Clever Geek Handbook

We encrypt in Russian, or domestic cryptoalgorithms

This article describes in simple words the cryptoalgorithms that are currently relevant Russian information security standards, and selected links to materials that, if desired, will help to understand them deeper. And also, at the end of the article, works with the results of cryptanalysis of one of the most important elements of these algorithms are given.





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F_p, p> 3, (x, y), x, y \ \ epsilon \ F_p, ( ) y ^ 2 = x ^ 3 + ax + b (mod \ p), 4a ^ 3 + 27b ^ 2 \ neq0 , a, \ b \ \ epsilon \ F_p.





, . x ^ 2 + y ^ 2 = 1 + dx ^ 2y ^ 2, d \ \ epsilon \ F_p \ backslash \ {0,1 \}.





(x_1, y_1), (x_2, y_2) (x_3, y_3), , x_3 = \ lambda ^ 2 -x_1 -x_2 (mod \ p), y_3 = \ lambda ^ 2 (x_1 -x_3) -y_1 (mod \ p), \ lambda = \ frac {y_2 - y_1} {x_2-x_1} (mod \ p).





C = kP, C = P + P + ... + P.





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โ€” -() - h = h (M), , - โ€” .





โ€” e = \ alpha (mod \ q), \ alphaโ€” , - h. \ alpha (mod \ q) = 0, e 1.

q โ€” , . Pโ€” .





โ€” k, 0 <k <q, . C = kP. C (x_c, y_c).





โ€” (r, s), r = x_c (mod \ q), \ s = (rd + ke) (mod \ q). r, s 0, .





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: Mc (r, s) Q





โ€” , , 0 <r <q, \ 0 <s <q , .





โ€” - h = h (M) , .





โ€” e = \ alpha (mod \ q), \ alpha , - h. \ alpha (mod \ q) = 0, e 1. \ nu = e ^ {- 1} (mod \ q).





โ€” C = s \ nu P -r \ nu Q, R = x_c (mod \ q).





โ€” r = R ,





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Reverse-Engineering the S-Box of Streebog, Kuznyechik and STRIBOBr1 โ€” Alex Biryukov, L ฬeo Perrin, and Aleksei Udovenko





Exponential S-Boxes: a Link Between the S-Boxes of BelT and Kuznyechik/Streebog โ€” Lรฉo Perrin and Aleksei Udovenko





Partitions in the S-Box of Streebog and Kuznyechik โ€” Lรฉo Perrin





, SageMath.





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