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Are `Strong' Primes Needed for RSA?
 In The 1997 RSA Laboratories Seminar Series, Seminars Proceedings
, 1999
"... We review the arguments in favor of using socalled "strong primes" in the RSA publickey cryptosystem. There are two types of such arguments: those that say that strong primes are needed to protect against factoring attacks, and those that say that strong primes are needed to protect against "cy ..."
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We review the arguments in favor of using socalled "strong primes" in the RSA publickey cryptosystem. There are two types of such arguments: those that say that strong primes are needed to protect against factoring attacks, and those that say that strong primes are needed to protect against "cycling" attacks (based on repeated encryption).
Verifiable Escrowed Signature
, 1997
"... . We combine a publicly verifiable encryption technique and a Schnorr type signature scheme to achieve a verifiable escrowed signature scheme. The scheme allows a signer to convince a verifier the validity of a signature without letting him see the signature value. The unavailable but verifiable sig ..."
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. We combine a publicly verifiable encryption technique and a Schnorr type signature scheme to achieve a verifiable escrowed signature scheme. The scheme allows a signer to convince a verifier the validity of a signature without letting him see the signature value. The unavailable but verifiable signature is encrypted under a public key of someone (e.g., a trusted third party) who stays offline. The technique will have useful applications in such as fair exchange of contracts between two untrusted parties without using online help of a commonly trusted third party, and fair escrow cryptosystems using offline escrow agents. 1 Introduction In [14], Stadler presented a publicly verifiable encryption (PVE) technique that allows to verifiably encrypt the discrete logarithm of a known value. In other words, Alice (prover) sends to Bob (verifier) a value V and ciphertext C which encrypts a plaintext message under someone's public key (of course, other than the verifier's); Alice can convi...
Atkin's test: news from the front
 In Advances in Cryptology
, 1990
"... We make an attempt to compare the speed of eeme primality testing algorithms for certifying loodigit prime numbers. 1. Introduction. The ..."
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We make an attempt to compare the speed of eeme primality testing algorithms for certifying loodigit prime numbers. 1. Introduction. The
DISTRIBUTED PRIMALITY PROVING AND THE PRIMALITY OF (2^3539+ 1)/3
, 1991
"... We explain how the Elliptic Curve Primality Proving algorithm can be implemented in a distributed way. Applications are given to the certification of large primes (more than 500 digits). As a result, we describe the successful attempt at proving the primality of the lO65digit (2^3539+ l)/3, the fir ..."
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We explain how the Elliptic Curve Primality Proving algorithm can be implemented in a distributed way. Applications are given to the certification of large primes (more than 500 digits). As a result, we describe the successful attempt at proving the primality of the lO65digit (2^3539+ l)/3, the first ordinary Titanic prime.
Secure Computations on Handheld Devices with the Help of an Untrusted Server
 Server. The 7th World Multiconference on Systemics, Cybernetics and Informatics (SCI 2003
, 2003
"... Recently, handheld devices have become one of the most popular computing tools. Although handheld devices are able to perform anything that a PC can do, their lack of computing power makes it next to impossible to perform some heavy calculations. Hence it appears very useful to have a combination of ..."
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Recently, handheld devices have become one of the most popular computing tools. Although handheld devices are able to perform anything that a PC can do, their lack of computing power makes it next to impossible to perform some heavy calculations. Hence it appears very useful to have a combination of a handheld with a PC, where the PC can perform heavy calculations to assist the handheld. However, we must be assured that the PC will not have learnt anything from the interaction. In this paper, we show two schemes which involve some serveraided computation where the server has not learnt anything from the interaction with the handheld device. The first scheme is to generate a strong prime number in a handheld, which can be used as a candidate for the RSA algorithm. The second scheme is to allow the server to behave as an authentication oracle on behalf of the handheld. The handheld will prepare a message that needs to be authenticated by sending it to the server in a blinded form, so that the server will not learn about the message. On the other hand, the handheld will not learn about the server's secret.
Short Signatures from Difficulty of Factorization Problem
"... New ways are proposed to design short signature schemes based on difficulty of factorizing a composite number n that is a product of two large secret primes. The paper presents digital signature schemes in which the signature represents a pair of numbers (k, g) and its length is reduced to 320 bits ..."
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New ways are proposed to design short signature schemes based on difficulty of factorizing a composite number n that is a product of two large secret primes. The paper presents digital signature schemes in which the signature represents a pair of numbers (k, g) and its length is reduced to 320 bits providing security of the RSA cryptosystem with 1024bit modulus.
Pseudoprimes: A Survey Of Recent Results
, 1992
"... this paper, we aim at presenting the most recent results achieved in the theory of pseudoprime numbers. First of all, we make a list of all pseudoprime varieties existing so far. This includes Lucaspseudoprimes and the generalization to sequences generated by integer polynomials modulo N , elliptic ..."
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this paper, we aim at presenting the most recent results achieved in the theory of pseudoprime numbers. First of all, we make a list of all pseudoprime varieties existing so far. This includes Lucaspseudoprimes and the generalization to sequences generated by integer polynomials modulo N , elliptic pseudoprimes. We discuss the making of tables and the consequences on the design of very fast primality algorithms for small numbers. Then, we describe the recent work of Alford, Granville and Pomerance, in which they prove that there
Enjeux Et Avancées De La Théorie Algorithmique Des Nombres
, 1992
"... Introduction L'apparition des syst`emes de chiffrement `a clefs publiques de fa¸con g'en'erale [DH76], et du syst`eme de chiffrement RSA en particulier [ARS78], a caus'e un regain d'int'eret pour la th'eorie des nombres et en particulier l'arithm'etique dans ses aspects calculatoires. Pour r'epondr ..."
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Introduction L'apparition des syst`emes de chiffrement `a clefs publiques de fa¸con g'en'erale [DH76], et du syst`eme de chiffrement RSA en particulier [ARS78], a caus'e un regain d'int'eret pour la th'eorie des nombres et en particulier l'arithm'etique dans ses aspects calculatoires. Pour r'epondre `a des questions aussi simples que celles concernant la d'ecomposition des nombres en facteurs premiers, il a fallu donner des r'eponses algorithmiques prenant en compte la faisabilit'e des calculs ainsi que le temps imparti pour donner une r'eponse satisfaisante. Cela a provoqu'e l'essor de la th'eorie algorithmique des nombres. Cet expos'e est destin'e `a mettre en lumi`ere les progr`es accomplis depuis une dizaine d'ann'ees dans les domaines de la primalit'e des entiers (comment peuton prouver qu'un entier de quelques centaines de chiffres d'ecimaux est premier) ; factorisation des entiers (quels sont les facteurs d'un nombre qui n'est pas premier) ; logarithme
unknown title
"... The literature of cryptography has a curious history. Secrecy, of course, has always played a central role, but until the First World War, important developments appeared in print in a more or less timely fashion and the field moved forward in much the same way as other specialized disciplines. As l ..."
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The literature of cryptography has a curious history. Secrecy, of course, has always played a central role, but until the First World War, important developments appeared in print in a more or less timely fashion and the field moved forward in much the same way as other specialized disciplines. As late as 1918, one of the most influential cryptanalytic papers of the twentieth century, William F. Friedman’s monograph The Index of Coincidence and Its Applications in Cryptography, appeared as a research report of the private Riverbank Laboratories [577]. And this, despite the fact that the work had been done as part of the war effort. In the same year Edward H. Hebern of Oakland, California filed the first patent for a rotor machine [710], the device destined to be a mainstay of military cryptography for nearly 50 years. After the First World War, however, things began to change. U.S. Army and Navy organizations, working entirely in secret, began to make fundamental advances in cryptography. During the thirties and forties a few basic papers did appear in the open literature and several treatises on the subject were published, but the latter were farther and farther behind the state of the art. By the end of the war the transition was complete. With one notable exception, the public literature had died. That exception was Claude Shannon’s paper “The Communication Theory of Secrecy Systems, ” which
Cryptoschemes Based on Difficulty of Simultaneous Solving Two Different Difficult Problems ∗
"... The paper proposes a general method for construction cryptoschemes based on difficulty of simultaneous solving factoring (FP) and discrete logarithm modulo prime problem (DLpP). The proposed approach is applicable for construction digital signatures (usual, blind, collective), public key encryption ..."
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The paper proposes a general method for construction cryptoschemes based on difficulty of simultaneous solving factoring (FP) and discrete logarithm modulo prime problem (DLpP). The proposed approach is applicable for construction digital signatures (usual, blind, collective), public key encryption algorithms, public key distribution protocols, and cryptoschemes of other types. Moreover, the proposed approach provides reducing the signature size and increasing the rate of the cryptoschemes, while comparing with the known designs of the digital signature protocols based on the FP and DLpP.