For example, in RSA, we use this for encryption: $ciphertext = (m^e \mod n)$ and for decryption.

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If our post is "hello world", climate what number execute we need to put as $m$ in the RSA formula?  Say you want to encrypt "Hello World" through RSA.

The very first important thing below is the encoding of that text. "Hello World" as such cannot be encrypted due to the fact that characters are a non-numerical concept.So one encoding is used convert the personalities of that message to numeric values (e.g. The ASCII / Unicode table, but there are plenty of others, specifically for non-latin characters). Making use of Unicode-8, "Hello World" turns right into this sequence of bytes (hex-notation):

48 65 6C 6C 6F 20 57 6F 72 6C 64Such a sequence of bytes deserve to then be construed as a number by assigning a most-significant and also least-significant byte (e.g. The an ext left-sided, the an ext significant). The sequence would then same the number

SEJPM already said), a padding is applied. The succession of bytes then could look something favor this:

01 48 65 6C 6C 6F 20 57 6F 72 6C 64 98 9C 38 83 E1 64 E7 0B BC F2 43 C0 6B26 D4 5E AC 9B C9 DC 2F 1B 87 46 3D 2E 6F 86 66 5E 1B CB 44 DA 5A 50 79 2F40 79 88 83 84 3E 16 9D 7F 1F 05 2C DF F2 9B 9B 07 11 F6 7A CB 1C 35 9B 76BD 8D 46 1C E0 09 2A 9F C5 B8 A9 FB 61 41 ... Approximately the bitsize of NThat succession is then understood as a number and also shoved with the algorithm.

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edited Apr 30 "20 at 6:23
answer Jul 20 "16 at 12:35 marstatomarstato
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…what number do we need to put together $m$ in the RSA formula?

There room three possibilities what $m$ have the right to be.

A full-sized arbitrarily bit-sequence, e.g. A random sort-of-key i m sorry is around as huge as the modulus and will be supplied to derive a symmetric key for message encryption.(not recommended) some unpadded message. This would skip the padding stage and also directly apply the RSA primitive to her message. This is highly dangerous and also should not be done in a production setting as really simple attacks deserve to recover the plaintext.
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edited Jul 21 "16 at 5:24 e-sushi
reply Jul 20 "16 at 12:28 SEJPM♦SEJPM
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ASCII is one method to encode one alphabet into integers, i beg your pardon in return are mostly represented in binary or hexadecimal notation. However of course over there are numerous other methods to encode alphabets right into numbers, and also exactly just how you carry out that is completely up to you.

For example you just have the letters from A come Z and got the cable $s = s_0s_1s_2s_3....s_n$. Climate you consider all the $s_i$ together numerical worths in $\0,1,2,3,...,25\$ according to your aphabetical order. Climate you encode a post like this:

$$x = s_0 + 26 \cdot s_1 + 26^2 \cdot s_2 + ... + 26^n \cdot s_n$$

Basically, you just take into consideration a message to it is in a number in basic 26, which deserve to be expressed in any kind of other number system, regardless of numbers of signs in the alphabet. Binary numbers space nothing else 보다 numbers represented in base 2, and also it doesn"t matter if we create $01011$, $ABABB$ or even $\oplus\otimes\oplus\otimes\otimes$.

On a comparable note, if you embedd the really message right into some special format, e.g. Through concatenating a solved head and tail come the message, that doesn"t change anything. Any kind of encoding works, as lengthy as each message has actually a unique number assigned.

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If you consider strings of arbitrarily length, you also need arbitrary large integers for her encoding. However, RSA only enables messages smaller sized than $N$, which boundaries the length of the string in return. In the case, hybrid encryption is typically used: friend don"t encrypt the blog post itself, but you encrypt a random an essential for a symmetric cypher, and then use a setting of procedure with the symmetric cipher and also the random key in the RSA ciphertext.