Alum is a short-form word for an ingredient otherwise known as "potassium aluminum sulfate."
Sold in crystals, there are both food and commercial grades; the food grade is available at some pharmacies.
Alum was called for in older pickling recipes to give pickles a good, crisp crunch and helped ensure that they didn't just come out soft and "mooshy." It also increased the pH of the pickling solution, making it safer. It was used about 1/4 teaspoon per US quart (more than that tended to actually start making the pickles soft, and gave a bitter flavour.) The American pickling writer Linda Ziedrich suggests using only 1/8th teaspoon per US quart. 
The compound, as both its short and long-form name would indicate, has aluminum in it. Just the knowledge that it was there in some quantity was enough to create a health scare around it, even amongst some nutrition experts. Some academic sources are now saying it can be safely used in very small quantities, and that most people wouldn't eat enough pickles to have harmful results from it.
Methods now used, instead of adding alum to get the crispness, include using food-grade lime, or soaking the unprocessed cucumbers in iced water for 4 to 5 hours before using.
Alum was never called for in quick pickle recipes as the pickles wouldn't have been in the solution long enough for the alum to do its work.
"Alum, an aluminum compound that is used medicinally to induce vomiting and check bleeding, was a popular pickle ingredient in the 1950s and 1960s. Like like, alum makes pickles crisp and crunchy. Its use went out of favour, however, when people began to worry about the health effects of aluminum in the diet. Since only a very little alum is needed to make pickles crisp, and since pickles play only a small part in the American diet, adding alum to your pickles probably won't hurt anyone. The astringent taste of alum is detectable, though, even when only a mimimal amount is used. Many people like this taste. As my husband (with a grimace) described my alum-firmed fresh dills, 'They taste like store-bought.' Alum is sometimes sold in spice sections of supermarkets; you can also buy it at a pharmacy. I suggest using no more than 1/8th teaspoon per [US] quart." -- Ziedrich, Linda. The Joy of Pickling. Boston, Massachusetts: The Harvard Common Press. 2009. Page 18.
Literature & Lore
 Ziedrich, Linda. The Joy of Pickling. Boston, Massachusetts: The Harvard Common Press. 2009. Page 18.
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