Computer Security and Cryptography

12.3 THE RSA ENCIPHERMENT AND DECIPHERMENT OF ASCII-PLAINTEXT

RSA enciphers and deciphers integers in . To encipher data, RSA needs to be extended to encipher n-grams of ASCII characters x = (x⁽⁰⁾, x⁽¹⁾, …, x⁽ⁿ⁻¹⁾). An Internet standard is described in [Linn, 1989]; I describe a slightly modified version, using 7 bits for each ASCII character rather than 8 bits.

The extension replaces ASCII text by a binary sequence, which is segmented into bit-vectors of length N₂ − 1 where 2^{N_{2 − 1}} − 1 ≤ N < 2^N₂. Each such bit-vector corresponds to an integer k in to which RSA-exponentiation E_e can be applied. The resulting integer j = E_e(k) in general requires N₂ bits in its base-2 representation so that there is an expansion under RSA encipherment.

12.3.1 RSA Encipherment of ASCII Plaintext

E1. Replace each character x⁽ⁱ⁾ of ASCII plaintext x = (x⁽⁰⁾, x⁽¹⁾, …, x⁽ⁿ⁻¹⁾) by the 7-bit binary encoding of its ordinal value in the ASCII character code (Table 12.1).

E2. Concatenate to form the (0,1)-plaintext z (x⁽⁰⁾, x⁽¹⁾, …, x⁽ⁿ⁻¹⁾) → z = (z₀, z₁, …, z_7n−1).

E3. Assume integers in require N₂ bits in their ...