Geodesic
On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix
Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part IX, Tome 316 (2004), pp. 163-187

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We reexamine the Wiedemann–Coppersmith–Kaltofen–Villard algorithm for randomized computation of the determinant of integer matrices and substantially simplify and accelerate its bottleneck stage of computing the minimum generating matrix polynomial, to make the algorithm practically promising while keeping it asymptotically fast. 
@article{ZNSL_2004_316_a8,
     author = {V. Ya. Pan},
     title = {On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {163--187},
     publisher = {mathdoc},
     volume = {316},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_316_a8/}
}
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V. Ya. Pan. On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix. Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part IX, Tome 316 (2004), pp. 163-187. http://geodesic.mathdoc.fr/item/ZNSL_2004_316_a8/