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Quadratic orders for NESSIE  Overview and parameter sizes of three public key families
, 2000
"... . In the scope of the European project NESSIE 1 there was issued a Call for Cryptographic Primitives [NESSIE] soliciting proposals for block ciphers, stream ciphers, hash functions, pseudorandom functions and public key primitives for digital signatures, encryption and identification. Since ..."
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. In the scope of the European project NESSIE 1 there was issued a Call for Cryptographic Primitives [NESSIE] soliciting proposals for block ciphers, stream ciphers, hash functions, pseudorandom functions and public key primitives for digital signatures, encryption and identification. Since the security of all popular puplic key cryptosystems is based on unproven assumptions and therefore nobody can guarantee that schemes based on factoring or the computation of discrete logarithms in some group, like the multiplicative group of a finite field or the jacobian of (hyper) elliptic curves over finite fields, will stay secure forever, it is especially important to provide a variety of different primitives and groups which may be utilized if a popular class of cryptosystems gets broken. In this work we propose three different public key families based on the discrete logarithm problem in quadratic orders to be considered for NESSIE. The two families based on (maximal) real...
About Generic Conversions from any Weakly Secure Encryption Scheme into a ChosenCiphertext Secure Scheme
 In Proceedings of the Fourth Conference on Algebraic Geometry, Number Theory, Coding Theory and Cryptography
, 2001
"... Abstract. Since the appearance of publickey cryptography in the seminal DiffieHellman paper, many schemes have been proposed, but many have been broken. Indeed, for many people, the simple fact that a cryptographic algorithm withstands cryptanalytic attacks for several years is considered as a kin ..."
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Abstract. Since the appearance of publickey cryptography in the seminal DiffieHellman paper, many schemes have been proposed, but many have been broken. Indeed, for many people, the simple fact that a cryptographic algorithm withstands cryptanalytic attacks for several years is considered as a kind of validation. But some schemes took a long time before being widely studied, and maybe thereafter being broken. A much more convincing line of research has tried to provide “provable ” security for cryptographic protocols, in a complexity theory sense: if one can break the cryptographic protocol, one can efficiently solve the underlying problem. Unfortunately, very few practical schemes can be proven in this socalled “standard model ” because such a security level rarely meets with efficiency. A convenient way to achieve some kind of validation of efficient schemes has been to identify some concrete cryptographic objects with ideal random ones: hash functions are considered as behaving like random functions, in the socalled “random oracle model”, and groups are used as blackbox groups, in which one has to ask for additions to get new elements, in the socalled “generic model”. In this paper we present some generic designs for asymmetric encryption with provable security in the random oracle model.
The ThreeLargePrimes Variant of the Number Field Sieve
"... The Number Field Sieve (NFS) is the asymptotically fastest known factoring algorithm for large integers. This method was proposed by John Pollard [20] in 1988. Since then several variants have been implemented with the objective of improving the siever which is the most time consuming part of this ..."
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The Number Field Sieve (NFS) is the asymptotically fastest known factoring algorithm for large integers. This method was proposed by John Pollard [20] in 1988. Since then several variants have been implemented with the objective of improving the siever which is the most time consuming part of this method (but fortunately, also the easiest to parallelise). Pollard's original method allowed one large prime. After that the twolargeprimes variant led to substantial improvements [11]. In this paper we investigate whether the threelargeprimes variant may lead to any further improvement. We present theoretical expectations and experimental results. We assume the reader to be familiar with the NFS.
Comments on the Transition Paper
"... Hi, I am reading the document and was wondering what distinguishes "data authentication" from "entity authentication". For example, when IKE applies a signature it is certainly doing entity authentication but it is also signing data, for example, negotiated algorithms. As another example, is a signa ..."
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Hi, I am reading the document and was wondering what distinguishes "data authentication" from "entity authentication". For example, when IKE applies a signature it is certainly doing entity authentication but it is also signing data, for example, negotiated algorithms. As another example, is a signature in a certificate "entity authentication " or "data authentication"? A clue to what you mean by differentiating between the two cases seems to be the following text in page 5: "signature verification for entity authentication is performed immediately after signature generation; therefore. there is no requirement to retain a signature for later verification. " Would I be correct to say that the actual differeniation you are doing is between signatures with longterm verification needs and those with shortterm (or ephemeral) needs? This may still require an understanding of what is shortterm and longterm (*) but still
Natarajan Vijayarangan, TCS Innovation Labs.................................................................18
"... Hi, I am reading the document and was wondering what distinguishes "data authentication" ..."
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Hi, I am reading the document and was wondering what distinguishes "data authentication"
Contemporary Cryptology Birkhäuser Verlag Basel • Boston • BerlinAuthors:
"... Département d’Informatique ..."
Factorization of a 1061bit number by the Special Number Field Sieve
, 2012
"... I provide the details of the factorization of the Mersenne number 2 1061 − 1 by the Special Number Field Sieve. Although this factorization is easier than the completed factorization of RSA768, it represents a new milestone for factorization using publicly available software. 1 ..."
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I provide the details of the factorization of the Mersenne number 2 1061 − 1 by the Special Number Field Sieve. Although this factorization is easier than the completed factorization of RSA768, it represents a new milestone for factorization using publicly available software. 1
Number Theory and PublicKey Cryptography
"... Abstract. For a long time, cryptology had been a mystic art more than a science, solving the confidentiality concerns with secret and private techniques. Automatic machines, electronic and namely computers modified the environment and the basic requirements. The main difference was the need of publi ..."
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Abstract. For a long time, cryptology had been a mystic art more than a science, solving the confidentiality concerns with secret and private techniques. Automatic machines, electronic and namely computers modified the environment and the basic requirements. The main difference was the need of public mechanisms to allow largescale communications with just a small secret shared between the interlocutors, but that furthermore resist against adversaries with more powerful computers. Unfortunately, the security remained heuristic: with a permanent fight between designers (the cryptographers) and breakers (the cryptanalysts). In 1976, Diffie and Hellman claimed the possibility of achieving confidentiality between two people without any common secret information. However, they needed quite new objects: (trapdoor) oneway functions. Hopefully, mathematics, with algorithmic number theory, have been realized to provide such objects. A new direction in cryptography was under investigations: asymmetric cryptography and provable security. In this paper we review the main problems that cryptography tries to solve, and how it achieves these goals thanks to the algorithmic number theory. After a brief history of the ancient and conventional cryptography, we review the DiffieHellman’s suggestion with the apparent paradox. Then, we survey the solutions based on the integer factorization or the discrete logarithm, two problems that nobody knows how to efficiently solve.