To encrypt the message “HELLO THERE” with a key (shift) of 5, we replace H with the letter 5 later, M, etc, so that we arrive at the ciphertext “MJQQT YMJWJ”. Here, the number of places, \(k\), in the shift is the key to the encryption. To encrypt a message, one simply replaces each letter in the message with its shifted version. The shift “wraps around” the alphabet, so that, for example, a shift of 1 maps Z to A. For example, a shift of 1 maps A to B, B to C, and so on, while a shift of 2 maps A to C, B to D, etc. The idea of the scheme is to replace each letter in the alphabet by shifting the alphabet some number-\(k\)-letters later. One of the earliest encryption schemes is attributed to Julius Caesar. If the scheme is to offer any real security, we would like for it to be difficult (or impossible) to find the cleartext from a ciphertext without the key, even if the encryption and decryption methods are known. Crucially, the encryption and decryption method should have the property that, given the same key, applying the decryption method to the ciphertext gives the original cleartext. Here, the key is some (secret) information, such as a password, that should not be shared with anyone except those with whom one wants to share the cleartext. a decryption method that transforms a ciphertext and a key into a (clear)text.an encryption method that transforms a cleartext and a key into a ciphertext, and.Further, the encryption should be reversible so that, given the right (secret) information, the ciphertext can be transformed back into the original cleartext.Ī bit more formally, an encryption scheme consists of two functions: Ideally, someone who sees only the ciphertext should not be able to gain any useful information about the contents of the cleartext. The goal of an encryption scheme is to convert a cleartext-a text whose contents you wish to remain secret-into a ciphertext that obscures the cleartext. It's important that \( x \) or \( -x \) is an integer such as \( -14, 3, 17 \) etc.A program to encrypt and decrypt text Encryption Schemes we have to find the minimum value of \( -x \) such that \( 5 \cdot -x \geq -27 \). In this case the integer \( x \) is negative and should be the closest integer that exceed -27, i.e.
\( -27 \: mod \: 5 \) we have to do it slightly different and the answer is \( -27 \: mod \: 5 = 3 \). Then by subtracting 27 with 25 we get the answer \( 27 - 25 = 2\). In this case we have that \( x = 5 \) because \( 5 \cdot 5 = 25 \leq 27 \). we have to find the maximun value of \( x \) such that \( 5 \cdot x \leq 27 \). But how did we get this result?įirst we compute the number of times it's possible to multiply 5 with the number \( x \) such that we get an integer as close as possible to 27 without exceeding it, i.e. look at \( 27 \: mod \: 5 \) then modulo computes the number of times 5 divides 27 and then returns the remainder of the result which is 2 in this case, i.e. The result of a modulo computation is an integer between 0 and the modulus minus 1.
In words we say 11 plus 3 modulo 12 is equal 2. Where 12 is the modulus because we want the time as an integer between 0 and 11 (12 o'clock is in this case denoted by 0). needs to figure out what time it's 3 hours after 11 o'clock, which is 2 o'clock.
You already use modulo computation when you look at the clock and e.g.