Why the Exact Same Lottery Numbers Came Up Twice in One Week. You may also like. Half a million chances at fourteen million total outcomes isn't that improbable. The chances of getting two identical guids are astronomically slim even if you are generating guids as fast as you can. (Generating, say, thousands of guids per second for the sole purpose of finding a duplicate.) Of course, if you want my opinion, I do believe that there will be a time, in a couple of thousand years from now.

1. Chance Of Ever Generating Same Key Twice 10 Letters Words
2. Chance Of Ever Generating Same Key Twice 10 Letters Worksheet

Tool to decrypt/encrypt Vigenere automatically. Vigenere cipher is a poly-alphabetic substitution system that use a key and a double-entry table.

Answers to Questions

How to encrypt using Vigenere cipher?

Encryption with Vigenere uses a key made of letters (and an alphabet). There are several ways to achieve the ciphering manually :

Vigenere Ciphering by adding letters

In order to cipher a text, take the first letter of the message and the first letter of the key, add their value (letters have a value depending on their rank in the alphabet, starting with 0). The result of the additionmodulo 26 (26=the number of letter in the alphabet) gives the rank of the ciphered letter.

Example: To crypt DCODE, the key is KEY and the alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ.

Example: Take the first letters of the plaintext D (value = 3) and of the key K (value = 10) and add them (3+10=13), the letter with value 13 is N.

Continue with the next letter of the plaintext, and the next letter of the key. When arrived at the end of the key, go back to the first letter of the key.

Example:DCODE
KEYKE

Example:NGMNI is the ciphertext.

Vigenere Cipher using a table

In order to encrypt using Vigenere method, the easiest way is to have a double entry grid, here is one (when the alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ):

Example: The key is KEY, and the plaintext is DCODE.

Locate the first letter of the plaintext message in the first line of the table and the first letter of the key on the left column. The cipher letter is at the intersection.

Example: Locate the letter D on the first row, and the letter K on the first column, the ciphered letter is the intersection cell N.

Continue with the next letter of the plaintext, and the next letter of the key. When arrived at the end of the key, go back to the first letter of the key.

Example:NGMNI is the ciphertext.

How to decrypt Vigenere cipher?

Vigenere decryption requires a key (and an alphabet). As for encryption, two ways are possible.

Decryption of Vigenere by subtracting letters

Example: To decrypt NGMNI, the key is KEY and the alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ.

To decrypt, take the first letter of the ciphertext and the first letter of the key, and subtract their value (letters have a value equals to their position in the alphabet starting from 0). If the result is negative, add 26 (26=the number of letters in the alphabet), the result gives the rank of the plain letter.

Example: Take the first letters of the ciphertext N (value = 13) and the key K (value = 10) and subtract them (13-10=3), the letter of value 3 is D.

Continue with the next letters of the message and the next letters of the key, when arrived at the end of the key, go back the the first key of the key.

Example:NGMNI
KEYKE

Example:DCODE is the plain text.

Decryption of Vigenere with a table

To decrypt Vigenere with a double entry square table, use the following grid (case alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ):

Example: To decrypt NGMNI, the key is KEY.

Locates the first letter of the key in the left column, and locates on the row the first letter of the ciphered message. Then go up in the column to read the first letter, it is the corresponding plain letter.

Example: Locate the letter K on the first column, and on the row of it, find the cell of the letter N, the name of its column is D, it is the first letter of the plain message.

Continue with the next letters of the message and the next letters of the key, when arrived at the end of the key, go back the the first key of the key.

Example: The original plain text is DCODE.

How to recognize Vigenere ciphertext?

Following a Vigenere encryption, the message has a coincidence index which decreases between 0.05 and 0.04 depending on the length of the key, it decreases towards 0.04 the longer the key is.

How to decipher Vigenere without knowing the key?

Most common keyless techniques uses statistical methods in order to find the key length, then a simple frequency analysis allow to find the key.

Kasiski test

Kasiski test consists in finding repeating sequences of letters in the ciphertext.

Example:ABC appears three times in the message ABCXYZABCKLMNOPQRSABC

The fact that repeating letters can be found means two things : either a same sequence of letter of the plaintext is crypted with the same part of the key, either different sequences letters are crypted with different parts of the key but they ends with the same crypted letters. this second possibility is poorly probable.

By analyzing the gaps between two identical redunding sequences, an attacker can find multiples of the key length. By analyzing each gaps in term of number of letters, and by calculating divisors, an attacker can deduct with a high probability the size of the key.

Example: Positions of ABC are 0, 6 et 18, gaps are 6, 12 and 18 letters length, their most common divisors are 2, 3 and 6, so the key has an high probability to be 2, 3 or 6 letters long.

Index of coincidence test

The test using the index of coincidence consists in taking one letter out of n in the ciphertext and calculate the IC. The higher it is, the higher the probability n is the key size.

Indeed, taking one letter every n where n is the key-length, ends with a sequence of letters that are always crypted using the same shift. The index of coincidence is then equals to the one of the plain text.

How to find the key when having both cipher and plaintext?

When encrypting, the key is added to the plain text to get encrypted text. So, from the encrypted text, subtract the plain text to get the key.

NB: This is equivalent to decrypting the encrypted text with the plain text as key. The key will then appear repeated.

Example: The cipher text is NGMNI and the corresponding plaintext is DCODE. Use DCODE as key to decrypt NGMNI and find as plaintext KEYKE which is in fact the key KEY (repeated).

What are the variants of the Vigenere cipher?

Multiple variants exists, as Beaufort Cipher, VigenereAutoclave, vigenere'>Vernam Cipher

How to choose the encryption key?

In order to make Vigenere resistant to attacks, the coder must determine the most secure encryption key possible. All attacks are based on detections of key repetitions, so to avoid this pitfall, it is necessary to use a key as long as possible so that it does not repeat, or even longer than the size of the text to encrypt. This is the case of the vigenere'>Vernam cipher.

What is the running key vigenere cipher ?

The variant by running key uses a key lenght at least equal to that of the text. This technique makes it possible to secure Vigénère's cipher as Kasiski's attack is no longer valid.

To get a long enough key, it is common to use a long book or other message. The use of this kind of key then opens the possibility of other attacks, by probable word and / or by analysis of the frequencies of the characters if the message is long enough.

In the particular case where the entire key is made up of random characters (see Vernam one time pad), then the message becomes completely unbreakable by any method of cryptanalysis (unconditional security).

What is the keyed vigenere cipher ?

By using a disordered alphabet, or with a key that modify the traditional Latin alphabet, then the majority of the tools of cryptanalysis become useless and the Vigenère cipher is then resistant to classical attacks.

What is a Saint-Cyr slide ?

Chance Of Ever Generating Same Key Twice 10 Letters Words

Saint-Cyr slide is a rule-shaped instrument, a tool that simplifies manual encryption and decryption of a message encrypted with Vigenere. Its fixed part consists of the alphabet, and its sliding mobile part is a double alphabet.

To encrypt a letter, move the slider so that the A of the fixed part matches the letter of the key. Then look at the letter of the mobile part directly below the letter of the plain message written on the fixed part.

Why the name Vigenere ?

Blaise de Vigenère (1523-1596) was a French diplomate.

What are the advantages of the Vigenere cipher versus Caesar Cipher ?

Caesar cipher is in fact a Vigenere cipher with a 1-letter long key. Vigenere code uses longer keys that allows the letters to be crypted in multiple ways. The frequency analysis is no more anough to break a code.

When Vigenere have been invented?

Blaise de Vigenère wrote a treaty describing this cipher in 1586. An full reedition is available here (link) However another treaty from 1553 by Giovan Battista Bellaso already described a very similar system.

Source code

dCode retains ownership of the source code of the script Vigenere Cipher online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Vigenere Cipher script for offline use on PC, iPhone or Android, ask for price quote on contact page !

Questions / Comments

By: Aaron Bertrand | Updated: 2013-09-17 | Comments (20) | Related: More >T-SQL

Chance Of Ever Generating Same Key Twice 10 Letters Worksheet

Problem

From time to time, I see a requirement to generate random identifiers for things like users or orders. People want to use random numbers so that the 'next' identifier is not guessable, or to prevent insight into how many new users or orders are being generated in a given time frame. They could use NEWID() to solve this, but they would rather use integers due to key size and ease of troubleshooting.

Let's say we want all users to have a random number between 1,000,000 and 1,999,999 - that's a million different user IDs, all 7 digits, and all starting with the number 1. We may use one of these calculations to generate a number in this set:

(These are just quick examples - there are probably at least a dozen other ways to generate a random number in a range, and this tip isn't about which method you should use.)

These seem to work great at the beginning - until you start generating duplicates. Even when you are pulling from a pool of a million numbers, you're eventually going to pull the same number twice. And in that case, you have to try again, and sometimes try again multiple times, until you pull a number that hasn't already been used. So you have to write defensive code like this:

Never mind that this is really ugly, and doesn't even contain any transaction or error handling, this code will logically take longer and longer as the number of 'available' IDs left in the range diminishes.

Solution

One idea I've had to 'solve' this problem is to pre-calculate a very large set of random numbers; by paying the price of storing the numbers in advance, we can guarantee that the next number we pull won't have already been used. All it requires is a table and some code to pull the next number from the set. One way to populate such a table:

This took about 15 seconds to populate on my system, and occupied about 20 MB of disk space (30 MB if uncompressed). I'll assume that you have 20 MB of disk and memory to spare; if you don't, then this 'problem' is likely the least of your worries. :-)

Now, in order to generate the next ID, we can simply delete the lowest RowNumber available, and output its NextID for use. We'll use a CTE to determine the TOP (1) row so that we don't rely on 'natural' order - if you add a unique constraint to NextID, for example, the 'natural' order may turn out to be based on that column rather than RowNumber. We'll also output the result into a table variable, rather than insert it directly into the Users table, because certain scenarios - such as foreign keys - prevent direct inserts from OUTPUT.

When we come close to exhausting the first million values (likely a good problem), we can simply add another million rows to the table (moving on to 2,000,000 to 2,999,999), and so on. It may be wise to set up some automation to periodically checking how many rows are left, so that you can re-populate well in advance of actually running out of numbers.

Performance Metrics for Generating Random Values in SQL Server

I ran both methods 1,000,000 times, filling the Users table up with these random UserID values. The following chart shows that, while generating a random number at runtime is faster out of the gates, the cost of duplicate checking (and retrying in the event of a collision) quickly overtakes the read cost of the predefined table, and grows rapidly and eventually exponentially as more and more values are used up:

In the first 1,000 inserts, there were zero collisions. In the last 1,000 inserts, the average collision count was over 584,000. This, of course, is a problem that doesn't occur when you *know* that the next number you pull can't possibly be a duplicate (unless someone has populated the Users table through some other means).

Conclusion

We can trade a bit of disk space and relatively predictable (but not optimal) performance for the guarantee of no collisions, no matter how many random numbers we've already used. This doesn't seem like a good trade in the early going, but as the number of ID values used increases, the performance of the predefined solution does not change, while the random numbers generated at runtime really degrades performance-wise as more and more collisions are encountered.

Next Steps

• I encourage you to perform your own testing to see if a predefined set of random numbers might make more sense in your environment.
• Review the following tips and other resources:
  • Documentation for CRYPT_GEN_RANDOM(), CHECKSUM(), NEWID() and RAND().

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