To conclude, we compute the correlation by using the Piling-up Lemma and aggregating the correlations of Lemma15 and Eqs. Both these ciphers were designed by D. Bernstein in 2005 and 2008 respectively. RFC7905, 18 (2016), IANIX: ChaCha usage and deployment. Using the keystream output from ChaCha can be used to implement a deterministic random bit generator. No, ChaCha20 is just a stream cipher, by itself it doesn't provide message integrity / authenticity; not without significant alteration - and then it would be called something else. Provided by the Springer Nature SharedIt content-sharing initiative, International Journal of Information Technology, \((m_{i}^{n})_{4x4} = R \Big [(m_{i}^{n-1})_{4x4}\Big ] (0 \le i \le 15)\), $$\begin{aligned}\left[ {\begin{array}{cc} m_{0}^{n-1} = m_{0}^{n-1} + m_{4}^{n-1}; &{} m_{12}^{n-1} = (m_{12}^{n-1} \oplus m_{0}^{n-1})<<< 16; \\ m_{8}^{n-1} = m_{8}^{n-1} + m_{12}^{n-1}; &{} m_{4}^{n-1} = (m_{4}^{n-1} \oplus m_{8}^{n-1})<<< 12; \\ m_{0}^{n} = m_{0}^{n-1} + m_{4}^{n-1}; &{} m_{15}^{n} = (m_{12}^{n-1} \oplus m_{0}^{n})<<< 8; \\ m_{10}^{n} = m_{8}^{n-1} + m_{15}^{n}; &{} m_{5}^{n} = (m_{4}^{n-1} \oplus m_{10}^{n})<<< 7; \end{array} } \right] \end{aligned}$$, $$\begin{aligned}\left[ {\begin{array}{cc} m_{1}^{n-1} = m_{1}^{n-1} + m_{5}^{n-1}; &{} m_{13}^{n-1} = (m_{13}^{n-1} \oplus m_{1}^{n-1})<<< 16; \\ m_{9}^{n-1} = m_{9}^{n-1} + m_{13}^{n-1}; &{} m_{5}^{n-1} = (m_{5}^{n-1} \oplus m_{9}^{n-1})<<< 12; \\ m_{1}^{n} = m_{1}^{n-1} + m_{5}^{n-1}; &{} m_{12}^{n} = (m_{13}^{n-1} \oplus m_{1}^{n})<<< 8; \\ m_{11}^{n} = m_{9}^{n-1} + m_{12}^{n}; &{} m_{6}^{n} = (m_{5}^{n-1} \oplus m_{11}^{n})<<< 7; \end{array} } \right] \end{aligned}$$, $$\begin{aligned}\left[ {\begin{array}{cc} m_{2}^{n-1} = m_{2}^{n-1} + m_{6}^{n-1}; &{} m_{14}^{n-1} = (m_{14}^{n-1} \oplus m_{2}^{n-1})<<< 16; \\ m_{10}^{n-1} = m_{10}^{n-1} + m_{14}^{n-1}; &{} m_{6}^{n-1} = (m_{6}^{n-1} \oplus m_{10}^{n-1})<<< 12; \\ m_{2}^{n} = m_{2}^{n-1} + m_{6}^{n-1}; &{} m_{13}^{n} = (m_{14}^{n-1} \oplus m_{2}^{n})<<< 8; \\ m_{8}^{n} = m_{10}^{n-1} + m_{13}^{n}; &{} m_{7}^{n} = (m_{6}^{n-1} \oplus m_{8}^{n})<<< 7; \end{array} } \right] \end{aligned}$$, $$\begin{aligned}\left[ {\begin{array}{cc} m_{3}^{n-1} = m_{3}^{n-1} + m_{7}^{n-1}; &{} m_{15}^{n-1} = (m_{15}^{n-1} \oplus m_{3}^{n-1})<<< 16; \\ m_{11}^{n-1} = m_{11}^{n-1} + m_{15}^{n-1}; &{} m_{7}^{n-1} = (m_{7}^{n-1} \oplus m_{11}^{n-1})<<< 12; \\ m_{3}^{n} = m_{3}^{n-1} + m_{7}^{n-1}; &{} m_{14}^{n} = (m_{15}^{n-1} \oplus m_{3}^{n})<<< 8; \\ m_{9}^{n} = m_{11}^{n-1} + m_{14}^{n}; &{} m_{4}^{n} = (m_{7}^{n-1} \oplus m_{9}^{n})<<< 7; \end{array} } \right] \end{aligned}$$, \((m_{i}^{n-1})_{4x4} = R^{-1} \Big [(m_{i}^{n})_{4x4}\Big ] (0 \le i \le 15)\), $$\begin{aligned}\left[ {\begin{array}{cc} m_{4}^{n} = (m_{4}^{n} \oplus m_{8}^{n})>>> 7; &{} m_{8}^{n} = m_{8}^{n} - m_{12}^{n}; \\ m_{12}^{n} = (m_{12}^{n} \oplus m_{0}^{n})>>> 8; &{} m_{0}^{n} = m_{0}^{n} - m_{4}^{n}; \\ m_{5}^{n-1} = (m_{4}^{n} \oplus m_{8}^{n})>>> 12; &{} m_{10}^{n-1} = m_{8}^{n} - m_{12}^{n}; \\ m_{15}^{n-1} = (m_{12}^{n} \oplus m_{0}^{n})>>> 16; &{} m_{0}^{n-1} = m_{0}^{n} - m_{5}^{n-1}; \end{array} } \right] \end{aligned}$$, $$\begin{aligned}\left[ {\begin{array}{cc} m_{5}^{n} = (m_{5}^{n} \oplus m_{9}^{n})>>> 7; &{} m_{9}^{n} = m_{9}^{n} - m_{13}^{n}; \\ m_{13}^{n} = (m_{13}^{n} \oplus m_{1}^{n})>>> 8; &{} m_{1}^{n} = m_{1}^{n} - m_{5}^{n}; \\ m_{6}^{n-1} = (m_{5}^{n} \oplus m_{9}^{n})>>> 12; &{} m_{11}^{n-1} = m_{9}^{n} - m_{13}^{n}; \\ m_{12}^{n-1} = (m_{13}^{n} \oplus m_{1}^{n})>>> 16; &{} m_{1}^{n-1} = m_{1}^{n} - m_{6}^{n-1}; \end{array} } \right] \end{aligned}$$, $$\begin{aligned}\left[ {\begin{array}{cc} m_{6}^{n} = (m_{6}^{n} \oplus m_{10}^{n})>>> 7; &{} m_{10}^{n} = m_{10}^{n} - m_{14}^{n}; \\ m_{14}^{n} = (m_{14}^{n} \oplus m_{2}^{n})>>> 8; &{} m_{2}^{n} = m_{2}^{n} - m_{6}^{n}; \\ m_{7}^{n-1} = (m_{6}^{n} \oplus m_{10}^{n})>>> 12; &{} m_{8}^{n-1} = m_{10}^{n} - m_{14}^{n}; \\ m_{13}^{n-1} = (m_{14}^{n} \oplus m_{2}^{n})>>> 16; &{} m_{2}^{n-1} = m_{2}^{n} - m_{7}^{n-1}; \end{array} } \right] \end{aligned}$$, $$\begin{aligned}\left[ {\begin{array}{cc} m_{7}^{n} = (m_{7}^{n} \oplus m_{11}^{n})>>> 7; &{} m_{11}^{n} = m_{11}^{n} - m_{15}^{n}; \\ m_{15}^{n} = (m_{15}^{n} \oplus m_{3}^{n})>>> 8; &{} m_{3}^{n} = m_{3}^{n} - m_{7}^{n}; \\ m_{4}^{n-1} = (m_{7}^{n} \oplus m_{11}^{n})>>> 12; &{} m_{9}^{n-1} = m_{11}^{n} - m_{15}^{n}; \\ m_{14}^{n-1} = (m_{15}^{n} \oplus m_{3}^{n})>>> 16; &{} m_{3}^{n-1} = m_{3}^{n} - m_{4}^{n-1}; \end{array} } \right] \end{aligned}$$, https://doi.org/10.1007/s41870-022-00904-1, access via (49), we have that for subrounds 9 and 10 we do not update the word \(X_{10}\), then we get \( x_{10,0}^{[8]} = x_{10,0}^{[9]} = x_{10,0}^{[10]}. What would a potion that increases resistance to damage actually do to the body? c = c + d Lecture Notes in Computer Science, vol. This is so huge that even for random nonces one has to generate $2^{96}$ uniform nonces so that a collision occurs with 50% probability. 484513, C. Beierle, A. Biryukov, L. Cardoso DosSantos, J. Groszschdl, L.P. Perrin, A. Udovenko, V. Velichkov, Q. Wang, Schwaemm and Esch: lightweight authenticated encryption and hashing using the Sparkle permutation family (2019), J.P. Aumasson, L. Henzen, W. Meier, R.C.W. Revamped Differential-Linear Cryptanalysis on Reduced Round ChaCha To learn more, see our tips on writing great answers. tecnol. INDOCRYPT 2012. c++ - How to use salsa20 (or ChaCha)? - Stack Overflow \), $$\begin{aligned} x_{b,i}^{[s-1]} = \mathcal {L}^{[s]}_{b,i} \oplus \Theta _i(x^{\prime [s-1]}_{c}, x^{[s]}_{d}) \oplus x^{\prime [s-1]}_{c,i-1} \end{aligned}$$, \(\frac{1}{2}\left( 1+\frac{1}{2}\right) \), $$\begin{aligned} x_{b,i}^{[s-1]} = \mathcal {L}^{[s]}_{b,i} \oplus \Theta _i(x^{\prime [s-1]}_{c}, x^{[s]}_{d}) \oplus x_{c,i-1}^{[s]} \oplus x_{d,i-1}^{[s]} \oplus \Theta _{i-1}(x^{\prime [s-1]}_{c}, x^{[s]}_{d}). Many existing software AES implementations are vulnerable to a considerable number of attacks depending on the threat model, and proper software implementations without appropriate operating system or hardware support may suffer performance problems leading to deployment of insecure code in practice. } Finally, we developed CryptDances, a new tool for the cryptanalysis of Salsa, ChaCha, and Forr designed to be used in high performance environments with several GPUs. Which encryption method just needs an EX-OR to encrypt? \end{aligned}$$, $$\begin{aligned} \begin{array}{c} x^{[12]}_{1,0} \oplus x^{[12]}_{10,0} \oplus x^{[12]}_{14,0} \oplus x^{[12]}_{14,27} = \\ x^{[13]}_{1,0} \oplus x^{[13]}_{3,0} \oplus x^{[13]}_{10,0} \oplus x^{[13]}_{14,0} \oplus x^{[13]}_{14,27} \oplus x^{[13]}_{15,0} \oplus x^{[13]}_{15,27}, \end{array} \end{aligned}$$, $$\begin{aligned} \begin{array}{c} x^{[13]}_{1,0} \oplus x^{[13]}_{3,0} \oplus x^{[13]}_{10,0} \oplus x^{[13]}_{14,0} \oplus x^{[13]}_{14,27} \oplus x^{[13]}_{15,0} \oplus x^{[13]}_{15,27} = \\ x^{[14]}_{1,8} \oplus x^{[14]}_{3,0} \oplus x^{[14]}_{10,0} \oplus x^{[14]}_{11,0} \oplus x^{[14]}_{14,0} \oplus x^{[14]}_{14,27} \oplus x^{[14]}_{15,0} \oplus x^{[14]}_{15,27} \end{array} \end{aligned}$$, $$\begin{aligned} \begin{array}{c} x^{[14]}_{1,8} \oplus x^{[14]}_{3,0} \oplus x^{[14]}_{10,0} \oplus x^{[14]}_{11,0} \oplus x^{[14]}_{14,0} \oplus x^{[14]}_{14,27} \oplus x^{[14]}_{15,0} \oplus x^{[14]}_{15,27} = x^{[15]}_{1,8} \oplus \\ x^{[15]}_{2,16} \oplus x^{[15]}_{3,0} \oplus x^{[15]}_{7,7} \oplus x^{[15]}_{7,8} \oplus x^{[15]}_{10,0} \oplus x^{[15]}_{11,0} \oplus x^{[15]}_{14,0} \oplus x^{[15]}_{14,27} \oplus x^{[15]}_{15,0} \oplus x^{[15]}_{15,27}, \end{array} \end{aligned}$$, \(x^{[15]}_{2,16}, x^{[15]}_{3,0}, x^{[15]}_{14,0}\), $$\begin{aligned} \begin{array}{l} x^{[15]}_{1}[8] \oplus x^{[15]}_{2}[16] \oplus x^{[15]}_{3}[0] \oplus x^{[15]}_{7}[7,8] \oplus x^{[15]}_{10}[0] \oplus x^{[15]}_{11}[0] \oplus x^{[15]}_{14}[0,27] \oplus \\ x^{[15]}_{15}[0,27] = x^{[16]}_{1}[8] \oplus x^{[16]}_{2}[16] \oplus x^{[16]}_{3}[2,3,24] \oplus x^{[16]}_{4}[0,15,16,26,27] \oplus \\ x^{[16]}_{7}[7,8] \oplus x^{[16]}_{9}[0] \oplus x^{[16]}_{10}[0] \oplus x^{[16]}_{11}[0] \oplus x^{[16]}_{14}[22,27] \oplus x^{[16]}_{15}[0,27] \end{array} \end{aligned}$$, \(\frac{1}{2}\left( 1+\frac{1}{2^4}\right) \), $$\begin{aligned} \begin{array}{l} x^{[16]}_{1}[8] \oplus x^{[16]}_{2}[16] \oplus x^{[16]}_{3}[2,3,24] \oplus x^{[16]}_{4}[0,15,16,26,27] \oplus x^{[16]}_{7}[7,8] \oplus \\ x^{[16]}_{9}[0] \oplus x^{[16]}_{10}[0] \oplus x^{[16]}_{11}[0] \oplus x^{[16]}_{14}[22,27] \oplus x^{[16]}_{15}[0,27] = x^{[17]}_{0}[0,10,11] \oplus \\ x^{[17]}_{1}[8] \oplus x^{[17]}_{2}[16] \oplus x^{[17]}_{3}[2,3,24] \oplus x^{[17]}_{4}[2,3,4,5,10,23,24,25,26] \oplus \\ x^{[17]}_{7}[7,8] \oplus x^{[17]}_{8}[0,4,5,10,15,16,25,27] \oplus x^{[17]}_{9}[0] \oplus x^{[17]}_{10}[0] \oplus x^{[17]}_{11}[0] \oplus \\ x^{[17]}_{12}[0,15,16,26,27] \oplus x^{[17]}_{14}[22,27] \oplus x^{[17]}_{15}[0,27], \end{array} \end{aligned}$$, \(\frac{1}{2}\left( 1+\frac{1}{2^6}\right) \), $$\begin{aligned} \begin{array}{l} x^{[17]}_{0}[0,10,11] \oplus x^{[17]}_{1}[8] \oplus x^{[17]}_{2}[16] \oplus x^{[17]}_{3}[2,3,24] \oplus \\ x^{[17]}_{4}[2,3,4,5,10,23,24,25,26] \oplus x^{[17]}_{7}[7,8] \oplus x^{[17]}_{8}[0,4,5,10,15,16,25,27] \oplus \\ x^{[17]}_{9}[0] \oplus x^{[17]}_{10}[0] \oplus x^{[17]}_{11}[0] \oplus x^{[17]}_{12}[0,15,16,26,27] \oplus x^{[17]}_{14}[22,27] \oplus x^{[17]}_{15}[0,27] \\ =x^{[18]}_{0}[10,11] \oplus x^{[18]}_{1}[8,16,18,19] \oplus x^{[18]}_{2}[16] \oplus x^{[18]}_{3}[2,3,24] \oplus \\ x^{[18]}_{4}[2,3,4,5,10,23,24,25,26] \oplus x^{[18]}_{5}[0,10,11] \oplus x^{[18]}_{7}[7,8] \oplus \\ x^{[18]}_{8}[0,4,5,10,15,16,25,27] \oplus x^{[18]}_{9}[0,7,8] \oplus x^{[18]}_{10}[0] \oplus x^{[18]}_{11}[0] \oplus \\ x^{[18]}_{12}[0,15,16,26,27] \oplus x^{[18]}_{13}[0,27] \oplus x^{[18]}_{14}[22,27] \oplus x^{[18]}_{15}[0,27] \end{array} \end{aligned}$$, \(x^{[18]}_{1,16} \oplus x^{[18]}_{2,16}\), $$\begin{aligned} \begin{array}{l} x^{[18]}_{0}[10,11] \oplus x^{[18]}_{1}[8,16,18,19] \oplus x^{[18]}_{2}[16] \oplus x^{[18]}_{3}[2,3,24] \oplus \\ x^{[18]}_{4}[2,3,4,5,10,23,24,25,26] \oplus x^{[18]}_{5}[0,10,11] \oplus x^{[18]}_{7}[7,8] \oplus \\ x^{[18]}_{8}[0,4,5,10,15,16,25,27] \oplus x^{[18]}_{9}[0,7,8] \oplus x^{[18]}_{10}[0] \oplus x^{[18]}_{11}[0] \oplus \\ x^{[18]}_{12}[0,15,16,26,27] \oplus x^{[18]}_{13}[0,27] \oplus x^{[18]}_{14}[22,27] \oplus x^{[18]}_{15}[0,27] =\\ x^{[19]}_{0}[10,11] \oplus x^{[19]}_{1}[0,8,16,18,19] \oplus x^{[19]}_{2}[2,3,16,26,27,29,30] \oplus \\ x^{[19]}_{3}[2,3,24] \oplus x^{[19]}_{4}[2,3,4,5,10,23,24,25,26] \oplus x^{[19]}_{5}[0,10,11] \oplus \\ x^{[19]}_{6}[7,8,15,16,18,19,21,22,26,27] \oplus x^{[19]}_{7}[7,8] \oplus x^{[19]}_{8}[0,4,5,10,15,16,25,27] \oplus \\ x^{[19]}_{9}[0,7,8] \oplus x^{[19]}_{10}[0,15,16] \oplus x^{[19]}_{11}[0] \oplus x^{[19]}_{12}[0,15,16,26,27] \oplus \\ x^{[19]}_{13}[0,27] \oplus x^{[19]}_{14}[0,17,22,27] \oplus x^{[19]}_{15}[0,27] \end{array} \end{aligned}$$, \(\frac{1}{2}\left( 1+\frac{1}{2^9}\right) \), \(x^{[19]}_{2}[26,27]\oplus x^{[19]}_{15,27}\), \(x^{[19]}_{2}[2,3]\oplus x^{[19]}_{3}[2,3]\), $$\begin{aligned} \begin{array}{l} x^{[19]}_{0}[10,11] \oplus x^{[19]}_{1}[0,8,16,18,19] \oplus x^{[19]}_{2}[2,3,16,26,27,29,30] \oplus x^{[19]}_{3}[2,3,24] \oplus \\ x^{[19]}_{4}[2,3,4,5,10,23,24,25,26] \oplus x^{[19]}_{5}[0,10,11] \oplus x^{[19]}_{6}[7,8,15,16,18,19,21,22,26,27] \oplus \\ x^{[19]}_{7}[7,8] \oplus x^{[19]}_{8}[0,4,5,10,15,16,25,27] \oplus x^{[19]}_{9}[0,7,8] \oplus x^{[19]}_{10}[0,15,16] \oplus x^{[19]}_{11}[0] \oplus \\ x^{[19]}_{12}[0,15,16,26,27] \oplus x^{[19]}_{13}[0,27] \oplus x^{[19]}_{14}[0,17,22,27] \oplus x^{[19]}_{15}[0,27] =\\ x^{[20]}_{0}[10,11] \oplus x^{[20]}_{1}[0,8,16,18,19] \oplus x^{[20]}_{2}[0,2,3,16,26,27,29,30] \oplus x^{[20]}_{3}[0,5,6,8,24] \oplus \\ x^{[20]}_{4}[2,3,4,5,10,23,24,25,26] \oplus x^{[20]}_{5}[0,10,11] \oplus x^{[20]}_{6}[7,8,15,16,18,19,21,22,26,27] \oplus \\ x^{[20]}_{7}[0,2,3,15,16,17,18,29,30] \oplus x^{[20]}_{8}[0,4,5,10,15,16,25,27] \oplus x^{[20]}_{9}[0,7,8] \oplus \\ x^{[20]}_{10}[0,15,16] \oplus x^{[20]}_{11}[0,2,3,7,8,17,18,23,24] \oplus x^{[20]}_{12}[0,15,16,26,27] \oplus x^{[20]}_{13}[0,27] \oplus \\ x^{[20]}_{14}[0,17,22,27] \oplus x^{[20]}_{15}[0,7,8,22] \end{array} \end{aligned}$$, \(\frac{1}{2}\left( 1+\frac{1}{2^{10}}\right) \), \(\varepsilon _L = \frac{1}{2^{5+6+3+9+10}}\), \(x^{[20]}_{15}[7,8]\oplus x^{[20]}_{3,8}\), $$\begin{aligned} \begin{array}{l} x^{[20]}_{0}[10,11] \oplus x^{[20]}_{1}[0,8,16,18,19] \oplus x^{[20]}_{2}[0,2,3,16,26,27,29,30] \oplus \\ x^{[20]}_{3}[0,5,6,8,24] \oplus x^{[20]}_{4}[2,3,4,5,10,23,24,25,26] \oplus x^{[20]}_{5}[0,10,11] \oplus \\ x^{[20]}_{6}[7,8,15,16,18,19,21,22,26,27] \oplus x^{[20]}_{7}[0,2,3,15,16,17,18,29,30] \oplus \\ x^{[20]}_{8}[0,4,5,10,15,16,25,27] \oplus x^{[20]}_{9}[0,7,8] \oplus x^{[20]}_{10}[0,15,16] \oplus \\ x^{[20]}_{11}[0,2,3,7,8,17,18,23,24] \oplus x^{[20]}_{12}[0,15,16,26,27] \oplus x^{[20]}_{13}[0,27] \oplus \\ x^{[20]}_{14}[0,17,22,27] \oplus x^{[20]}_{15}[0,7,8,22] =\\ x^{[21]}_{0}[0,13,14,15,18,19,29,30] \oplus x^{[21]}_{1}[0,8,16,18,19] \oplus x^{[21]}_{2}[0,2,3,16,26,27,29,30] \oplus \\ x^{[21]}_{3}[5,6,8,15,16,24] \oplus x^{[21]}_{4}[2,3,4,5,10,23,24,25,26] \oplus x^{[21]}_{5}[5,7,10,20,22,23,24] \\ \oplus x^{[21]}_{6}[7,8,15,16,18,19,21,22,26,27] \oplus x^{[21]}_{7}[0,2,3,15,16,17,18,29,30] \oplus \\ x^{[21]}_{8}[0,4,5,10,15,16,25,27] \oplus x^{[21]}_{9}[0,7,8] \oplus x^{[21]}_{10}[10,15,16,20,21] \oplus \\ x^{[21]}_{11}[0,2,3,7,8,17,18,23,24] \oplus x^{[21]}_{12}[0,15,16,26,27] \oplus x^{[21]}_{13}[0,27] \oplus x^{[21]}_{14}[0,17,22,27] \oplus \\ x^{[21]}_{15}[2,3,15,16,17] \end{array} \end{aligned}$$, \(\frac{1}{2}\left( 1+\frac{1}{2^{14}}\right) \), https://doi.org/10.1007/s00145-023-09455-5, https://github.com/murcoutinho/cryptDances, access via
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