Discrete logarithm

This paper proposes methods for developing digital signature scheme based on the difficulty of the discrete logarithm problem. From the establishment of overview scheme, some digital signature schema have been proposed for practical applications.
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Using a recent idea of Gaudry and exploiting rational representations of algebraic tori, we present an index calculus type a lgorithm for solving the discrete logarithm problem that works directly in these groups.
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(BQ) Part 2 book "Introduction to modern cryptography" has contents: Number theory and cryptographic hardness assumptions, factoring and computing discrete logarithms, private key management and the public key revolution, digital signature schemes,....and other contents.
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TRAPDOOR ONEWAY FUNCTIONThe main idea behind asymmetrickey cryptography is the concept of the trapdoor oneway function. TrapdoorOneWayFunction(TOWF) OneWayFunction(OWF) 1.fiseasytocompute. 2. f −1 is difficult to compute. 3. Given y and a trapdoor, x can be computed easily.
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USE OF MODERN BLOCK CIPHERS Symmetrickey encipherment can be done using modern block ciphers. Modes of operation have been devised to encipher text of any size employing either DES or AES. Error Propagation A single bit error in transmission can create errors in several in the corresponding block.
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USE OF MODERN BLOCK CIPHERS Symmetrickey encipherment can be done using modern block ciphers. Modes of operation have been devised to encipher text of any size employing either DES or AES. 1 USE OF MODERN BLOCK CIPHERS Electronic codebook (ECB) mode Error Propagation A single bit error in transmission can create errors in several in the corresponding block. However, the error does not have any effect on the other blocks.
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How many padding bits must be added to a message of 100 characters if 8bit ASCII is used for encoding and the block cipher accepts blocks of 64 bits? Suppose that we have a block cipher where n = 64. If there are 10 1’s in the ciphertext, how many trialanderror tests does Eve need to do to recover the plaintext from the intercepted ciphertext in each of the following cases?
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How many padding bits must be added to a message of 100 characters if 8bit ASCII is used for encoding and the block cipher accepts blocks of 64 bits? 1 MODERN BLOCK CIPHERS Substitution or Transposition ? To be resistant to exhaustivesearch attack, a modern block cipher needs to be designed as a substitution cipher. Suppose that we have a block cipher where n = 64. If there are 10 1’s in the ciphertext, how many trialanderror tests does Eve need to do to recover the plaintext from the intercepted ciphertext in each of the following cases? a. The cipher is designed as a...
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This paper presents an approach related to authenticate mutually a RFID (Radio Frequency Identification) tag from a RFID reader by using the cryptography based on Elliptic curve. Our proposal mutual authentication lies on the Elliptic curve discrete logarithm problem, which is considered the core in order to fight against all of attacks like replay attack, forgery attack and maninthemiddle attack. Scientifically, we prove not only the accuracy and the security of our approach, but also its performance in the mutual authentication between a RFID tag and a reader. ...
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The paper discusses the implementation of ECC on two finite fields, prime field and binary field. It also gives an overview of ECC implementation on different coordinate systems called the projective coordinate systems.
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The paper gives an introduction to elliptic curve cryptography (ECC) and how it is used in the implementation of digital signature (ECDSA) and key agreement (ECDH) Algorithms. The paper discusses the implementation of ECC on two finite fields, prime field and binary field.
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The Digital Signature Algorithm (DSA) was speciﬁed in a U.S. Government Federal Information Processing Standard (FIPS) called the Digital Signature Standard (DSS [70]).
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THE recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signaltonoise ratio has intensified the interest in a general theory of communication. A basis for such a theory is contained in the important papers of Nyquist1 and Hartley2 on this subject. In the present paper we will extend the theory to include a number of new factors, in particular the effect of noise in the channel, and the savings possible due to the statistical structure of the original message and due to the nature of the final destination of the information....
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14 Exponential functions, continuous growth and differential equations Use the exponential function and natural logarithms to derive the ﬁnal sum, initial sum and growth rate when continuous growth takes place. Compare and contrast continuous and discrete growth rates.
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Topological Hochschild homology and localization 2. The homotopy groups of T (AK) 3. The de RhamWitt complex and TR· (AK; p) ∗ 4. Tate cohomology and the Tate spectrum 5. The Tate spectral sequence for T (AK) 6. The prosystem TR· (AK; p, Z/pv ) ∗ Appendix A. Truncated polynomial algebras References Introduction In this paper we establish a connection between the Quillen Ktheory of certain local ﬁelds and the de RhamWitt complex of their rings of integers with logarithmic poles at the maximal ideal.
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