Since everyone until now has simply defined what a hash function was, I will bite. A one-way function is not just a hash function — a function that loses information — but a function f for which, given an image y (“SE” or 294 in existing answers), it is difficult to find a pre-image x … Read more
What you describe is called a collision. Collisions necessarily exist, since SHA-1 accepts many more distinct messages as input that it can produce distinct outputs (SHA-1 may eat any string of bits up to 2^64 bits, but outputs only 160 bits; thus, at least one output value must pop up several times). This observation is … Read more
RSA encrypts a single message which has a length which is somewhat smaller than the modulus. Specifically, the message is first “padded”, resulting in a sequence of bytes which is then interpreted as a big integer between 0 and n-1, where n is the modulus (a part of the public key) — so the padded … Read more
(Expanding more than I feel is appropriate for an edit.) PKCS1, available in several versions as rfcs 2313 2437 3447 and 8017, is primarily about using the RSA algorithm for cryptography including encrypting decrypting signing and verifying. But since crypto is often used between systems or at least programs it is convenient to have a … Read more
The short answer to your question is: SHA-1 is as secure as you can get. MD5 would be fine too, even MD4; but it could make some investors nervous. For public relations, it is best to use a “better” hash function, e.g. SHA-256, even if you truncate its output to 160 or 128 bits (to … Read more
xor is a dangerous default function to use when hashing. It is better than and and or, but that doesn’t say much. xor is symmetric, so the order of the elements is lost. So “bad” will hash combine the same as “dab”. xor maps pairwise identical values to zero, and you should avoid mapping “common” … Read more