LCS35 is a cryptographic challenge and a puzzle set by Ron Rivest in 1999. The challenge is to calculate the value
where t is a large integer (79685186856218) and n is a 616 digit (or 2048 bit) integer which is the product of two large primes (which are not given). The value of w can then be used to decrypt the ciphertext z, another 616 digit integer. The plaintext provides the concealed information about the factorisation of n, allowing the solution to be easily verified.
The idea behind the challenge is that the only known way to find the value of w without knowing the factorisation of n is by t successive squarings. The value of t was chosen to make this brute force calculation take about 35 years using 1999 chip speeds as a starting point and taking into account Moore's law. Rivest notes that "just as a failure of Moore's Law could make the puzzle harder than intended, a breakthrough in the art of factoring would make the puzzle easier than intended."
The challenge was set at (and takes its name from) the 35th anniversary celebrations of the MIT Laboratory for Computer Science, now part of MIT Computer Science and Artificial Intelligence Laboratory.