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 Dec3 comment Weakness in using only one RSA key pair for two-way communication? As far as padding, see my edited question; let's assume OEAP padding. "Secure" is defined as Cindy not being able to discover the plaintexts of either message given only the ciphertexts; we can assume that Cindy has no access to Alice or Bob's plaintext messages on either end (before encryption or after decryption), or their keys. Dec3 revised Weakness in using only one RSA key pair for two-way communication? added 300 characters in body Dec3 comment Weakness in using only one RSA key pair for two-way communication? @CodesInChaos - Obviously there are other possible solutions when secure key transmission is possible. I was merely curious if the inverse-operation nature of the RSA scheme could be used as a two-way communication channel, or if being able to see messages enciphered using both keys would present a mathematical vulnerability. Dec3 comment Weakness in using only one RSA key pair for two-way communication? @fgrieu - Cindy does not know any part of the keyset including the shared modulo. She does not know any plaintexts involved. All she can see are the ciphertexts passed back and forth. Dec3 comment Weakness in using only one RSA key pair for two-way communication? @RickyDemer For the sake of argument we'll say both parties are padding using OAEP. Dec3 comment Weakness in using only one RSA key pair for two-way communication? By "encrypting with the secret key", I mean that by Wikipedia, a decryption exponent d can be derived from e and n, and given that, the decryption formula is nearly identical to the encryption formula. Alice's key is (e,n) and Bob's is (d,n). Since the two modulo operations are shown to be inverses, the only question in my mind is whether Cindy could derive d and e by seeing messages encrypted with both exponents (but not their plaintexts). Dec1 revised Weakness in using only one RSA key pair for two-way communication? added 29 characters in body Dec1 awarded Commentator Dec1 comment Weakness in using only one RSA key pair for two-way communication? By half, I mean that both parties are in possession of an RSA key, the two keys forming a normal asymmetric key pair. Usually, this keypair provides a one-way channel by distributing a public key to encrypt and keeping the other secret to decrypt; however, if both keys of the keypair were considered "private" (the keys were securely transmitted), and each side used their key both to encrypt messages they were sending and decrypt messages they received, would the encryption still be secure, or would the math allow a user to derive the keys given only the ciphertexts encrypted with each key? Dec1 comment Weakness in using only one RSA key pair for two-way communication? How would that make a difference? Nov30 asked Weakness in using only one RSA key pair for two-way communication? Nov19 comment Is this a valid real-time authentication scheme? RSA doesn't differentiate between "encrypting" and "decrypting" keys; given a pair of them, you can encrypt with either one and then decrypt with the other. While it may become possible to discover both keys given the plaintexts and ciphertexts as encrypted with each half of the pair, it can't be done until the purpose of the process has been accomplished, at which time those keys are discarded. Nov19 comment Is this a valid real-time authentication scheme? Ah. got it. Well, this is still two-way; most clients don't have X.509 certificates, but you could use it to have two clients of the same secure server handshake and trust each other based on them both being authenticated by the server, with disposable proof of authentication between the two clients that does not involve exchanging the credentials or authentication results from their server auth. Nov19 comment Is this a valid real-time authentication scheme? MACs can be spoofed, and long-term-use keys like in signatures can be cracked. The key pair in question here is used for a couple of seconds at most, it's near useless forever after, and the only thing it tests is that both Alice and Bob know Cindy well enough to get the two halves of the key pair, and thus that they should trust each other. The information actually encrypted with it would be plainly visible to any man in the middle, and as long as the information is highly unlikely to be repeated, that's just fine. Nov19 revised Is this a valid real-time authentication scheme? added 190 characters in body Nov19 asked Is this a valid real-time authentication scheme? Oct19 awarded Student Oct18 awarded Scholar Oct18 awarded Supporter Oct18 revised Is AES in CBC mode secure if a known and/or fixed IV is used? added 274 characters in body