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60From this value to the private key we deduce how strong the private key which composed of 904 bytes 2048 bits as shown. The algorithm will encrypt the user's passwords by the public key while the private key will be used for decryption purposes using the following code for encryption public function RSA_encrypt data if openssl_public_encrypt data, encrypted this pubkey data base64_encode encrypted else throw new Exception Unable to encrypt data. Perhaps it is bigger than the key size return data In other hand the following codes used for decryption public function RSA_decrypt data if openssl_private_decrypt base64_decode data decrypted this privkey data decrypted else data return data Where openssl_public_encrypt function is used inside RSA_encrypt data function to encrypt data with public key and stores the result into encrypted variable. As well as openssl_private_decrypt function used inside RSA_decrypt data function to decrypt data with private key and stores the result into the decrypted variable. First after the creation of both public and private keys and prepare them using setkey val function. This is followed by compression of the data to be sent in encrypted form which in our case are the passwords for users using the following piece of codes, plaintext, gzcompress plaintext. Then a created system gets the public key of the recipient using a command publicKey, openssl_pkey_get_public public key. Generate the public key for the private key using a command a_key openssl_pkey_get_details publicKey.

The previous operations are completed by segmenting the data user password into small chunks to be encrypted and then combine to send it using the following piece of code while plaintext chunk substr plaintext 0 chunkSize plaintext substr plaintext chunkSize encrypted if openssl_public_encrypt chunk encrypted _SESSION pubKey die. Failed to encrypt data output encrypted encrypted output return encrypted. Where encrypted variable contains the final encrypted data to be sent to the recipient in our case the recipient is SQL database. In other hand the data is decrypted by using the following code steps if openssl_private_decrypt base64_decode data decrypted this privkey data decrypted else data return data. Where data variable contains the final decrypted data to be sent to the recipient in our case the recipient is the data owner who request viewing the stored file in the created cloud system. Modulus ie n is a variable defined by var modulus command, RSA private exponent represented as d and RSA public exponent represented by e so e and d are defined by var exponent command. Primes used for the famous theorem called Chinese Remainder.

Theorem p and q is a variable of type array defined by var primes command Where createKey function creates both public and private pairs during returning variable of type array with the following three attributes. Privatekey variable represent the RSA private key. Publickey variable represent the RSA public key partialkey. A partially processed key used in case if the execution time exceeded the specified time by variable named timeout a partial key passed back to create. Key function as one of the parameter for additional processing. In fact RSA algorithm was chosen to be a secure gate that protects user passwords become famous as One Way Trapdoor function. This is due to the difficulty of encryption and decryption without knowing the value of. Here we come to the question of why we find it difficult to find n the answer is the prime factorization. For example it's easy to find the product of two large prime numbers but it s hard to take a very large product result and factor it to find the 2 primes that compose it such follow prime _1 prime _2 6 700 283. Of course the challenge would be greater if the public key is 2d 2d 2d 2d 2d 42 45 47 49 4e 20 50 55 42 4c 49 43 20 4b 45 59 2d 2d 2d 2d 2d 0d 0a 4d 49 47 66 4d 41 30 47 43 53 71 47 53 49 62 33 44 51 45 42 41 51 55 41 41 34 47 4e 41 44 43 42 69 51 4b 42 67 51 43 71 47 4b 75 6b 4f 31 44 65 37 7a 68 5a 6a 36 2b 48 30 71 74 6a 54 6b 56 78 77 54 43 70 76 4b 65 6e 6f 6f 6e 65 0d 0a 46 50 71 72 69 30 63 62 32 4a 5a 66 58 4a 2f 44 67 59 53 46 36 76 55 70 77 6d 4a 47 38 77 56 51 5a 4b 6a 65 47 63 6a 44 4f 4c 35 55 6c 73 75 75 73 46 6e 63 43 7a 57 42 51 37 52 4b 4e 55 53 65 73 6d 51 52 4d 53 47 6d 6f 6f 6e 2f 0d 0a 33 6a 2b 73 6b 5a 36 55 74 57 2b 35 75 30 39 6c 48 4e 73 6a 36 74 51 35 31 73 31 53 50 72 43 42 6b 65 64 62 4e 66 30 54 70 30 47 62 4d 4a 44 79 52 34 65 39 54 30 34 5a 5a 77 49 44 41 51 43 44 0d 0a 2d 2d 2d 2d 2d 45 4e 44 20 50 55 42 4c 49 43 20 4b 45 59 2d 2d 2d 2d 2d 0d 0a. Is big challenge when we trying to analyze the two numbers composed the previous public key. Finally the RSA has the disadvantage that it slower than symmetric crypto algorithms such as AES. But what supports our policy to choose this slow algorithm is the high level of security and the slow can be forgiven because the user log and encrypt the user data will be mostly once. However compression of encrypted files will relatively eliminate the problem of slow performance in this high security algorithm named RSA.

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