EXPLICIT NON-MALLEABLE CODES RESISTANT TO PERMUTATIONS Shashank Agrawal (UIUC), Divya Gupta (UCLA), Hemanta Maji (UCLA), Omkant Pandey (UIUC), Manoj Prabhakaran (UIUC)

OUTLINE Non-malleability and importance Non-malleable codes, brief survey, contribution More details.

NON-MALLEABILITY Cannot be easily changed, influenced. An important property required in several cryptographic applications. Non-malleable encryption, signatures, commitments,… Non-malleable code: Difficult to change encoded message.

ENCRYPTION: SEALED-BID AUCTION Encrypt (PK, $200) Public Key PK Encrypt (PK, $201) Unfair Advantage!! IMAGE COURTESY:

SIGNATURE: MAN-IN-THE-MIDDLE Pay $100 -Bob Pay $100*100*100 -Bob UIUC Grad Student

NON-MALLEABLE CODES

EncDec mcc* = f(c)m*

RELATED WORK

OUR CONTRIBUTION Tampering function can PERMUTE bits and perturb them. EXPLICIT and efficient encoding/decoding procedure. RATE 1. Information-theoretic setting.

DETECTION/CORRECTION?

MORE DETAILS

DEFINITION EncDec mcc* = f(c)m*

TAMPERING FAMILY Admissible channel: Transition probabilities are constants, but output should not be a fixed value. Adversary can permute the bits in the codeword (global attack). Then, pass each bit through an admissible channel. Size of function family infinite! Bit Flipping Random output Bit Fixing 1/2

CONSTRUCTION: BASIC …… Outer Code AG Codes Inner Code Balanced Unary Encoding ……

CONSTRUCTION: RATE 1

CONCLUSION Open problems: There are hardly any closed problems. Our NM code has applications to NM commitments. Other interesting families that may have applications to cryptography. Paper would be on eprint very soon. Keep looking.

Thank you Questions?