A Different Text Attack Algorithm in Integer Factoring Based Schemes

Text attack in integer factoring based schemes is generally calculated as an intrinsic characteristic of its symmetric attack. In this article, we illustrate that asymmetric integer factoring based schemes are also vulnerable to a text attack. Also, we show that a single message is required to increase a successful text attack versus the Lucas scheme.


INTRODUCTION
The widely employed public key encryption schemes now base their security on the difficulty of the integer factoring problems such as the RSA scheme [1] . Its security based on the difficulty of factoring a modulus which is the product of two large primes. On account of its reputation, the RSA scheme is liable to considerable attacks. Various attacks are relied on the multiplicative inverse [2][3][4] . To conquer this weakness, many ideas are suggested and defeated. Other methods are considered to apply analogues of RSA. This is being the right technique to break the symmetric attack. Thus, encryption relied on Lucas sequences is suggested [5][6] . In this article, we use the Lucas sequences [7][8] to construct the proposed scheme. The Lucas scheme is being intractable versus symmetric attack. Though, the availability of a message forgery that requires two messages [9] . In this article, we introduce a novel text attack algorithm that requires a single message. The proposed attack algorithm illustrate that the integer factoring based schemes are similar to RSA scheme. This means that all attacks are relied on the multiplicative inverse of the RSA scheme and can easily be modified to any RSA based scheme.
Lucas type RSA scheme: we introduce a scheme that relied on Lucas sequences [8] . However, the Lucas scheme can be described as follows. Entity A selects two prime numbers p and q and a public key e which is co-prime to ) 1 The signature is generated correspondingly by swapping the tasks of the public and private keys e and d .
Lucas System: Suppose q p, are both integer numbers, is a non-square, The recurrence function in certain times is employed as another definition of Lucas sequences. As long as multiplication is swappable it tracks that: From this formula and from formula (1) it tracks that: And s g Theorem 1: This theorem contains certain public characteristics of Lucas sequences Proof 1: formula (4) can be proofs as follows: , , Evaluating the coefficients of this formula with (5) and (6). Finding as total of Lucas sequences and evaluating the coefficients demonstrates formulas (7) and (8).
Such that (11) is a result of formula (6) since Therefore Formula (12) is a reference of formula (7). Notice that this attack is an analogue to the message attack on composite modulus introduced in former section, by employing algebraic numbers replace m by + = m g 2 / z and employ formula (1). The only extra step can be verify is that . This can be illustrated by employing formula (6) and noticing that, Then a signature mod . Therefore formula (10) and formula (11) corresponds to the calculation of j w − and formula (12) corresponds to the multiplication of j w − by a m in formula (9).
General modulus attack: Many reports [10][11] stated that the employ of a general composite modulus is risky. Certainly, if a message is transmitted to two entities that have relatively prime public keys, then the message can be decrypted. Since the text attack needs single message, the Lucas type scheme is susceptible to the general modulus attack. We will show this in the following assumption. Suppose

CONCLUSION
We are introduced a different attack method on integer modulus. The new scheme has allowed raising an invulnerable message attack with a single message versus Lucas type scheme. This also verifies that the employ of asymmetric schemes is not really the best method to prevent the attacks.