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Key generation
To allow for decryption, the modulus used in Blum-Goldwasser encryption should be a Blum integer. This value is generated in the same manner as an RSA modulus, except that the prime factors $$(p, q)$$ must be congruent to 3 mod 4. (See RSA, key generation for details.)

$$ap + bq = 1$$ (Bezout's identity) using the extended euclidean algorithm.
 * 1) Alice generates two large prime numbers $$p \,$$ and $$q \,$$ such that $$p \ne q$$, randomly and independently of each other, where $$(p, q) \equiv 3$$ mod $$4$$.
 * 2) Alice computes $$N = p q$$.
 * 3) Alice can also precompute now $$q^{-1} \,$$ and $$p^{-1} \,$$, so that

The public key is $$N$$. The secret key is the factorization $$(p, q)$$.

Message decryption
Alice receives $$(c_0, \dots, c_{L-1}), y$$. She can recover $$m$$ using the following procedure:


 * 1) Using the prime factorization $$(p, q)$$, Alice computes $$r_p = y^{((p+1)/4)^{L}}~mod~(p-1)$$ and $$r_q = y^{((q+1)/4)^{L}}~mod~(q-1)$$.
 * 2) Compute the initial seed $$x_0=q(q^{-1}~{mod}~p)r_p + p(p^{-1}~{mod}~q)r_q~{mod}~N$$
 * 3) From $$x_0$$, recompute the bit-vector $${\vec b}$$ using the BBS generator, as in the encryption algorithm.
 * 4) Compute the plaintext by XORing the keystream with the ciphertext: $${\vec m} = {\vec c} \oplus {\vec b}$$.

Alice recovers the plaintext $$m=(m_0, \dots, m_{L-1})$$.

Inversion of 3 x 3 matrices
The cofactor equation listed above yields the following result for 3 x 3 matrices. Inversion of these matrices can be done quite easily as follows:

$$A^{-1} = \begin{bmatrix}

a & b & c\\ d & e & f \\ g & h & i \\ \end{bmatrix}^{-1} = \frac{1}{|A|} \begin{bmatrix} ei - fh & ch - bi & bf - ce \\ fg - di & ai - cg & cd - af \\ dh - eg & bg - ah & ae - bd \end{bmatrix}$$

$$|A| = a(ei-fh) - b(di-fg) + c(dh-eg)$$

MT-TV
Category:Musical group stubs

MT-TV is a British female punk/metal/goth band, formed from the remnants of the band Rockbitch.

Personnel

 * Krow (former Julie?): Vocals, Writer
 * Alex (former Babe): Lead Guitar, Backing Vocals
 * Brooke (former Luci?): Guitar, Stage Slut
 * Fuse (former Amanda): Bass
 * Nikki: Keyboards
 * Jo: Drums
 * The Stereotypes: Bunny, Adrienne, Kali: Performance

Discography

 * SHEVOLUTION