A discrete logarithm is a mathematical concept used in number theory and cryptography. It refers to the problem of finding the exponent k in the equation b^k \equiv g \mod p , where b is the base, g is the result, and p is a prime number. This problem is considered difficult to solve, especially for large numbers, making it useful for secure communications. In cryptography, the discrete logarithm problem underpins several algorithms, such as the Diffie-Hellman key exchange and the Digital Signature Algorithm (DSA). These methods rely on the difficulty of calculating discrete logarithms to ensure the security of data transmission and authentication processes.