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The exact cost of the number field sieve algorithm is somewhat fuzzy (the usually quoted complexity is only valid in a log-asymptotic sense). Lenstra and Verheul tried to capture a more usable version of the complexity which has been broadly accepted. For parameter sets of interest the related estimates published by NIST would probably be generally agreed on:...


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Using its notation, the question is about the difficulty of the Discrete Logarithm Problem in a Schnorr Group modulo $P$, of prime order $q$. I'll assume $b^q\bmod P=1$ and $b\bmod P\ne1$. That DLP problem is finding $c$ chosen at random in $[0,q)$ given $P$, $q$, $b$, and $a$ obtained as $b^c\bmod P$. Depending on parameters, the best known algorithms fall ...


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1996 - NTRU patent, 1998 - NTRU article Lattice Attacks 1996 - Lattice attack on the Rump Session of Crypto'96 1997 - Don Coppersmith and Adi Shamir. Lattice attacks on NTRU. In EUROCRYPT, pages 52–61, 1997. No need to find the exact secret key to be able to decrypt 2008 - Nicolas Gama and Phong Q. Nguyen. Predicting lattice reduction. In Proceedings of ...


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Let's have a look at how these are implemented: RSA RSA is probably the example, showing how prime numbers are used in cryptography. In order to calculate a private key, two prime numbers, $p$ and $q$ are "chosen". What that means in practice is that your computer will generate a random number (and set a few bits) and then check whether or not the ...


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For most purposes, your computer generates a random prime. It does this by taking a random odd number and checking whether that's prime. Repeat until such a number has been found. In some cases, it is possible to create cryptographic material with your own, chosen, prime numbers. For example, RSA keys consist of two prime numbers multiplied together. If you ...


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I would think that traffic analysis is a method to do a variety of things and not limited to 'Eavesdropping'. For instance, a network security engineer may conduct traffic analysis to determine if there are any suspicious inbound/outbound traffic in a controlled network. In this case, the purpose is threat detection and not 'Eavesdropping'. On the other hand,...


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The first common modulus attack is described by G. J. Simmons 1983 A ‘weak’ privacy protocol using the RSA crypto algorithm and if there is a common modulus and the public exponents are relatively prime (i.e. $\gcd(e_1,e_2)=1$) then recovering the message is easy ( no factoring). As pointed in section 5 of your linked article; Howgrave-Graham and Seifert’...


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