Dear all, We are pleased to announce a new computation of a discrete logarithm modulo a 180 digit (596-bit) prime using the number field sieve algorithm. Previous records are 130-digit (431-bit), 135-digit (448 bits) and 160-digit (530-bit) primes (see [1], [2] and [3]). We chose the following module: p = RSA180 + 625942 = 191147927718986609689229466631454649812986246276667354864188503638\ 807260703436799058776201365135161278134258296128109200046702912984\ 568752800330221777752773957404540495707852046983 such that ell=(p-1)/2 is prime too. The element g=5 is a generator of the multiplicative group mod p. The "random" element for which we computed the logarithm is: rsa1024 = 135066410865995223349603216278805969938881475605667027524485\ 143851526510604859533833940287150571909441798207282164471551\ 373680419703964191743046496589274256239341020864383202110372\ 958725762358509643110564073501508187510676594629205563685529\ 475213500852879416377328533906109750544334999811150056977236\ 890927563 The result is: logrsa1024 = 138670566126823584879625861326333326312363943825621039220\ 215583346153783336272559955521970357301302912046310782908\ 659450758549108092918331352215751346054755216673005939933\ 186397777 Polynomial selection: This step was performed using Kleinjung's algorithm. The computation took around 2 core-months (2-GHz Intel E5-2650) and we have selected the two following polynomials: f(x) = 17153280*x^5 + 55645402596756*x^4 + 289642429100355466945*x^3 -5839034183672356481708253628*x^2 -3489195459822344127350367941464660*x -24774668987371397084528618164507418928 g(x) = 633287365084897327346023*x - 25668325089522756076511361508720291 Sieving: Relations were generated by lattice sieving. Algebraic and rational primes below 800M were sieved and we allowed 2 large primes less than 2^29 on the rational side and 3 large primes less than 2^30 on the algebraic side. We sieved over special-q's between 80M and 380M. The sieving generated 253M relations and took around 49.5 core-years (2-GHz Intel E5-2650) Filtering: In the 253M relations, there were 175M unique relations. The filtering step produced a final matrix of 7.28M rows. The computation time is equivalent to 5 hours on one core (2-GHz Intel E5-2650). Computing the Schirokauer maps took 0.9 core-year (2-GHz Intel E7540). Linear algebra: The linear algebra is modulo the 595-bit prime ell=(p-1)/2. The matrix contains 7.28M rows and columns with an average weight of 150 non-zero coefficients per row. The matrix contains also 4 dense Schirokauer maps columns, whose elements are modulo ell. We could consider only 3 Schirokauer maps columns. The linear algebra was solved using the Block Wiedemann algorithm with the blocking parameters m=24,n=12. The computation was run on a 768-core cluster that contains 48 nodes connected with FDR Infiniband. Each node hosts two 2-GHZ 8-core Intel Xeon E5-2650 processors. We have run 12 sequences in parallel, each running over 4 cores. The scalar products and the evaluation phases required 38 days (around 80 core years). The linear generator phase took 15 hours on 144 cores (around 0.25 core year). Once the linear algebra finished, we obtained the logarithms for many small primes: log2 = 143947424249804046894686521225835011553404529825698596989394995\ 375091895197189866520496832751897255017764700065133297734751766\ 543876760760613084110998852530852594071731064764347608 log3 = 125402553747091869459488367561520716928144625407579598051736139\ 492527074873860357866906935921636923016180989364604005475590952\ 635245779460745381246844568885972683224283333939126584 Individual logarithm: It was calculated by special-q descent. Computing one individual logarithm required a few hours. Most of the code we used is freely available as part of the cado-nfs software project (see [4]). More details on the algorithms we used for the filtering and the linear algebra are described in the papers [5] and [6]. Best regards, Cyril Bouvier, Pierrick Gaudry, Laurent Imbert, Hamza Jeljeli and Emmanuel Thomé. [1] Antoine Joux and Reynald Lercier. Discrete logarithms in GF(p) --- 130 digits. E-mail to the NMBRTHRY mailing list; http://listserv.nodak.edu/archives/nmbrthry.html, June 2005. [2] Andrey Dorofeev, Denis Dygin and Dmitry Matyukhin. Discrete logarithms in GF(p) --- 135 digits. E-mail to the NMBRTHRY mailing list; http://listserv.nodak.edu/archives/nmbrthry.html, December 2006. [3] Thorsten Kleinjung. Discrete logarithms in GF(p) --- 160 digits. E-mail to the NMBRTHRY mailing list; http://listserv.nodak.edu/archives/nmbrthry.html, February 2007. [4] S. Bai, C. Bouvier, A. Filbois, P. Gaudry, L. Imbert, A. Kruppa, F. Morain, E. Thomé and P. Zimmermann. Cado-nfs: Crible algébrique: Distribution, optimisation - number field sieve. http://cado-nfs.gforge.inria.fr/ [5] C. Bouvier. The filtering step of discrete logarithm and integer factorization algorithms. Preprint, http://hal.inria.fr/hal-00734654, 2013. [6] H. Jeljeli. Resolution of Linear Algebra for the Discrete Logarithm Problem Using GPU and Multi-core Architectures. To appear in the proceedings of Euro-par 2014, http://http://hal.inria.fr/hal-00946895, 2014.