it can beexploited, as well as more familiarity with the RSA algorithm andEuclid's algorithm.

This challenge is aimed at novice programmers who want to practice theirprogramming skills with some real-world cryptography, and at anyone whowas interested in Lenstra et al. and Heninger et al.'sresearch but found the math involved daunting or unfamiliar.

I'll start with an explanation about RSA to put these attacks in somecontext and explain some of the steps involved in solving this challenge.If you're already familiar with the RSA algorithm and with the details ofthese attacks, you could skip directly to thechallenge part.

RSA and RSA keys

RSA is animportant encryption technique first publicly invented by Ron Rivest,Adi Shamir, and Leonard Adleman in 1978. RSA is based onthefact that there is only one way to break a given integer down into aproduct of prime numbers, and a so-calledtrapdoor problemassociated with this fact. It's easy to fall through a trap door, butpretty hard to climb up through it again; remember what the Sybil said:

[...] Sate sanguine divom,
Tros Anchisiade, facilis descensus Averno;
noctes atque dies patet atri ianua Ditis;
sed revocare gradum superasque evadere ad auras,
hoc opus, hic labor est.

O goddess-born of great Anchises' line,
The gates of hell are open night and day;
Smooth the descent, and easy is the way:
But to return, and view the cheerful skies,
In this the task and mighty labor lies.

John Dryden translation

The particular problem at work is that multiplication is pretty easyto do, but reversing the multiplication — in the form offactoring — is apparently pretty hard. Multiplying given numbersp and q together to calculate p × q = n is pretty straightforward; evenelementary school children are taught to do it quickly and accurately bylong multiplication.

For example, if I asked you to multiply

17477852958781876547 × 15241555427044345769 = ?

you would probably need only a matter of minutes with pencil and paper,or a tiny fraction of a second with a computer, to answer

17477852958781876547 × 15241555427044345769 = 266389664617004986624097978187739779643

What if we turn the question around and ask what two integers would have tobe multiplied together to yield a given number? For example,

? × ? = 281512008712700373730275954373439628511

Suddenly, this task is remarkably difficult; you'd have little hope ofever getting the answer by guessing with pencil and paper, and even witha computer you might have to write a new program to find the answer, andit might take a noticeable amount of time to do so.

However, if I reveal that the answer is

17627949842247424607 × 15969639761398924673 = 281512008712700373730275954373439628511

you can pretty easily check that this is right. If you need moreconvincing that it seems to be vastly harder to go in one direction thanthe other, try these two problems without answers:

18324413790489873917 × 16753053665517997013 = ?

and

? × ? = 231780035703803150278713557377368328099

It seems as though thispattern continues, and factoring gets drastically harder as the numbersinvolved get larger, while multiplication remains easy and quick. Infact, there is alsoa longstanding publicchallenge to see what the public state-of-the art in factorizationis; the largest number from this challenge that we know has beensuccessfully factored is called RSA-768:

1230186684530117755130494958384962720772853569595334792197322452151726400507263657518745202199786469389956474942774063845925192557326303453731548268507917026122142913461670429214311602221240479274737794080665351419597459856902143413

This number wasfactored in 2009.

The RSA algorithm requires a user to generate a key-pair, made up ofa public key and a private key, using this asymmetry. Descriptions ofRSA often say that the private key is a pair of large prime numbers(p, q), while the public key is their product n =p × q.

This is almost right; in reality there are alsotwo numbers called d and e involved; e, which isused for encryption, is usually 65537, while d, which isused for decryption, is calculated from e, p, andq. Thewaywe calculate d is straightforward to do but complicatedto explain, and isn't really necessary for our purposes here. (Below, I'llgive you some source code and a web app to automate theprocess so that you don't have to worry about it while solving the puzzle.)The end result is that d can be used to decrypt what e and nencrypt (using an operation called modular exponentiation), but only the privatekey's owner knows or can calculate d.

n is, indeed, published as part of the public key. Not onlyis the public allowed to know this number, butforsecurity reasons the public key holder normally wants everyoneto know it, to prevent someone else from maliciouslyimpersonatingthem by giving out some other value of n. We can goout and look at various people's values of n; for example, the onefor Gmail's web site is

149629486786262270606941307578089677590454201237165984499971154966664749889451716079416569797686937215029720424638195271847598792512505659659231590931086898924727016171274343552925314345847614671125708664971820722165639121705555274122142443910339820898963056278550522067594972363524619215467622112312405988881

while the one for PayPal's site is

19907789316973232571709388139491358666929454999402440962751418618453573264955089051420528817897891333335369381181336604286912201113757821941217467558226280838933785489616679977332178809112857355692902776754821604616983317242449495394362748115124468692900781573694743868331219952099224674513107154770709045556420165907683219901455612366432477179986702075209386343768097176233191423040304881401194366954739922445951906916747808916845352010407952710079897810642551273099204890952309865459288708489866066485327182895626969651191379209124433725745943676165198426636198495665286419097106110163852891072181715030605705150303

and the one for my personal PGP key is

84183018955490272102600624773954613697296519247162624797776488402136621164618721856613244871400488537762018554822342234060198882680450913714703244895991014211576478153635620444776100758000814497619911492172618982141707345554401834325856631449515585181294391705950925162457376922832610333917475697722700423490803726182040155989152929240149229431819589146218147023051160490047490036948728955362940670424299360024272207080040698078084479622972598619384845461714212613013116744906618460220064765218359970970085681281819372663398587522312393795493713246599934575694

Blackjack Rsa Meaning