Is there functionality to generate a random character in Java?

private static char rndChar () {
    int rnd = (int) (Math.random() * 52); // or use Random or whatever
    char base = (rnd < 26) ? 'A' : 'a';
    return (char) (base + rnd % 26);

}

Generates values in the ranges a-z, A-Z.

You could also use the RandomStringUtils from the Apache Commons project:

Dependency:

<dependency> 
  <groupId>org.apache.commons</groupId> 
  <artifactId>commons-lang3</artifactId> 
  <version>3.8.1</version> 
</dependency>

Usages:

RandomStringUtils.randomAlphabetic(stringLength);
RandomStringUtils.randomAlphanumeric(stringLength);

To generate a random char in a-z:

Random r = new Random();
char c = (char)(r.nextInt(26) + 'a');

There are many ways to do this, but yes, it involves generating a random int (using e.g. java.util.Random.nextInt) and then using that to map to a char. If you have a specific alphabet, then something like this is nifty:

    import java.util.Random;

    //...

    Random r = new Random();

    String alphabet = "123xyz";
    for (int i = 0; i < 50; i++) {
        System.out.println(alphabet.charAt(r.nextInt(alphabet.length())));
    } // prints 50 random characters from alphabet

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Do note that java.util.Random is actually a pseudo-random number generator based on the rather weak linear congruence formula. You mentioned the need for cryptography; you may want to investigate the use of a much stronger cryptographically secure pseudorandom number generator in that case (e.g. java.security.SecureRandom).