Maple handles strings as a type. There is two-way conversion of strings to lists of numbers (based on character ASCII codes):
Congruence-based cryptography in the direction of the method known as RSA treats these number lists as lists of numbers modulo m for some suitably large modulus m. One takes some large power of each number in a number list. Encryption is enabled when one finds a pair (d, e) of these exponents for a given m such that the operation of taking the e-th power inverts the operation of taking the d-th power.
For the modulus m = 19781 the pair (d, e) = (761, 41) is a pair of such exponents.
The 95 printable ASCII codes have values in the range from 32 to 126 (hexadecimal 20 - 7E). If one works with these as unencoded numeric values, one will then want any prime factor of m to be larger than 126. Consider the case where m is a prime p. By Fermat's theorem a^{p-1} EQUIV 1 (mod p) for each a EQUIV0 (mod p), or a^{p} EQUIV a (mod p) for all a. It follows that if r EQUIV s (mod p-1) and r, s >= 0, then a^{r} EQUIV a^{s} (mod p) for all a. In the case that m = p is prime, one wants a pair (d, e) such that de EQUIV 1 (mod p-1). This makes it necessary that d, e both be coprime to p-1. For a given e that is coprime to p-1 there is a unique such d mod p-1.
For example, with m = p = 131, one has p-1 = 130 = 2· 5· 13. Then e = 77 = 7· 11 is coprime to p-1.
Therefore, d = 103 may be paired with e = 77 when working mod 131.
This generalizes to the case where m = p_{1} … p_{n} is the product of distinct primes p_{1}, …, p_{n}. In this case a congruence mod m is equivalent to simultaneous congruences modulo each of the primes p_{j}. Thus, with u = lcm(p_{1} - 1, …, p_{n} - 1) if r EQUIV s (mod u) and r, s >= 0, then a^{r} EQUIV a^{s} (mod m) for all a. Thus, for a given e that is coprime to u one finds d as the unique solution of the congruence ex EQUIV 1 (mod u).