RSA algorithm invented three
RSA public key encryption algorithm in 1977 by Ron Rivest, Adi Shamirh and LenAdleman in (MIT) development. RSA to develop their name from the three names. RSA is the most influential public-key encryption algorithm, it can resist all known password attack so far, has been recommended for ISO public key data encryption standard. RSA algorithm is based on number theory a very simple fact: multiplying two large prime numbers is very easy, but when you want to be factoring the product is its extremely difficult, so the product can be open as the encryption key.
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What is a RSA, RSA Security II, RSA speed of about three, RSA's four chosen ciphertext attack, RSA public modulus five attacks, RSA encryption algorithm of the shortcomings of six , has publicly attack
What is the RSA RSA algorithm can be used for both the first encryption and digital signature algorithms, but also easy to understand and operate. RSA is the most widely studied public key algorithm, which made nearly two decades now, through the various attacks the test, was gradually accepted, generally considered the best public key is one of the options. RSA's security relies on the factorization of large numbers, but not theoretically prove the difficulty of deciphering the RSA and the difficulty of large integer equivalent. RSA's major flaw is that in theory can not grasp how the performance of its security and passwords, many academics are not the NPC tends to factorization problems. RSA's drawbacks are: A) the key generation is in trouble, by the prime number generation technology limitations, making it difficult to do once a secret. B) packet size too large, to ensure the security, n at least 600 bits or more, so that costly operation, especially the slower, slower than the symmetric encryption algorithm is orders of magnitude; and technology development with the decomposition of large numbers This length is increasing, is not conducive to standardization of data formats. Currently, SET (Secure Electronic Transaction) protocol requested by CA's key 2048 bits long, the other entity to use 1024-bit key. C) RSA key length increase with the level of confidentiality to increase rapidly. The following table lists the same security level corresponding to the key length. Level of confidentiality symmetric key length (bit) RSA key length (bit) ECC key length (bit) secret life of 80801024160201011211220482242030128128307225620401 9219276803842080256256153605122120 this algorithm appeared in 1978, it was the first not only for data encryption can also be used for digital signature algorithm. It is easy to understand and operate, and very popular. Algorithm, named after the name of the inventor: Ron Rivest, AdiShamir and Leonard Adleman. As early as 1973, the British mathematician State Administration of Communications Clifford Cocks discovered a similar algorithm. But his findings were classified as top secret, made public until 1998. RSA algorithm is an asymmetric cryptographic algorithm, the so-called non-symmetric, meaning that the algorithm requires a pair of keys, using one of the encryption, you need to be decrypted with another. RSA algorithm involves three parameters, n, e1, e2. Where, n is the two large prime numbers p, q of the product, n when the binary representation of the number of bits occupied, is called the key length. e1 and e2 are a pair of related values, e1 free to take, but asked e1 and (p-1) * (q-1) prime; choose e2, requirements (e2 * e1) mod ((p-1) * (q-1)) = 1. (N and e1), (n and e2) is the key pair. RSA encryption and decryption algorithms are identical, as expressly set A, B for the ciphertext, then: A = B ^ e1 mod n; B = A ^ e2 mod n; e1 and e2 can be used interchangeably, namely: A = B ^ e2 mod n; B = A ^ e1 mod n; a, RSA Security RSA's security relies on the decomposition of large numbers, but is equivalent to the decomposition of large numbers has not been proved theoretically,
air force 1 high, because there is no proof to crack RSA will need to make large integer. Assuming the existence of a large number of the algorithm without decomposition, then it is certainly a large number decomposition algorithm can be modified. Currently, RSA algorithm for a number of variants have been proved equivalent to the decomposition of large numbers. Anyway, decomposition n is the most obvious method of attack. Now, it has been able to break down a large number of decimal places prime. Therefore, the modulus n must be selected larger, due to the specific case may be. Second, RSA's speed as a result of large numbers are calculated, making the fastest RSA case several times slower than DES, either software or hardware. RSA has been the defect rate. Generally used only for small amounts of data encryption. Faster than RSA, the security level corresponding to the same symmetric encryption algorithm is about 1000 times slower. Third, RSA's RSA chosen ciphertext attack in front of the chosen ciphertext attack is very fragile. General information about the attacker is a camouflage for what (Blind),
air force one low nike, so that the entity has the private key to sign. Then, it can be obtained by calculating the desired information. In fact, the attacks are using the same weakness, namely, the existence of such a fact: the power retained by the multiplication of the input structure: (XM) ^ d = X ^ d * M ^ d mod n As mentioned earlier, the inherent questions from the public key cryptography system is the most useful feature - everyone can use the public key. However, the algorithms can not solve this problem,
nike air force one low, there are two main measures: one is the use of a good public key protocols to ensure the work of other entities, during the entity does not decrypt any of the information generated, and do not know anything about the information their own signature; the other is not a random document sent to strangers signature, signature One-Way HashFunction the first to use the document as a HASH processing, or use a different signature algorithm. IV, RSA public modulus attack if the system is there a module, but different people have different e and d, the system will be dangerous. The most common is the same information in different public key encryption, the public and common-mode coprime, then the message without the private key can be restored. Let P for information specifically, the two encryption keys for the e1 and e2, is the public modulus n, is: C1 = P ^ e1 mod n C2 = P ^ e2 mod n cryptanalysis knows n, e1, e2, C1 and C2, will be able to get P. E1 and e2 for each quality, so use Euclidean algorithm to find r and s, satisfy: r * e1 + s * e2 = 1 Suppose r is negative, then Euclidean algorithm to calculate the required C1 ^ (-1), then (C1 ^ (-1)) ^ (-r) * C2 ^ s = P mod n addition, there are several other attacks using the method of public modulus. In short, if you know the model number of a given pair of e and d, one is conducive to modular decomposition of the attacker, the attacker first calculate the benefit of other pairs of e 'and d', without having to break modulus. There is only one solution, that is not shared modulus n. Small exponent attack RSA. There is a proposal to improve the speed RSA public key e is to take a smaller value, it would become easy to implement encryption, the speed increased. But doing so is unsafe way to deal with e and d are taking a larger value. V., RSA encryption algorithm disadvantage 1) generate keys is cumbersome, subject to the restrictions prime number generation technology, making it difficult to do once a secret. 2) security, RSA's security relies on the factorization of large numbers,
air force one low, but not theoretically prove the difficulty of deciphering the RSA and the difficulty of large integer equivalent, and passwords, many academics are not the NPC tends to factorization problems. Currently, more than 140 people have been able to break down large prime numbers in decimal places, which requires the use of longer keys, more slowly; addition, the current attacks on RSA that people are actively looking for ways, such as the chosen ciphertext attack, the attacker usually is to make certain information about camouflage (Blind),
nike air force one high, so that the entity has the private key to sign. Then, it can be obtained by calculating the desired information. In fact, the attacks are using the same weakness, namely, the existence of such a fact: the power retained by the multiplication of the input structure: (XM) d = Xd * Md mod n As mentioned earlier, the inherent problem stems from the public key cryptosystem of the most useful feature - everyone can use public key. However, the algorithms can not solve this problem, there are two main measures: one is the use of a good public key protocols to ensure the work of other entities, during the entity does not decrypt any of the information generated, and do not know anything about the information their own signature; the other is not a random document sent to strangers signature, signature the first to use One-Way Hash Function HASH document for processing, or the simultaneous use of different signature algorithms. In addition to use of public module, it also attempts to decrypt the index number of the use or φ (n), etc. attacks. 3) is too slow, due to RSA packet size too large, to ensure the security, n at least 600 bitx more, so that costly operation, especially the slower, slower than the symmetric encryption algorithm is orders of magnitude; and technology development with the decomposition of large numbers, the length is still increasing,
nike air force one, is not conducive to standardization of data formats. Currently, SET (Secure Electronic Transaction) protocol requested by CA's key 2048 bits long, the other entity to use 1024-bit key. In order to speed problem is the widespread use of single, combined with public key cryptography methods, strengths and weaknesses complement each other: single key password encryption speed, longer people use it to encrypt files, and then to a file with the RSA key encryption, a very good solution of a single key cryptography the key distribution problem. Sixth, has publicly attack the most popular method of attack against RSA is generally based on factoring large numbers. In 1999, RSA-155 (512 bits) was successfully decomposed, spent five months (about 8000 MIPS years) and 224 CPU hours on a central memory have 3.2G done on the computer Cray C916. In 2002, RSA-158 was successful factorization. Atlas Atlas entry for more extended reading: 1
RSA asymmetric encryption of some unconventional applications
http://www.icylife.net/yunshu/show.php?id=471
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RSA explanation
http://hi.baidu.com/yhgzi/blog/item/...5f7365431.html
3
http://www.cngr.cn/article/60/402/2006/2006071947799_3 . shtml
Open Category: Internet, IT, computers, algorithms, encryption
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