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Symmetric and asymmetric encryption
 ACM Computing Surveys
, 1979
"... All cryptosystems currently m use are symmetrm m the sense that they require the transmitter and receiver to share, m secret, either the same pmce of reformation (key) or one of a paLr of related keys easdy computed from each other, the key is used m the encryption process to introduce uncertainty t ..."
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All cryptosystems currently m use are symmetrm m the sense that they require the transmitter and receiver to share, m secret, either the same pmce of reformation (key) or one of a paLr of related keys easdy computed from each other, the key is used m the encryption process to introduce uncertainty to an unauthorized receiver. Not only is an
A Knapsack Cryptosystem Based on The Discrete Logarithm Problem By
"... Abstract This paper introduces a knapsack cryptosystem based on the problem of discrete logarithm. The proposed algorithm obtains the public knapsack values by finding the discrete logarithms of the secret knapsack ones. Also, it encrypts the message block by obtaining its binary bits and then comp ..."
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Abstract This paper introduces a knapsack cryptosystem based on the problem of discrete logarithm. The proposed algorithm obtains the public knapsack values by finding the discrete logarithms of the secret knapsack ones. Also, it encrypts the message block by obtaining its binary bits and then computing the modular multiplication of the public knapsack values corresponding to the 1bits of the binary form. The decryption is done by obtaining the inverse of the discrete logarithm of the encrypted message. The computation of this inverse is known inverse is known to be a hard problem. The block length is as the same as the knapsack length. The paper discusses the security issues of the system.
How to Choose Secret Parameters for RSA and its Extensions to Elliptic Curves
, 2001
"... Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA and its extensions to elliptic curves. Over elliptic curves, the analysis is more di#cult because ..."
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Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA and its extensions to elliptic curves. Over elliptic curves, the analysis is more di#cult because the underlying groups are not always cyclic.
How to Choose Secret Parameters for RSAtype Cryptosystems over Elliptic Curves
, 1997
"... . Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSAtype cryptosystems over elliptic curves. The analysis is more difficult because the underlying grou ..."
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. Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSAtype cryptosystems over elliptic curves. The analysis is more difficult because the underlying groups are not always cyclic. Previous papers suggested the use of strong primes in order to prevent factoring attacks and cycling attacks. In this paper, we only focus on cycling attacks because for both RSA and its elliptic curvebased analogues, the length of the RSAmodulus n is typically the same. Therefore, a factoring attack will succeed with equal probability against all RSAtype cryptosystems. We also prove that cycling attacks reduce to find fixed points, and derive a factorization algorithm which (most probably) completely breaks RSAtype systems over elliptic curves if a fixed point is found. Keywords: RSAtype cryptosystems, Cycling attacks, Elliptic curves, Strong primes. 1. Introd...
BIT 19 (1979k 27~275 CRITICAL REMARKS ON "CRITICAL REMARKS ON SOME PUBLICKEY
"... Cryptosystems", [5] suggests a method for attacking the RSA publickey cryptosystem. In this note we show that Herlestam's proposed attack is highly impractical, and that his analysis is erroneous. The RSA cryptosystem [1] encodes a message M using the key (e,n) via the equation: (1) C = ..."
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Cryptosystems", [5] suggests a method for attacking the RSA publickey cryptosystem. In this note we show that Herlestam's proposed attack is highly impractical, and that his analysis is erroneous. The RSA cryptosystem [1] encodes a message M using the key (e,n) via the equation: (1) C = E~(M) M e (modn). Here the original message M and the ciphertext C are considered as integers in the range 0 to n 1. The integer n is the product of two large prime numbers p and q. The integer e is relatively prime to (p1)(q1). To decrypt a received ciphertext C the recipient computes (2) M Dd,(M) C d (modn) where d is chosen to satisfy the equation de 1 (modlcm(pl,q1)). The attack proposed by Herlestam runs as follows: Let P(x) be a polynomial in x such that