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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 ${\displaystyle (p,q)}$ must be congruent to 3 mod 4. (See RSA, key generation for details.)

1. Alice generates two large prime numbers ${\displaystyle p\,}$ and ${\displaystyle q\,}$ such that ${\displaystyle p\neq q}$, randomly and independently of each other, where ${\displaystyle (p,q)\equiv 3}$ mod ${\displaystyle 4}$.
2. Alice computes ${\displaystyle N=pq}$.
3. Alice can also precompute now ${\displaystyle q^{-1}\,}$ and ${\displaystyle p^{-1}\,}$, so that

${\displaystyle ap+bq=1}$ (Bezout's identity) using the extended euclidean algorithm.

The public key is ${\displaystyle N}$. The secret key is the factorization ${\displaystyle (p,q)}$.

Alice receives ${\displaystyle (c_{0},\dots ,c_{L-1}),y}$. She can recover ${\displaystyle m}$ using the following procedure:

1. Using the prime factorization ${\displaystyle (p,q)}$, Alice computes ${\displaystyle r_{p}=y^{((p+1)/4)^{L}}~mod~(p-1)}$ and ${\displaystyle r_{q}=y^{((q+1)/4)^{L}}~mod~(q-1)}$.
2. Compute the initial seed ${\displaystyle x_{0}=q(q^{-1}~{mod}~p)r_{p}+p(p^{-1}~{mod}~q)r_{q}~{mod}~N}$
3. From ${\displaystyle x_{0}}$, recompute the bit-vector ${\displaystyle {\vec {b}}}$ using the BBS generator, as in the encryption algorithm.
4. Compute the plaintext by XORing the keystream with the ciphertext: ${\displaystyle {\vec {m}}={\vec {c}}\oplus {\vec {b}}}$.

Alice recovers the plaintext ${\displaystyle m=(m_{0},\dots ,m_{L-1})}$.

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:

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

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

This article on a band or other musical ensemble is a stub. You can help by expanding it.

Category:Musical group stubs

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

• 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

• SHEVOLUTION

• Band website