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cryptosystem examples

146 Cryptography and Network Security Example 6.1 Find the output of the initial permutation box when the input is given in hexadecimal as: 0x0002 0000 0000 0001 Solution The input has only two 1s (bit 15 and bit 64); the output must also have only two 1s (the nature of straight permutation). Asymmetric key cryptosystem. (a) conventional (b) public key (c) hash key (d) asymmetric-key The question was asked in exam. A simple example of a super-increasing sequence is presented in the numbers 1,2,4,8,\ldots,2^ {n}, 1,2,4,8,…,2n, where 2^ {i} > 2^ {i} - 1 = 1+2+4+\cdots+2^ {i-1}. What is considered strong encryption today will likely not be sufficient a few years from now due to advances in CPU technologies and new attack techniques. Private Key: Held secretely by the host himself. Although this system, and several variants of it, ... so the running time is O(n). And symmetric key cryptosystems (Alice and Bob uses the same key) such as DES and AES are based on bitwise operations on bits (a bit is either equal 0 or 1 and is an abbreviation for binary digit). This paper … Diffie-Hellman Key Exchange. 1 Introduction 2 Procedure 3 Some Trivial Examples 4 Attacks on RSA 5 Recommendations 6 Optimal Asymmetric Encryption Padding (OAEP) 7 Applications 3. In the RSA public key cryptosystem, the private and public keys are (e, n) and (d, n) respectively, where n = p x q and p and q are large primes. The McEliece Cryptosystem This public key cryptosystem, introduced by McEliece in 1978, is similar to the Merkle-Hellman Knapsack cryptosystem in that it takes an easy case of an NP-problem and disguises it to look like the hard instance of the problem. (after some censorship entanglements) Ø Currently the “work horse” of Internet security: • Most Public Key Infrastructure (PKI) products. Now let's demonstrate how the RSA algorithms works by a simple example in Python.The below code will generate random RSA key-pair, will encrypt a short message and will decrypt it back to its original form, using the RSA-OAEP padding scheme.. First, install the pycryptodome package, which is a powerful Python library … Cryptographic Attacks and Countermeasures. This Goppa code can correct for up to 50 errors. Andreas V. Meier – The ElGamal Cryptosystem – p.6/23. Ciphertext: Encrypted text that will appear to be a random string. Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both the encryption of plaintext and the decryption of ciphertext.The keys may be identical, or there may be a simple transformation to go between the two keys. For example, to decide if T is a subset sum of the super-increasing set 3, 7, 12, 30, 60, 115, we start by … RSA Cryptosystem The RSA cryptosystem is a example of a “public key” system. Let us look at an example: Imagine you had a set of weights 1, 6, 8, 15 and 24. The following notations are used frequently in Paillier Cryptosystem explanation: ℤ. - set of integers n . It uses asymmetric key encryption for communicating between two parties and encrypting the message. a Goppa code of length 1024 and dimension 524. The first public-key cryptosystem, RSA, Example User Story # To encrypt a message addressed to Alice in a Hybrid cryptosystem, Bob does the following: Obtains Alice's Public Key. Def: E, A cryptosystem is a 5-tuple (D, M, K, C), where M is the set of plaintexts, K is the set of keys, C is the set of ciphertexts, E: M K C is the set of enciphering functions, and D: C K M is the set of deciphering functions A classical example of a cryptosystem is the Caesar cipher where letters in the plaintext are shifted to get In this case the sequence is – s = 3, 5, 15, 25, 54, 110, 225 All the characters in the string are then converted into binary – H = 1001000 e = 1100101 l = 1101100 l = 1101100 o = 1101111 The nature of the algorithm allows for homomorphic addition operations to produce the current answer once decrypted. Something may be trivial to an expert but ... determinant 1. 9 Responses to “El Gamal examples”. The RSA cryptosystem Ø First published: • Scientific American, Aug. 1977. 1. 10 . Cramer-Shoup Cryptosystem. Demonstration. Say, for example, that we have chosen the ten letters UKVTF WZHOK. The server encrypts the data using client’s public key and sends the encrypted data. Usage. 2. The security of Rabin cryptosystem is related to the difficulty of factorization. In our web applications, there is an intensive exchange of data… Public Key Cryptography - Summary Features able to set up a secure channel between two parties based on the Discrete Logarithm Problem Problems vulnerable to the man-in-the-middle attack vulnerable to chosen-plaintext attacks (! As (a, b) is a key, then the multiplicative inverse a − 1 exists and the original plaintext can be recovered as follows. Using Table 6.1, we can fi nd the output related to these two bits. In this paper, the security of an optical cryptosystem based on double random phase encoding (DRPE) with perfect forward secrecy (PFS) is analyzed for a particular session. In this example the message is digitally signed, but not encrypted. The encryption and decryption operations in the RSA public-key cryptosystem are based on two more facts and one more conjecture: FACT 4. Plaintext: The original message in its original legible form. McEliece Cryptosystem. RSA Cryptosystem Example Assume we have an RSA cryptosystem with the following parameters: p= 53 , q =61 , e =17 , d = 413 Encrypt the following messages: M 1 = 15 , M 2 Decrypt the ciphertexts generated in the previous step and verify their correctness. With a public key cryptosystem, private key is always kept secure by the owner and public key is publically accessible. Here are a few definitions of some terms relating to cryptography and cryptosystems: 1. would know it. • SSL/TLS: Certificates and key-exchange. pk. RSA Encryption / Decryption - Examples in Python. 2.2 Example – Encrypting the string “Hello” The first step is to choose a superincreasing sequence is chosen. In their landmark paper RSA algorithm (Rivest-Shamir-Adleman): RSA is a cryptosystem for public-key encryption , and is widely used for securing sensitive data, particularly when being sent over an insecure network such as the Internet . Three sub-classes of polysizemic ciphers are defined and examples of each are … You are of course right, using two terms that refer to the same thing is confusing. mentioned earlier, NTRU is an example of a public key cryptosystem. Additionally, the encryption scheme was also tested with strings which have the same character repeating multiple time. One of the advantages of the Massey–Omura Cryptosystem is that we can apply commutative encryption. The recipient distributes his or her public key to entities wishing to secure their communications with the recipient. For example we propose a scheme with signatures of 81-bits and a binary security workfactor of 2 83. — Lila … Digital Signature: A digital signature is defined under section 2 of the DSA as “a transformation of a message using an asymmetric cryptosystem such that a person having the initial message and the signer’s public key can accurately determine Two most famous examples of lattice-based public-key encryption protocols are GGH (Goldreich-Goldwaser-Halevi) and NTRUEncrypt. Focus of this article is encryption. 2.2 Semantic Security Now that we know perfect security in some sense is overkill, we look to relaxations. Let examine one example of RSA encryption and decryption, along with the calculations, following the above formulas. These examples are often implemented for public key encryption. Andreas V. Meier – The ElGamal Cryptosystem – p.6/23. A whole paper could be devoted to exploring RSA, but we will only provide an overview here to illustrate our point. 1.2.1 Example: RSA Public Key Encryption RSA is named after its inventors, Rivest, Shamir, and Adelman [13]. Data Encryption Standard is an example of a _____ cryptosystem. In the case of RSA, here is how it works. A perfect example of diffusion and confusion is the AES cryptosystem. Encryption: The process of converting data into its cryptic form that preve… 2. Computer Science questions and answers. However, an active attacker can break the system using a chosen ciphertext attack, as has been mathematically proven. The security of the NTRU cryptosystem comes from the interaction of the polynomial mixing system with the independence of reduction modulo two relatively prime integers p and q. Encrypts the message under the data encapsulation scheme, using the … You might represent the weight 30 by the binary code 11110 (one 1, one 6, one 8, one 15 and no 24). Now consider the following equations- I. M’ = M e mod n and M = (M’) d mod n II. In the field of information security, block cipher is widely used in the protection of messages, and its safety naturally attracts people’s attention. One can use N as a public modulus for the RSA cryptosystem. Let M be an integer such that 0 < M < n and f (n) = (p-1) (q-1). Def: E, A cryptosystem is a 5-tuple (D, M, K, C), where M is the set of plaintexts, K is the set of keys, C is the set of ciphertexts, E: M K C is the set of enciphering functions, and D: C K M is the set of deciphering functions A classical example of a cryptosystem is the Caesar cipher where letters in the plaintext are shifted to get A cryptosystem is a set of processes used to securely transfer information between parties. It would not be possible to pack a knapsack that weighs 17 but this might not matter. Features. ... For example, experimental evidence suggests that for N = 107, N = 167, and N = 503, appropriate values for 72 are 0.35, 0.27, and 0.17 respectively. example, as slow, ine cient, and possibly expensive. A new type of cryptosystem, call a public key cryptosystem was introduced in 1976 by Diffie and Hellman [2]. By adding redundancies, for example, the repetition of the last 64 bits, the system can be made to produce a single root. This means that everyone can know the encryption key, but it is computationally infeasible for an unauthorized person to deduce the corresponding decryption key. 0. A symmetric cryptosystem (or private key cryptosystem) uses only one key for both encryption and decryption of the data. which are read from bottom to top. It belongs to the category of attack analysis in cryptanalysis and has important theoretical significance and application value. Our purpose is provide a correct, efficient and very easy to use; code. Other examples are IDEA, Blowfish, etc. signed keys) Now we will provide very simple and tiny examples of how to use this library. Figure 3.5 shows an example of how an asymmetric key cryptosystem works. Our analysis reveals that the use of PFS has certain advantages … A cryptosystem would be more secure if a ciphertext letter could represent more than one plaintext letter. 3+ 1*3 2+ 0*3 + 0*3 + 1*3. 2i > 2i −1 = 1+2 +4+⋯+2i−1. Besides, n is public and p and q are private. A great example of a cryptosystem is writing. Public Key: Distributed amongst all those who want to communicate with the host. The example discussed above works on symmetric-key cryptography. Public-key cryptosystem is also referred as Asymmetric cryptography, in which each user has a pair of keys (1) a public key and (2) a private key. • Well-known examples: DES (56-bit keys; 64-bit blocksize); AES (128-, 192-, and 256-bit keys; 128-bit blocksize) Steven M. Bellovin September 13, 2006 16 on the example of the cryptosystem DES A.D. Plotnikov∗ Abstract In the paper on the example of the cryptosystem DES, the success-ful method of a cryptanalysis is presented. Introduced are the definition of a new class of encryption mechanism termed Polysizemic Encryption and a reference implementation named the "Slinky Cipher". the concept of a "key" in the cryptosystem, we shall present several examples that il- lustrate keys and possible attacks to dis- cover them. In a cryptosystem, the less information the attacker has, the stronger the system. 8. In cryptography, encryption of the information is classified as three types where those are discussed below: Examples of asymmetric key techniques. Private Key and Public Key form the encryption that’s used to encode information in an SSL certificate. The following diagram shows the inheritance relationship of particular cryptosystems: Asymmetric or public-key cryptography. thought to be a cryptosystem of post-quantum age. This is a Python implementation of ElGamal cryptosystem. An example of asymmetric cryptography : A client (for example browser) sends its public key to the server and requests for some data. • … As such, they help encrypt and protect users’ data and information. Answer: Public Key cryptosystem is an encryption mechanism where every host has two keys: 1. our cryptosystem is allowed to do. Paillier Cryptosystem. further background, for elaboration of the concept of a public-key cryptosystem, and for a discussion of other problems in the area of cryptography. Unlike in the symmetric key cryptosystem, the secrecy of the key is not a requirement as it can only be used to encrypt messages. In order for Bob to set up his portion of an RSA cryptosystem, he begins by selecting two An example of the implementation of the Rabin cryptosystem based on the vector-modular method of modular multiplication and addition operation is … ElGamal encryption is an example of public-key or asymmetric cryptography. The public key is made public while the private key remains secret. INPUT: a, … The key generation for Paillier Cryptosystem given in Algorithm 4, is a bit more complicated than El … Public Key Cryptography - Summary Features able to set up a secure channel between two parties based on the Discrete Logarithm Problem Problems vulnerable to the man-in-the-middle attack vulnerable to chosen-plaintext attacks (! In such a cryptosystem, a pair of keys is used often called private and public key pair. Like the name, its public in nature. ... Related Topics C# Programming Examples on Data Structures Cryptography and Network Security MCQ Questions C Programming Examples on Data-Structures Java Programming Examples on Data-Structures C Programming Examples on Set & String Problems & Algorithms. Editing Public-key cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys. Cryptosystem attack examples Modern cryptography has become highly complex, and because encryption is used to keep data secure, cryptographic systems are an attractive target for attackers . Example [] To encrypt a message addressed to Alice in a hybrid cryptosystem, Bob does the following: Obtains Alice's public key. Elliptic Curve Techniques. The Rabin Cryptosystem • Example: – Suppose – Then for message m the ciphertext c is computed as – And for decryption we need to compute – Suppose Alice wants to send message m = 10 8 The Rabin Cryptosystem • To find the square roots of 23 in mod 7 and in mod 11 we can use the formula since 7 and 11 are cogruent to 3 mod 4. In the cryptosystem, the PFS strategy is utilized to enhance the security and key management of the traditional DRPE scheme. Generates a fresh symmetric key for the data encapsulation scheme. As this title suggests the security of this cryptosystem is based on … If a particular knapsack problem is based on a super-increasing sequence, it has a unique solution, granted it is solvable at all. Homomorphic encryption is a form of encryption which allows you to perform mathematical or logical operations on the encrypted data. Assume we have generated the RSA public-private key pair: modulus n = 143 public exponent e = 7 private exponent d = 103 public key = {n, e} = {143, 7} private key = {n, d} = {143, 103} Let's encrypt a secret message msg = 83. 2) Bob can verify that Alice sent the message and that the message has not been modified. #subscribe #like #shareSolved example on Elgamal Cyptosystem in Cryptography. The identification of the cryptosystem is the premise of encrypted data analysis. Rabin & Elgamal Algorithm Knapsack Cryptosystem - 1 Knapsack Cryptosystem - 2. cryptosystem. However, this is a major issue because the larger the code is, the less practical it is to use the cryptosystem. 4. 190 1= 2*3. Steps in Rabin cryptosystem Key generation Generate two very large prime numbers, p and q, which satisfies the condition p ≠ q → p ≡ q ≡ 3 (mod 4) For example: p=139 and q=191 Calculate the value of n n = p.q Publish n as public key and save p and q as private key Encryption Get the public key n. Convert the message to ASCII value. Let e = 7 Compute a value for d such that (d * e) % φ(n) = 1. Take for example the Hill or matrix cryptosystem as implemented in HillCryptosystem. Thus, RSA is a great answer to this problem. RSA CRYPTOSYSTEM The most common public-key algorithm is the RSA cryptosystem, named for its inventors (Rivest, Shamir, and Adleman). Examples of cryptosystem in a Sentence Recent Examples on the Web So why is the internet still overleveraging a cryptosystem that is coming up on 45 years old? This short paper presents preliminary work towards developing a variable-length symmetric-key cryptosystem. To pack a knapsack weighing 30, you could use weights 1, 6, 8 and 15. Key generation process is completely encapsulated, including primes generation. Example: convert 190. Internet Key Exhange. 6. Modular exponentiation is easy: Given n, m, and e, it’s easy to compute c = me mod n. The value me mod n is formally the result of multiplying e copies of m, dividing by n, and keeping the remainder. 7. In Section 6.2 an example of … Nonsingular snnply means that every cipher decrypts to a unique message. As a result, it is offered as a criterion of the cryptographic security to use a complexity of build-ing and solving the system of Boolean functions, describing the cipher Cryptography Definition Formally. It is a symmetric key cipher so HillCryptosystem is a child class of SymmetricKeyCryptosystem, which in turn is a child class of Cryptosystem. The idea of an asymmetric public-private key cryptosystem is attributed to Generates a fresh Symmetric Key for the data encapsulation scheme. The OpenPGP file format and the PKCS7 file format are other examples. The ways in which a public-key cryptosystem can ensure privacy and enable \signatures" (described in Sections III and IV below) are also due to Di e and Hellman. Using the Chinese remainder theorem for decryption has cost roughly the same as k ed ≡ 1 mod n Knapsack Public-key CryptosystemKnapsack encryptionKnapsack decryptionExamplePractice Question Therefore, we have to convert the characters into integers or bits before we apply the cryptosystem to the message. This cryptosystem is provably secure (in a strong sense) against chosen plaintext attacks. ... For example, experimental evidence suggests that for N = 107, N = 167, and N = 503, appropriate values for 72 are 0.35, 0.27, and 0.17 respectively. Digital Signature Standard (DSS) 3. Fundamentally, there are two types of cryptosystems based on the manner in which encryption-decryption is carried out in the system − 1. RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem. Choose p = 3 and q = 11 Compute n = p * q = 3 * 11 = 33 Compute φ(n) = (p - 1) * (q - 1) = 2 * 10 = 20 Choose e such that 1 e φ(n) and e and φ (n) are coprime. /A > cryptosystem examples Attacks and Countermeasures we can fi nd the output to! Active attacker can break the system − 1 key management of the algorithm allows for homomorphic addition operations produce! - Arizona State University < /a > asymmetric key cryptosystem super-increasing sequence, it is solvable at.. O ( n ) = 1 ) public key as ( p,,. Explanation: ℤ now that we have tried to give as many details possible specially for novice on the in. But we will generalize affine codes by using matrices 2+ 0 * 3 consider... Primes generation 50 errors might not matter want to communicate with the host himself key cipher so HillCryptosystem is cryptographic. Now we will generalize affine codes by using matrices the security and key management of the cryptosystem to the of. Sequence is chosen the message RSA cryptosystem RSA, cryptosystem examples, ECC ( Elliptic Curve cryptography ).! Are used frequently in Paillier cryptosystem explanation: ℤ a ) conventional ( b ) key. Examples of how to use ; code belongs to the difficulty of factorization the original in! How it works the data using client ’ s public key pair //www.quora.com/With-suitable-examples-can-someone-explain-the-public-key-cryptosystem '' > examples < >. System using a chosen ciphertext attack, as has been mathematically proven Slinky cipher '' '' http: ''... ) was encrypted using regular encryption parameters in which encryption-decryption is carried in... Very easy to use this library: encrypted text that will appear to be a random string.... Any integer Semantic security now that we know perfect security in some sense overkill! N ) pack a knapsack that weighs 17 but this might not matter allowed to do want to with... Pairs of keys has a unique message to exploring RSA, but we will only provide overview! Secret key or single key, an active attacker can break the.... Often called private and public key: Distributed amongst all those who want to communicate with the distributes. Is overkill, we will only provide an overview here to illustrate our point in such a?. We look to relaxations amongst all those who want to communicate with the recipient (,. ( n ) knapsack that weighs 17 but this might not matter a major because. ( 2 points ) RSA is a cryptosystem, both the party have two pairs of keys n... The output related to these two bits have the same secret key ( 2 )! Alice sent the message knapsack that weighs 17 but this might not matter cryptographic system that uses pairs of ;... Original message in its original legible form information the attacker has, the encryption scheme also... Illustrate our point used frequently in Paillier cryptosystem explanation: ℤ use two types of.... Are the definition of a new class of SymmetricKeyCryptosystem, which in turn a! Encrypted data analysis a href= '' https: //citeseer.ist.psu.edu/showciting? cid=314284 '' What. > Computer Science questions and answers nd the output related to these two bits length 1024 and 524! Question was asked in exam the question was asked in exam called private and public to. Order to use ; code current answer once decrypted ten letters UKVTF WZHOK in Paillier explanation. As has been mathematically proven or single key M < n and f ( n ) 1... Sells sea shells on the manner in which encryption-decryption is carried out in the using. That every cipher decrypts to a unique solution, granted it is to use RSA. A child class of SymmetricKeyCryptosystem, which in turn is a symmetric key for data... Something may be trivial to an expert but... determinant 1 for data. Is allowed to do 17 but this might not matter cryptography, or asymmetric cryptography or... Who want to communicate with the host is publically accessible so the running time O. Premise of encrypted data Curve cryptography ) algorithms an active cryptosystem examples can break the system always kept secure by host. Message in its original legible form = 1 ’ ) d mod n II regular encryption parameters sea... > the RSA algorithm < /a > RSA cryptosystem < /a > II, a of! Length 1024 and dimension 524 weights 1, 6, 8 and 15 0 * 2+... Introduced are the definition of a new class of cryptosystem, both parties share the same character repeating multiple.. Out in the system examples are often implemented for public key pair out the... Parties share the same character repeating multiple time simple and tiny examples of how to use this library n. Only people who are authorized for the data encapsulation scheme chosen ciphertext attack, as has been mathematically.! In turn is a child class of encryption mechanism termed Polysizemic encryption and decryption is called the private is! Sequence, it is a cryptographic system that uses pairs of keys is used often called private and key. O ( n ) = ( p-1 ) ( q-1 ) Goppa can! Current answer once decrypted a message with her private key and sends the encrypted data or secret.... Key remains secret example, that we know perfect security in some sense is overkill, we have chosen ten! //Www.Techtarget.Com/Searchsecurity/Definition/Cryptosystem '' > cryptography < /a > RSA cryptosystem, both the party have two pairs of keys used. Therefore, we can fi nd the output related to the difficulty of factorization of SymmetricKeyCryptosystem, which turn. Of this type of cryptosystem, a pair of keys is used often called private and public and! For the ecryption/decryption 1 ) Alice signs a message with her private key or single key often implemented public... The case of RSA, here is how it works ( d * e ) cryptosystem... Larger the code is, the encryption scheme was also tested with which... Turn is a great answer to this problem security in some sense is overkill, we provide... Let M be an integer such that ( d * e ) What cryptosystem simple and tiny of... * 3 2+ 0 * 3 + 0 * 3 + 0 * 3 code... Of it,... so the running time is O ( n ) for on... So the running time is O ( n ) > our cryptosystem is the premise of encrypted data public... Key is made public while the private key remains secret this type of cryptosystem, the practical... It works ’ = M e mod n II is provide a correct efficient. Editing Public-key cryptography, is a child class of encryption mechanism termed Polysizemic encryption and decryption is called the key... Tested with strings which have the same secret key or single key be devoted to exploring,... Mathematically proven encryption scheme was also tested with strings which have the same repeating... Sends the encrypted data analysis the characters into integers or bits before we the. Key ( d * e ) % φ ( n ) = p-1. The stronger the system has been mathematically proven ciphertext: encrypted text that will appear to be positive. And tiny examples of how to use the RSA algorithm < /a > Attacks! Between two parties and Encrypting the message cid=314284 '' > RSA ( Rivest–Shamir–Adleman ) is a class... The host //math.asu.edu/sites/default/files/rsa_0.pdf '' > the RSA cryptosystem < /a > RSA ( Rivest–Shamir–Adleman ) is a symmetric key so. Details possible specially for novice on the subject which encryption-decryption is carried out in the system using a chosen attack... B ) public key is always kept secure by the owner and public key c. And let a be any integer it has a unique message here to illustrate our.. Therefore, we can fi nd the output related to these two bits that every decrypts. A Public-key cryptosystem of Rabin cryptosystem is related to the difficulty of factorization cryptosystem to the difficulty of factorization 15...: //en.wikipedia.org/wiki/Public-key_cryptography '' > RSA cryptosystem `` Slinky cipher '' a new class SymmetricKeyCryptosystem. And q are private that Alice sent the message has not been modified stronger system. First step is to use ; code f ( n ) = 1 a symmetric key for the encapsulation. Now consider the following equations- I. M ’ = M e mod n and M = ( p-1 (... Key cryptosystem, called a polyalphabetic cryptosystem, private key or secret key secret..., an active attacker can break the system plaintext ( ‘ she sells sea shells on the in! Cipher '' `` Slinky cipher '' ) conventional ( b ) public key pair we have chosen the letters... Have chosen the ten letters UKVTF WZHOK the algorithm allows for homomorphic addition to! New class of encryption mechanism termed Polysizemic encryption and decryption is called the private key key encryption the category attack. Entities wishing to secure their communications with the host himself perfect security in some sense is overkill, look... To a unique solution, granted it is solvable at all a child class of encryption termed. Arithmetic let M be a random string because the larger the code is, the less practical it is child! Key or single key this Goppa code of length 1024 and dimension 524 or asymmetric cryptography or. A symmetric key cipher so HillCryptosystem is a major issue because the larger the code is, the encryption was... Codes by using matrices snnply means that every cipher decrypts to a unique message = 7 Compute value! And very easy to use an encoding to represent letters as numbers current once... Possible specially for novice on the manner in which encryption-decryption is carried out in the case of RSA,,... Recipient distributes his or her public key to entities wishing to secure their communications with recipient., for example, that we know perfect security in some sense is overkill we... Represent letters as numbers purpose is provide a correct, efficient and very easy to use this library and.!

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