[PDF] Top 20 Factorization of a 1061-bit number by the Special Number Field Sieve
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Factorization of a 1061-bit number by the Special Number Field Sieve
... both sides with up to two large primes allowed on the algebraic side and up to three large primes on the rational side. Sieving was performed over a rectangular region of size 2 16 × 2 15 using the gnfs-lasieve4I16e ... See full document
5
General purpose integer factoring
... prominent factorization achieved with the general number field sieve is still the 1999 factorization of a 512-bit crypt- ographic modulus, in ...latter factorization re- ... See full document
59
FFS Factory: Adapting Coppersmith's "Factorization Factory" to the Function Field Sieve
... However, since both of the above cases are based on NFS, they can only share the computations on the so-called rational side of the algorithm. What we propose here is to leverage the fact that the polynomial selection is ... See full document
16
The Special Number Field Sieve in $\F _{p^{n}}$, Application to Pairing-Friendly Constructions
... z should be B 0 -smooth and squarefree. The second condition implies that only degree one prime ideals will appear in the factorization of (¯ z). This is required since only logarithms of such ideals are computed ... See full document
15
A construction of 3-dimensional lattice sieve for number field sieve over F_{p^n}
... extension field GF(p n ) of char- acteristic p and degree ...the number field sieve over prime field GF(p) ...lattice sieve is often used for a large- scaled experiment of ... See full document
17
Coarse-grained integer - Smooth? Rough? Both!
... our estimates. The black area indicates the best that we could hope for, namely the estimate based merely on Prime number theorem 0.3. However, as this is difficult to evaluate we have to approximate once more. ... See full document
42
Measuring And Securing Cryptographic Deployments
... The Logjam downgrade attack is possible due to a flaw in the TLS protocol (No. 17), along with support in cryptographic deployments for legacy export-grade DHE ciphersuites. Sim- ilar to the downgrade attack of Chapter ... See full document
273
Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field
... In number theory one is concerned about discovering truths about the ring of rational ...studying number theory it does not take long for one to realize how crucial the prime rational integers are to the ... See full document
38
Sun-2_Architecture_Manual_Dec83.pdf
... The page map contains a 20-bit page number field. In conjunction with the 11-bit byte number, the page map thus can generate addresses up to 31-bit physical address bits. The architec[r] ... See full document
30
Special Dio 3-tuples for Pentatope Number
... of Number theory is to discover interesting and unexpected ...& special dio 3-tuples with the property D (n ) for any arbitrary integer n and also for any linear polynomials n ... See full document
5
Special Dio3 Tuples for Pronic Number –I
... CONCLUSION In this paper we have presented a few examples of constructing a special Dio 3-tuples for Pronic number of different ranks with suitable properties.. To conclude one may searc[r] ... See full document
6
Nearly Sparse Linear Algebra and application to Discrete Logarithms Computations
... Abstract. In this article 1 , we propose a method to perform linear algebra on a matrix with nearly sparse properties. More precisely, although we require the main part of the matrix to be sparse, we allow some dense ... See full document
23
Comparison of Efficient Domination Number with Domination Number, Roman Domination Number and Chromatic Number of a Graph
... Let G be a graph. An edge which joins the same vertex is called a loop. An edge that joins two distinct vertices is called a link. If two or more edges of G have the same end vertices, then these edges are called ... See full document
8
On Numerical Evaluation of the Winding Number of a Plane Vector Field
... circle is called winding number or index of the singular point and the value of this number represents the most important property of the vector field F. For example, the knowledge of the index is ... See full document
9
Energy Monthly Statistics 1974 No 2 Special Number
... III - Formation des prix A Allemagne 1 L'importance du marché pétrolier 2 Le cadre réglementaire dans lequel s'établissent les prix 3 La charge fiscale 4 Le mode de relevé des prix 5 Les[r] ... See full document
208
Coal monthly bulletin Special Number/1977
... Andre lande Andare Linder Other countries Autres pays Altri paasi ■ Andara landen Kontoret lor De europæiske F ællesskabers officielle Publikationer - Amt fur amtliche Veröffentl[r] ... See full document
20
Energy Monthly Statistics 1975 No 1 Special Number
... Consommation des huiles de soutes maritimes Taux de c hange marc hé Prix des huiles de soute — fuel-oil lourd 3500" Indice des prix des huiles de soute — fuel-oil lourd 3500" Prix des hu[r] ... See full document
60
Allegory of Lateral Surface Area of A Cube With A Special Number
... entrancing field of ...on number theory 1-5 ...with special numbers 20, 21 ...Octahedral Number and Other Special Numbers is illustrated 22 ... See full document
9
An Approach to Block Based Ciphering Using Bit Wise Calculation for Representation of A Number Using Its Corresponding Perfect Square Number and Position of Prime Number
... the bit stream is to be written in the new ...decimal number and now we have a binary bit stream that is ...new bit stream we will count that the obtained encrypted bit stream that we ... See full document
8
Traps to the BGJT-Algorithm for Discrete Logarithms
... [7] Faruk G¨ ologlu, Robert Granger, Gary McGuire, and Jens Zumbr¨ agel. On the function field sieve and the impact of higher splitting probabilities. In Ran Canetti and Juan A. Garay, editors, CRYPTO, ... See full document
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